Finite Group Databasebeta

← C7×#14100 #13191316

Subgroups — C7×#14100 #13191316

Order 1792.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic, complemented
3C2×C7×#388C211yesmaximal, characteristic, complemented
4C2×C7×#386C211yesmaximal, characteristic, complemented
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
7C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
8C7×#1441C211yesmaximal, characteristic, complemented
9C7×#1438C211yesmaximal, characteristic, complemented
10C7×#1438C211yesmaximal, characteristic, complemented
11C7×#1438C211yesmaximal, characteristic, complemented
12C7×#1437C211yesmaximal, characteristic, complemented
13C7×#1437C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C24×C4×C7C2211yescharacteristic
21C2×C7×#121—24no—
22C2×C7×#121—24no—
23C2×C7×#121C418yescomplemented
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2211yescharacteristic
33C22×C7×C22⋊C4C2211yescharacteristic
34C22×C7×C22⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4C2211yescharacteristic
36C22×C7×C22⋊C4C2211yescharacteristic
37C22×C7×C22⋊C4C2211yescharacteristic
38C22×C7×C22⋊C4C2211yescharacteristic
39C22×C42×C7C2211yescharacteristic
40C22×C42×C7C2211yescharacteristic
41C22×C42×C7C2211yescharacteristic
42C7×#390—24no—
43C7×#388—24no—
44C7×#386—24no—
45C7×#386—24no—
46C4×C7×C22⋊C4—24no—
47C4×C7×C22⋊C4—24no—
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57C2×C7×#95C2211yescharacteristic
58C2×C7×#95C2211yescharacteristic
59C2×C7×#95C2211yescharacteristic
60#14100C711yesmaximal, characteristic, direct product factor, Sylow
61C25×C7C2311yescharacteristic
62C25×C7C2311yescharacteristic
63C25×C7C2311yescharacteristic
64C22×C7×D4—22no—
65C22×C7×D4—22no—
66C22×C7×D4—22no—
67C22×C7×D4—22no—
68C22×C7×D4—22no—
69C22×C7×D4—22no—
70C22×C7×D4—22no—
71C22×C7×D4—22no—
72C22×C7×D4—22no—
73C22×C7×D4—22no—
74C22×C7×D4—22no—
75C22×C7×D4—22no—
76C22×C7×D4—41no—
77C22×C7×D4—41no—
78C22×C7×D4—41no—
79C22×C7×D4—41no—
80C22×C7×D4—41no—
81C22×C7×D4—41no—
82C22×C7×D4C2×C414yes—
83C22×C7×D4C2×C414yes—
84C22×C7×D4C2×C414yescomplemented
85C23×C4×C7—22no—
86C23×C4×C7—22no—
87C23×C4×C7—22no—
88C23×C4×C7—22no—
89C23×C4×C7—22no—
90C23×C4×C7—22no—
91C23×C4×C7—22no—
92C23×C4×C7—22no—
93C23×C4×C7—22no—
94C23×C4×C7—41no—
95C23×C4×C7—41no—
96C23×C4×C7—41no—
97C23×C4×C7—41no—
98C23×C4×C7C2×C414yescomplemented
99C23×C4×C7C2311yescharacteristic
100C23×C4×C7C2311yescharacteristic
101C23×C4×C7C2311yescharacteristic
102C23×C4×C7C2311yescharacteristic
103C23×C4×C7C2311yescharacteristic
104C23×C4×C7C2311yescharacteristic
105C23×C4×C7C2311yescharacteristic
106C23×C4×C7C2311yescharacteristic
107C23×C4×C7C2311yescharacteristic
108C23×C4×C7C2311yescharacteristic
109C23×C4×C7C2311yescharacteristic
110C23×C4×C7C2311yescharacteristic
111C7×#121—232no—
112C2×C7×C4⋊C4—22no—
113C2×C7×C4⋊C4—22no—
114C2×C7×C4⋊C4—22no—
115C2×C7×C4⋊C4—22no—
116C2×C7×C4⋊C4—41no—
117C2×C7×C4⋊C4C2×C414yescomplemented
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—22no—
121C2×C7×C22⋊C4—22no—
122C2×C7×C22⋊C4—22no—
123C2×C7×C22⋊C4—22no—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—22no—
126C2×C7×C22⋊C4—22no—
127C2×C7×C22⋊C4—22no—
128C2×C7×C22⋊C4—22no—
129C2×C7×C22⋊C4—22no—
130C2×C7×C22⋊C4—22no—
131C2×C7×C22⋊C4—22no—
132C2×C7×C22⋊C4—22no—
133C2×C7×C22⋊C4—22no—
134C2×C7×C22⋊C4—22no—
135C2×C7×C22⋊C4—22no—
136C2×C7×C22⋊C4—22no—
137C2×C7×C22⋊C4—22no—
138C2×C7×C22⋊C4—22no—
139C2×C7×C22⋊C4—22no—
140C2×C7×C22⋊C4—22no—
141C2×C7×C22⋊C4—22no—
142C2×C7×C22⋊C4—22no—
143C2×C7×C22⋊C4—22no—
144C2×C7×C22⋊C4—41no—
145C2×C7×C22⋊C4—41no—
146C2×C7×C22⋊C4—41no—
147C2×C7×C22⋊C4—41no—
148C2×C7×C22⋊C4—41no—
149C2×C7×C22⋊C4—41no—
150C2×C7×C22⋊C4—41no—
151C2×C7×C22⋊C4—41no—
152C2×C7×C22⋊C4C2×C414yes—
153C2×C7×C22⋊C4C2×C414yescomplemented
154C2×C7×C22⋊C4D414yes—
155C2×C7×C22⋊C4D414yes—
156C2×C7×C22⋊C4D414yescomplemented
157C2×C42×C7—22no—
158C2×C42×C7—22no—
159C2×C42×C7—22no—
160C2×C42×C7—22no—
161C2×C42×C7—22no—
162C2×C42×C7—22no—
163C2×C42×C7—41no—
164C2×C42×C7—41no—
165C2×C42×C7—41no—
166C7×#95—22no—
167C7×#95—22no—
168C7×#95—22no—
169C7×#95—22no—
170C7×#95—22no—
171C7×#95—22no—
172C7×#95—22no—
173C7×#95—22no—
174C7×#95—22no—
175C7×#95—41no—
176C7×#95—41no—
177C7×#95D414yescomplemented
178C22×#121C2×C711yescharacteristic
179C2×#390C2×C711yescharacteristic, complemented
180C2×#388C2×C711yescharacteristic, complemented
181C2×#386C2×C711yescharacteristic, complemented
182C2×#386C2×C711yescharacteristic, complemented
183C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
184C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
185#1441C2×C711yescharacteristic, complemented
186#1438C2×C711yescharacteristic, complemented
187#1438C2×C711yescharacteristic, complemented
188#1438C2×C711yescharacteristic, complemented
189#1437C2×C711yescharacteristic, complemented
190#1437C2×C711yescharacteristic, complemented
191#1436C2×C711yescharacteristic, complemented
192C22⋊#95C2×C711yescharacteristic, complemented
193C24×C7—21no—
194C24×C7—21no—
195C24×C7—21no—
196C24×C7—21no—
197C24×C7—21no—
198C24×C7—21no—
199C24×C7—21no—
200C24×C7—21no—
201C24×C7—21no—
202C24×C7—21no—
203C24×C7—21no—
204C24×C7—21no—
205C24×C7—21no—
206C24×C7—21no—
207C24×C7—21no—
208C24×C7—21no—
209C24×C7—21no—
210C24×C7—21no—
211C24×C7—21no—
212C24×C7—21no—
213C24×C7—21no—
214C24×C7—21no—
215C24×C7—21no—
216C24×C7—21no—
217C24×C7—21no—
218C24×C7—21no—
219C24×C7—21no—
220C24×C7—21no—
221C24×C7—21no—
222C24×C7—21no—
223C24×C7—21no—
224C24×C7—21no—
225C24×C7—21no—
226C24×C7—21no—
227C24×C7—21no—
228C24×C7—21no—
229C24×C7—21no—
230C24×C7—21no—
231C24×C7C22×C412yes—
232C24×C7C22×C412yes—
233C24×C7C22×C412yes—
234C24×C7C2×D412yes—
235C24×C7C2×D412yes—
236C24×C7C2×D412yes—
237C24×C7#4112yes—
238C24×C7C2411yescharacteristic
239C2×C7×D4—28no—
240C2×C7×D4—28no—
241C2×C7×D4—28no—
242C2×C7×D4—28no—
243C2×C7×D4—28no—
244C2×C7×D4—28no—
245C2×C7×D4—44no—
246C2×C7×D4—44no—
247C2×C7×D4—44no—
248C2×C7×D4—44no—
249C2×C7×D4—44no—
250C2×C7×D4—44no—
251C2×C7×D4—44no—
252C2×C7×D4—44no—
253C2×C7×D4—44no—
254C2×C7×D4—44no—
255C2×C7×D4—44no—
256C2×C7×D4—44no—
257C2×C7×D4—44no—
258C2×C7×D4—44no—
259C2×C7×D4—44no—
260C22×C4×C7—21no—
261C22×C4×C7—21no—
262C22×C4×C7—21no—
263C22×C4×C7—21no—
264C22×C4×C7—21no—
265C22×C4×C7—21no—
266C22×C4×C7—21no—
267C22×C4×C7—21no—
268C22×C4×C7—21no—
269C22×C4×C7—21no—
270C22×C4×C7—21no—
271C22×C4×C7—21no—
272C22×C4×C7—21no—
273C22×C4×C7—21no—
274C22×C4×C7—21no—
275C22×C4×C7—21no—
276C22×C4×C7—28no—
277C22×C4×C7—21no—
278C22×C4×C7—21no—
279C22×C4×C7—21no—
280C22×C4×C7—21no—
281C22×C4×C7—21no—
282C22×C4×C7—21no—
283C22×C4×C7—21no—
284C22×C4×C7—21no—
285C22×C4×C7—21no—
286C22×C4×C7—21no—
287C22×C4×C7—21no—
288C22×C4×C7—21no—
289C22×C4×C7—21no—
290C22×C4×C7—21no—
291C22×C4×C7—21no—
292C22×C4×C7—21no—
293C22×C4×C7—21no—
294C22×C4×C7—21no—
295C22×C4×C7—21no—
296C22×C4×C7—21no—
297C22×C4×C7—21no—
298C22×C4×C7—21no—
299C22×C4×C7—21no—
300C22×C4×C7—21no—
301C22×C4×C7—21no—
302C22×C4×C7—21no—
303C22×C4×C7—21no—
304C22×C4×C7—21no—
305C22×C4×C7—21no—
306C22×C4×C7—21no—
307C22×C4×C7—21no—
308C22×C4×C7—21no—
309C22×C4×C7—21no—
310C22×C4×C7—21no—
311C22×C4×C7—21no—
312C22×C4×C7—21no—
313C22×C4×C7—28no—
314C22×C4×C7—28no—
315C22×C4×C7—21no—
316C22×C4×C7—21no—
317C22×C4×C7—21no—
318C22×C4×C7—21no—
319C22×C4×C7—21no—
320C22×C4×C7—21no—
321C22×C4×C7—21no—
322C22×C4×C7—21no—
323C22×C4×C7—21no—
324C22×C4×C7—21no—
325C22×C4×C7—21no—
326C22×C4×C7—21no—
327C22×C4×C7—21no—
328C22×C4×C7—21no—
329C22×C4×C7—44no—
330C22×C4×C7—44no—
331C22×C4×C7—44no—
332C22×C4×C7—44no—
333C22×C4×C7—44no—
334C22×C4×C7—44no—
335C22×C4×C7—44no—
336C22×C4×C7—44no—
337C22×C4×C7—44no—
338C22×C4×C7—44no—
339C22×C4×C7—44no—
340C22×C4×C7C22×C412yes—
341C22×C4×C7C22×C412yes—
342C22×C4×C7C22×C412yes—
343C22×C4×C7C22×C412yes—
344C22×C4×C7C2×D412yes—
345C22×C4×C7C2×D412yes—
346C22×C4×C7C2×D412yes—
347C22×C4×C7C2×D412yes—
348C22×C4×C7C2×D412yes—
349C22×C4×C7C2×D412yes—
350C22×C4×C7C2×D412yes—
351C22×C4×C7C2×D412yes—
352C22×C4×C7C2×D412yes—
353C22×C4×C7#4112yes—
354C22×C4×C7#4112yes—
355C22×C4×C7#4112yes—
356C22×C4×C7#4112yes—
357C22×C4×C7#4112yes—
358C7×C4⋊C4—28no—
359C7×C4⋊C4—44no—
360C7×C22⋊C4—28no—
361C7×C22⋊C4—28no—
362C7×C22⋊C4—28no—
363C7×C22⋊C4—28no—
364C7×C22⋊C4—44no—
365C7×C22⋊C4—44no—
366C7×C22⋊C4—44no—
367C7×C22⋊C4—44no—
368C7×C22⋊C4—44no—
369C7×C22⋊C4—44no—
370C7×C22⋊C4—44no—
371C7×C22⋊C4—44no—
372C7×C22⋊C4C22⋊C4116yescomplemented
373C42×C7—44no—
374C42×C7—44no—
375C42×C7—44no—
376C23×D4C22×C711yescharacteristic
377C23×D4C22×C711yescharacteristic
378C23×D4C22×C711yescharacteristic
379C24×C4C22×C711yescharacteristic
380C24×C4C22×C711yescharacteristic
381C2×#121—24no—
382C2×#121—24no—
383C2×#121C4×C718yescomplemented
384C22×C4⋊C4C22×C711yescharacteristic
385C22×C4⋊C4C22×C711yescharacteristic
386C22×C22⋊C4C22×C711yescharacteristic
387C22×C22⋊C4C22×C711yescharacteristic
388C22×C22⋊C4C22×C711yescharacteristic
389C22×C22⋊C4C22×C711yescharacteristic
390C22×C22⋊C4C22×C711yescharacteristic
391C22×C22⋊C4C22×C711yescharacteristic
392C22×C22⋊C4C22×C711yescharacteristic
393C22×C22⋊C4C22×C711yescharacteristic
394C22×C22⋊C4C22×C711yescharacteristic
395C22×C22⋊C4C22×C711yescharacteristic
396C22×C22⋊C4C22×C711yescharacteristic
397C22×C22⋊C4C22×C711yescharacteristic
398C22×C22⋊C4C22×C711yescharacteristic
399C22×C42C22×C711yescharacteristic
400C22×C42C22×C711yescharacteristic
401C22×C42C22×C711yescharacteristic
402#390—24no—
403#388—24no—
404#386—24no—
405#386—24no—
406C4×C22⋊C4—24no—
407C4×C22⋊C4—24no—
408C2×#95C22×C711yescharacteristic
409C2×#95C22×C711yescharacteristic
410C2×#95C22×C711yescharacteristic
411C2×#95C22×C711yescharacteristic
412C2×#95C22×C711yescharacteristic
413C2×#95C22×C711yescharacteristic
414C2×#95C22×C711yescharacteristic
415C2×#95C22×C711yescharacteristic
416C2×#95C22×C711yescharacteristic
417C2×#95C22×C711yescharacteristic
418C2×#95C22×C711yescharacteristic
419C2×#95C22×C711yescharacteristic
420C23×C7—22no—
421C23×C7—22no—
422C23×C7—22no—
423C23×C7—22no—
424C23×C7—22no—
425C23×C7—22no—
426C23×C7—22no—
427C23×C7—22no—
428C23×C7—22no—
429C23×C7—22no—
430C23×C7—22no—
431C23×C7—22no—
432C23×C7—22no—
433C23×C7—22no—
434C23×C7—22no—
435C23×C7—22no—
436C23×C7—22no—
437C23×C7—22no—
438C23×C7—22no—
439C23×C7—22no—
440C23×C7—22no—
441C23×C7—22no—
442C23×C7—22no—
443C23×C7—22no—
444C23×C7—22no—
445C23×C7—22no—
446C23×C7—22no—
447C23×C7—22no—
448C23×C7—22no—
449C23×C7—22no—
450C23×C7—22no—
451C23×C7—22no—
452C23×C7—22no—
453C23×C7—22no—
454C23×C7—22no—
455C23×C7—22no—
456C23×C7—22no—
457C23×C7—22no—
458C23×C7—22no—
459C23×C7—22no—
460C23×C7—22no—
461C23×C7—22no—
462C23×C7—22no—
463C23×C7—41no—
464C23×C7—41no—
465C23×C7—41no—
466C23×C7—41no—
467C23×C7—41no—
468C23×C7—41no—
469C23×C7—41no—
470C23×C7—41no—
471C23×C7—41no—
472C23×C7—41no—
473C23×C7—41no—
474C23×C7—41no—
475C23×C7—41no—
476C23×C7—41no—
477C23×C7—41no—
478C23×C7—41no—
479C23×C7—41no—
480C23×C7—41no—
481C23×C7—41no—
482C23×C7—41no—
483C23×C7—41no—
484C23×C7—41no—
485C23×C7—41no—
486C23×C7—41no—
487C23×C7—41no—
488C23×C7—41no—
489C23×C7—41no—
490C23×C7—41no—
491C23×C7—41no—
492C23×C7—41no—
493C23×C7—41no—
494C23×C7—41no—
495C23×C7—41no—
496C23×C7—41no—
497C23×C7—41no—
498C23×C7—41no—
499C23×C7—41no—
500C23×C7—41no—
501C23×C7—41no—
502C23×C7—41no—
503C23×C7—41no—
504C23×C7—41no—
505C23×C7—41no—
506C23×C7—41no—
507C23×C7—41no—
508C23×C7—41no—
509C23×C7—41no—
510C23×C7—41no—
511C23×C7—41no—
512C23×C7—41no—
513C23×C7—41no—
514C23×C7—41no—
515C23×C7—41no—
516C23×C7—41no—
517C23×C7—41no—
518C23×C7—41no—
519C23×C7—41no—
520C23×C7—41no—
521C23×C7—41no—
522C23×C7—41no—
523C23×C7C2×C22⋊C414yes—
524C23×C7C4×D414yes—
525C23×C7C23×C411yescharacteristic
526C23×C7C22×D411yescharacteristic
527C23×C7C22×D411yescharacteristic
528C23×C7C22×D411yescharacteristic
529C23×C7C22×D411yescharacteristic
530C23×C7C2×#4111yescharacteristic
531C23×C7C2×#4111yescharacteristic
532C23×C7C2×#4111yescharacteristic
533C23×C7C2×#4111yescharacteristic
534C23×C7C2×#4111yescharacteristic
535C23×C7C2×#4111yescharacteristic
536C23×C7H(5,𝔽2)11yescharacteristic
537C23×C7H(5,𝔽2)11yescharacteristic
538C23×C7H(5,𝔽2)11yescharacteristic
539C23×C7H(5,𝔽2)11yescharacteristic
540C7×D4—416no—
541C7×D4—416no—
542C7×D4—416no—
543C2×C4×C7—22no—
544C2×C4×C7—22no—
545C2×C4×C7—22no—
546C2×C4×C7—22no—
547C2×C4×C7—22no—
548C2×C4×C7—22no—
549C2×C4×C7—22no—
550C2×C4×C7—22no—
551C2×C4×C7—22no—
552C2×C4×C7—22no—
553C2×C4×C7—22no—
554C2×C4×C7—22no—
555C2×C4×C7—22no—
556C2×C4×C7—22no—
557C2×C4×C7—22no—
558C2×C4×C7—22no—
559C2×C4×C7—22no—
560C2×C4×C7—22no—
561C2×C4×C7—22no—
562C2×C4×C7—22no—
563C2×C4×C7—22no—
564C2×C4×C7—22no—
565C2×C4×C7—22no—
566C2×C4×C7—22no—
567C2×C4×C7—22no—
568C2×C4×C7—22no—
569C2×C4×C7—22no—
570C2×C4×C7—22no—
571C2×C4×C7—22no—
572C2×C4×C7—22no—
573C2×C4×C7—22no—
574C2×C4×C7—22no—
575C2×C4×C7—22no—
576C2×C4×C7—22no—
577C2×C4×C7—22no—
578C2×C4×C7—22no—
579C2×C4×C7—22no—
580C2×C4×C7—22no—
581C2×C4×C7—22no—
582C2×C4×C7—22no—
583C2×C4×C7—22no—
584C2×C4×C7—22no—
585C2×C4×C7—416no—
586C2×C4×C7—416no—
587C2×C4×C7—41no—
588C2×C4×C7—41no—
589C2×C4×C7—41no—
590C2×C4×C7—41no—
591C2×C4×C7—41no—
592C2×C4×C7—41no—
593C2×C4×C7—41no—
594C2×C4×C7—41no—
595C2×C4×C7—41no—
596C2×C4×C7—41no—
597C2×C4×C7—41no—
598C2×C4×C7—41no—
599C2×C4×C7—41no—
600C2×C4×C7—41no—
601C2×C4×C7—41no—
602C2×C4×C7—41no—
603C2×C4×C7—41no—
604C2×C4×C7—41no—
605C2×C4×C7—41no—
606C2×C4×C7—41no—
607C2×C4×C7—41no—
608C2×C4×C7—41no—
609C2×C4×C7—41no—
610C2×C4×C7—41no—
611C2×C4×C7—41no—
612C2×C4×C7—41no—
613C2×C4×C7—41no—
614C2×C4×C7—41no—
615C2×C4×C7—41no—
616C2×C4×C7—41no—
617C2×C4×C7—41no—
618C2×C4×C7—41no—
619C2×C4×C7—41no—
620C2×C4×C7—41no—
621C2×C4×C7—41no—
622C2×C4×C7—41no—
623C2×C4×C7—41no—
624C2×C4×C7—41no—
625C2×C4×C7C2×C22⋊C414yes—
626C2×C4×C7C2×C22⋊C414yes—
627C2×C4×C7C4×D414yes—
628C2×C4×C7#12114yescomplemented
629C25C23×C711yescharacteristic
630C25C23×C711yescharacteristic
631C25C23×C711yescharacteristic
632C22×D4—22no—
633C22×D4—22no—
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—22no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—41no—
645C22×D4—41no—
646C22×D4—41no—
647C22×D4—41no—
648C22×D4—41no—
649C22×D4—41no—
650C22×D4C2×C4×C714yes—
651C22×D4C2×C4×C714yes—
652C22×D4C2×C4×C714yescomplemented
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—41no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4—41no—
666C23×C4C2×C4×C714yescomplemented
667C23×C4C23×C711yescharacteristic
668C23×C4C23×C711yescharacteristic
669C23×C4C23×C711yescharacteristic
670C23×C4C23×C711yescharacteristic
671C23×C4C23×C711yescharacteristic
672C23×C4C23×C711yescharacteristic
673C23×C4C23×C711yescharacteristic
674C23×C4C23×C711yescharacteristic
675C23×C4C23×C711yescharacteristic
676C23×C4C23×C711yescharacteristic
677C23×C4C23×C711yescharacteristic
678C23×C4C23×C711yescharacteristic
679#121—232no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4C2×C4×C714yescomplemented
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4C2×C4×C714yes—
721C2×C22⋊C4C2×C4×C714yescomplemented
722C2×C22⋊C4C7×D414yes—
723C2×C22⋊C4C7×D414yes—
724C2×C22⋊C4C7×D414yescomplemented
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—41no—
732C2×C42—41no—
733C2×C42—41no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95C7×D414yescomplemented
746C22×C7—24no—
747C22×C7—24no—
748C22×C7—24no—
749C22×C7—24no—
750C22×C7—24no—
751C22×C7—24no—
752C22×C7—42no—
753C22×C7—42no—
754C22×C7—42no—
755C22×C7—42no—
756C22×C7—42no—
757C22×C7—42no—
758C22×C7—42no—
759C22×C7—42no—
760C22×C7—42no—
761C22×C7—42no—
762C22×C7—42no—
763C22×C7—42no—
764C22×C7—42no—
765C22×C7—42no—
766C22×C7—42no—
767C22×C7—42no—
768C22×C7—42no—
769C22×C7—42no—
770C22×C7—42no—
771C22×C7—42no—
772C22×C7—42no—
773C22×C7—42no—
774C22×C7—42no—
775C22×C7—42no—
776C22×C7—42no—
777C22×C7—42no—
778C22×C7—42no—
779C22×C7—42no—
780C22×C7—42no—
781C22×C7—42no—
782C22×C7—42no—
783C22×C7—81no—
784C22×C7—81no—
785C22×C7—81no—
786C22×C7—81no—
787C22×C7—81no—
788C22×C7—81no—
789C22×C7—81no—
790C22×C7—81no—
791C22×C7C22×C22⋊C411yescharacteristic
792C22×C7C2×C4×D411yescharacteristic
793C22×C7C2×C4×D411yescharacteristic
794C22×C7C4×#4111yescharacteristic
795C22×C7C4×#4111yescharacteristic
796C22×C7#51811yescharacteristic
797C22×C7#51811yescharacteristic
798C22×C7C2×#12111yescharacteristic
799C22×C7#52511yescharacteristic
800C22×C7#52511yescharacteristic
801C22×C7#52511yescharacteristic
802C22×C7#52911yescharacteristic
803C22×C7#53211yescharacteristic
804C22×C7#53211yescharacteristic
805C22×C7#53211yescharacteristic
806C22×C7#53811yescharacteristic
807C22×C7#53811yescharacteristic
808C22×C7#54011yescharacteristic
809C22×C7#54011yescharacteristic
810C22×C7D4211yescharacteristic
811C22×C7D4211yescharacteristic
812C22×C7D4211yescharacteristic
813C22×C7D4211yescharacteristic
814C22×C7#54611yescharacteristic
815C22×C7#54611yescharacteristic
816C22×C7#54611yescharacteristic
817C22×C7#54611yescharacteristic
818C22×C7#54611yescharacteristic
819C22×C7#54611yescharacteristic
820C22×C7#54611yescharacteristic
821C22×C7#55011yescharacteristic
822C22×C7#55311yescharacteristic
823C22×C7#55311yescharacteristic
824C22×C7#55311yescharacteristic
825C22×C7#55511yescharacteristic
826C4×C7—24no—
827C4×C7—24no—
828C4×C7—24no—
829C4×C7—24no—
830C4×C7—42no—
831C4×C7—42no—
832C4×C7—42no—
833C4×C7—42no—
834C4×C7—42no—
835C4×C7—42no—
836C4×C7—81no—
837C4×C7—81no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24C22×C4×C712yes—
877C24C22×C4×C712yes—
878C24C22×C4×C712yes—
879C24C2×C7×D412yes—
880C24C2×C7×D412yes—
881C24C2×C7×D412yes—
882C24C7×#4112yes—
883C24C24×C711yescharacteristic
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—28no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—28no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4C22×C4×C712yes—
986C22×C4C22×C4×C712yes—
987C22×C4C22×C4×C712yes—
988C22×C4C22×C4×C712yes—
989C22×C4C2×C7×D412yes—
990C22×C4C2×C7×D412yes—
991C22×C4C2×C7×D412yes—
992C22×C4C2×C7×D412yes—
993C22×C4C2×C7×D412yes—
994C22×C4C2×C7×D412yes—
995C22×C4C2×C7×D412yes—
996C22×C4C2×C7×D412yes—
997C22×C4C2×C7×D412yes—
998C22×C4C7×#4112yes—
999C22×C4C7×#4112yes—
1000C22×C4C7×#4112yes—
1001C22×C4C7×#4112yes—
1002C22×C4C7×#4112yes—
1003C4⋊C4—28no—
1004C4⋊C4—44no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—28no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4C7×C22⋊C4116yescomplemented
1018C42—44no—
1019C42—44no—
1020C42—44no—
1021C2×C7—44no—
1022C2×C7—44no—
1023C2×C7—82no—
1024C2×C7#229711yescharacteristic
1025C2×C7C4×#12111yescharacteristic
1026C2×C7#233311yescharacteristic
1027C2×C7D4×C22⋊C411yescharacteristic
1028C2×C7D4×C22⋊C411yescharacteristic
1029C2×C7#236311yescharacteristic
1030C2×C7#236411yescharacteristic
1031C2×C7#242411yescharacteristic
1032C2×C7#242811yescharacteristic
1033C2×C7#245611yescharacteristic
1034C2×C7#246411yescharacteristic
1035C2×C7#246411yescharacteristic
1036C2×C7#247611yescharacteristic
1037C2×C7#255511yescharacteristic
1038C2×C7#255911yescharacteristic
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23C2×C7×C22⋊C414yes—
1143C23C4×C7×D414yes—
1144C23C23×C4×C711yescharacteristic
1145C23C22×C7×D411yescharacteristic
1146C23C22×C7×D411yescharacteristic
1147C23C22×C7×D411yescharacteristic
1148C23C22×C7×D411yescharacteristic
1149C23C2×C7×#4111yescharacteristic
1150C23C2×C7×#4111yescharacteristic
1151C23C2×C7×#4111yescharacteristic
1152C23C2×C7×#4111yescharacteristic
1153C23C2×C7×#4111yescharacteristic
1154C23C2×C7×#4111yescharacteristic
1155C23C7×H(5,𝔽2)11yescharacteristic
1156C23C7×H(5,𝔽2)11yescharacteristic
1157C23C7×H(5,𝔽2)11yescharacteristic
1158C23C7×H(5,𝔽2)11yescharacteristic
1159D4—416no—
1160D4—416no—
1161D4—416no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—416no—
1205C2×C4—416no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4C2×C7×C22⋊C414yes—
1245C2×C4C2×C7×C22⋊C414yes—
1246C2×C4C4×C7×D414yes—
1247C2×C4C7×#12114yescomplemented
1248C7#1410011yescharacteristic, direct product factor, Sylow
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C7×C22⋊C411yescharacteristic
1295C22C2×C4×C7×D411yescharacteristic
1296C22C2×C4×C7×D411yescharacteristic
1297C22C4×C7×#4111yescharacteristic
1298C22C4×C7×#4111yescharacteristic
1299C22C7×#51811yescharacteristic
1300C22C7×#51811yescharacteristic
1301C22C2×C7×#12111yescharacteristic
1302C22C7×#52511yescharacteristic
1303C22C7×#52511yescharacteristic
1304C22C7×#52511yescharacteristic
1305C22C7×#52911yescharacteristic
1306C22C7×#53211yescharacteristic
1307C22C7×#53211yescharacteristic
1308C22C7×#53211yescharacteristic
1309C22C7×#53811yescharacteristic
1310C22C7×#53811yescharacteristic
1311C22C7×#54011yescharacteristic
1312C22C7×#54011yescharacteristic
1313C22C7×D4211yescharacteristic
1314C22C7×D4211yescharacteristic
1315C22C7×D4211yescharacteristic
1316C22C7×D4211yescharacteristic
1317C22C7×#54611yescharacteristic
1318C22C7×#54611yescharacteristic
1319C22C7×#54611yescharacteristic
1320C22C7×#54611yescharacteristic
1321C22C7×#54611yescharacteristic
1322C22C7×#54611yescharacteristic
1323C22C7×#54611yescharacteristic
1324C22C7×#55011yescharacteristic
1325C22C7×#55311yescharacteristic
1326C22C7×#55311yescharacteristic
1327C22C7×#55311yescharacteristic
1328C22C7×#55511yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C7×#229711yescharacteristic
1345C2C4×C7×#12111yescharacteristic
1346C2C7×#233311yescharacteristic
1347C2C7×D4×C22⋊C411yescharacteristic
1348C2C7×D4×C22⋊C411yescharacteristic
1349C2C7×#236311yescharacteristic
1350C2C7×#236411yescharacteristic
1351C2C7×#242411yescharacteristic
1352C2C7×#242811yescharacteristic
1353C2C7×#245611yescharacteristic
1354C2C7×#246411yescharacteristic
1355C2C7×#246411yescharacteristic
1356C2C7×#247611yescharacteristic
1357C2C7×#255511yescharacteristic
1358C2C7×#255911yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC22×C7×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C7×#390C2semidirect
3. C2×C7×#388C2semidirect
4. C2×C7×#386C2semidirect
5. C2×C7×#386C2semidirect
6. C2×C4×C7×C22⋊C4C2semidirect
7. C2×C4×C7×C22⋊C4C2semidirect
8. C7×#1441C2semidirect
9. C7×#1438C2semidirect
10. C7×#1438C2semidirect
11. C7×#1438C2semidirect
12. C7×#1437C2semidirect
13. C7×#1437C2semidirect
14. C7×#1436C2semidirect
15. C7×C22⋊#95C2semidirect
23. C2×C7×#121C4semidirect
60. #14100C7direct (N × H)
84. C22×C7×D4C2×C4semidirect
98. C23×C4×C7C2×C4semidirect
117. C2×C7×C4⋊C4C2×C4semidirect
153. C2×C7×C22⋊C4C2×C4semidirect
156. C2×C7×C22⋊C4D4semidirect
177. C7×#95D4semidirect
179. C2×#390C2×C7semidirect
180. C2×#388C2×C7semidirect
181. C2×#386C2×C7semidirect
182. C2×#386C2×C7semidirect
183. C2×C4×C22⋊C4C2×C7semidirect
184. C2×C4×C22⋊C4C2×C7semidirect
185. #1441C2×C7semidirect
186. #1438C2×C7semidirect
187. #1438C2×C7semidirect
188. #1438C2×C7semidirect
189. #1437C2×C7semidirect
190. #1437C2×C7semidirect
191. #1436C2×C7semidirect
192. C22⋊#95C2×C7semidirect
372. C7×C22⋊C4C22⋊C4semidirect
383. C2×#121C4×C7semidirect
628. C2×C4×C7#121semidirect
652. C22×D4C2×C4×C7semidirect
666. C23×C4C2×C4×C7semidirect
685. C2×C4⋊C4C2×C4×C7semidirect
721. C2×C22⋊C4C2×C4×C7semidirect
724. C2×C22⋊C4C7×D4semidirect
745. #95C7×D4semidirect
1017. C22⋊C4C7×C22⋊C4semidirect
1247. C2×C4C7×#121semidirect
1248. C7#14100direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C7×#1212
C2×C7×#3902
C2×C7×#3882
C2×C7×#3862
C2×C4×C7×C22⋊C42
C7×#14412
C7×#14382
C7×#14372
C7×#14362
C7×C22⋊#952
#141007