Finite Group Databasebeta

← C7×#14721 #13191937

Subgroups — C7×#14721 #13191937

Order 1792.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic, complemented
2C22×C4×C7×D4C211yesmaximal, characteristic, complemented
3C2×C7×#394C211yesmaximal, characteristic, complemented
4C2×C7×#392C211yesmaximal, characteristic
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C2×C7×#385C211yesmaximal, characteristic, complemented
7C7×#1444C211yesmaximal, characteristic, complemented
8C7×#1440C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×#1438C211yesmaximal, characteristic, complemented
12C7×#1438C211yesmaximal, 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×#123—24no—
22C2×C7×#123—24no—
23C2×C7×#123—24no—
24C2×C4×C7×D4—24no—
25C2×C4×C7×D4—24no—
26C2×C4×C7×D4—24no—
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×C7×C4⋊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×C7×C22⋊C4C2211yescharacteristic
40C22×C7×C22⋊C4C2211yescharacteristic
41C22×C7×C22⋊C4C2211yescharacteristic
42C22×C7×C22⋊C4C2211yescharacteristic
43C22×C7×C22⋊C4C2211yescharacteristic
44C22×C42×C7C2211yescharacteristic
45C7×#394—24no—
46C7×#392—24no—
47C7×#386—24no—
48C7×#385—24no—
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
60C2×C7×#95C2211yescharacteristic
61#14721C711yesmaximal, characteristic, direct product factor, Sylow
62C25×C7C2311yescharacteristic
63C25×C7C2311yescharacteristic
64C25×C7C2311yescharacteristic
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—22no—
77C22×C7×D4—22no—
78C22×C7×D4—22no—
79C22×C7×D4—22no—
80C22×C7×D4—22no—
81C22×C7×D4—41no—
82C22×C7×D4—41no—
83C22×C7×D4—41no—
84C22×C7×D4—41no—
85C22×C7×D4D414yes—
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—22no—
95C23×C4×C7—41no—
96C23×C4×C7—41no—
97C23×C4×C7—41no—
98C23×C4×C7—41no—
99C23×C4×C7D414yescomplemented
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
111C23×C4×C7C2311yescharacteristic
112C7×#123—232no—
113C4×C7×D4—232no—
114C2×C7×C4⋊C4—22no—
115C2×C7×C4⋊C4—22no—
116C2×C7×C4⋊C4—22no—
117C2×C7×C4⋊C4—22no—
118C2×C7×C4⋊C4—22no—
119C2×C7×C4⋊C4—22no—
120C2×C7×C4⋊C4—22no—
121C2×C7×C4⋊C4—22no—
122C2×C7×C4⋊C4—22no—
123C2×C7×C4⋊C4—22no—
124C2×C7×C4⋊C4—41no—
125C2×C7×C4⋊C4D414yescomplemented
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—22no—
145C2×C7×C22⋊C4—22no—
146C2×C7×C22⋊C4—22no—
147C2×C7×C22⋊C4—22no—
148C2×C7×C22⋊C4—22no—
149C2×C7×C22⋊C4—22no—
150C2×C7×C22⋊C4—22no—
151C2×C7×C22⋊C4—22no—
152C2×C7×C22⋊C4—22no—
153C2×C7×C22⋊C4—22no—
154C2×C7×C22⋊C4—22no—
155C2×C7×C22⋊C4—22no—
156C2×C7×C22⋊C4—22no—
157C2×C7×C22⋊C4—41no—
158C2×C7×C22⋊C4—41no—
159C2×C7×C22⋊C4—41no—
160C2×C7×C22⋊C4—41no—
161C2×C7×C22⋊C4—41no—
162C2×C7×C22⋊C4—41no—
163C2×C7×C22⋊C4D414yescomplemented
164C2×C7×C22⋊C4D414yescomplemented
165C2×C42×C7—22no—
166C2×C42×C7—22no—
167C2×C42×C7—22no—
168C7×#95—22no—
169C7×#95—22no—
170C7×#95—22no—
171C7×#95—22no—
172C7×#95—22no—
173C7×#95—22no—
174C7×#95—22no—
175C7×#95—22no—
176C7×#95—22no—
177C7×#95—41no—
178C7×#95—41no—
179C7×#95—41no—
180C22×#123C2×C711yescharacteristic, complemented
181C22×C4×D4C2×C711yescharacteristic, complemented
182C2×#394C2×C711yescharacteristic, complemented
183C2×#392C2×C711yescharacteristic
184C2×#386C2×C711yescharacteristic, complemented
185C2×#385C2×C711yescharacteristic, complemented
186#1444C2×C711yescharacteristic, complemented
187#1440C2×C711yescharacteristic, complemented
188#1439C2×C711yescharacteristic, complemented
189#1439C2×C711yescharacteristic, complemented
190#1438C2×C711yescharacteristic, complemented
191#1438C2×C711yescharacteristic, complemented
192#1437C2×C711yescharacteristic, complemented
193#1436C2×C711yescharacteristic, complemented
194C22⋊#95C2×C711yescharacteristic, complemented
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×C7—21no—
232C24×C7—21no—
233C24×C7C2×D412yes—
234C24×C7C2×D412yes—
235C24×C7C2×D412yes—
236C24×C7C2×D412yes—
237C24×C7C2×D412yes—
238C24×C7#4112yes—
239C24×C7#4112yes—
240C24×C7C2411yescharacteristic
241C2×C7×D4—28no—
242C2×C7×D4—28no—
243C2×C7×D4—28no—
244C2×C7×D4—28no—
245C2×C7×D4—28no—
246C2×C7×D4—28no—
247C2×C7×D4—28no—
248C2×C7×D4—28no—
249C2×C7×D4—28no—
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—
260C2×C7×D4—44no—
261C2×C7×D4—44no—
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—28no—
271C22×C4×C7—28no—
272C22×C4×C7—21no—
273C22×C4×C7—21no—
274C22×C4×C7—21no—
275C22×C4×C7—21no—
276C22×C4×C7—21no—
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—21no—
314C22×C4×C7—21no—
315C22×C4×C7—21no—
316C22×C4×C7—21no—
317C22×C4×C7—21no—
318C22×C4×C7—21no—
319C22×C4×C7—21no—
320C22×C4×C7—28no—
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—21no—
330C22×C4×C7—21no—
331C22×C4×C7—21no—
332C22×C4×C7—21no—
333C22×C4×C7—21no—
334C22×C4×C7—21no—
335C22×C4×C7—44no—
336C22×C4×C7—44no—
337C22×C4×C7—44no—
338C22×C4×C7—44no—
339C22×C4×C7—44no—
340C22×C4×C7—44no—
341C22×C4×C7—44no—
342C22×C4×C7—44no—
343C22×C4×C7—44no—
344C22×C4×C7—44no—
345C22×C4×C7—44no—
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×C7C2×D412yes—
354C22×C4×C7C2×D412yes—
355C22×C4×C7C2×D412yes—
356C22×C4×C7#4112yes—
357C22×C4×C7#4112yes—
358C22×C4×C7#4112yes—
359C22×C4×C7#4112yes—
360C7×C4⋊C4—28no—
361C7×C4⋊C4—28no—
362C7×C4⋊C4—28no—
363C7×C4⋊C4—44no—
364C7×C22⋊C4—28no—
365C7×C22⋊C4—28no—
366C7×C22⋊C4—28no—
367C7×C22⋊C4—28no—
368C7×C22⋊C4—28no—
369C7×C22⋊C4—28no—
370C7×C22⋊C4—44no—
371C7×C22⋊C4—44no—
372C7×C22⋊C4—44no—
373C7×C22⋊C4—44no—
374C7×C22⋊C4—44no—
375C7×C22⋊C4—44no—
376C7×C22⋊C4—44no—
377C42×C7—28no—
378C23×D4C22×C711yescharacteristic
379C23×D4C22×C711yescharacteristic
380C23×D4C22×C711yescharacteristic
381C24×C4C22×C711yescharacteristic
382C24×C4C22×C711yescharacteristic
383C2×#123—24no—
384C2×#123—24no—
385C2×#123—24no—
386C2×C4×D4—24no—
387C2×C4×D4—24no—
388C2×C4×D4—24no—
389C22×C4⋊C4C22×C711yescharacteristic
390C22×C4⋊C4C22×C711yescharacteristic
391C22×C4⋊C4C22×C711yescharacteristic
392C22×C4⋊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×C22⋊C4C22×C711yescharacteristic
400C22×C22⋊C4C22×C711yescharacteristic
401C22×C22⋊C4C22×C711yescharacteristic
402C22×C22⋊C4C22×C711yescharacteristic
403C22×C22⋊C4C22×C711yescharacteristic
404C22×C22⋊C4C22×C711yescharacteristic
405C22×C22⋊C4C22×C711yescharacteristic
406C22×C42C22×C711yescharacteristic
407#394—24no—
408#392—24no—
409#386—24no—
410#385—24no—
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
420C2×#95C22×C711yescharacteristic
421C2×#95C22×C711yescharacteristic
422C2×#95C22×C711yescharacteristic
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—22no—
464C23×C7—22no—
465C23×C7—22no—
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×C7—41no—
524C23×C7—41no—
525C23×C7—41no—
526C23×C7#12014yes—
527C23×C7#12314yescomplemented
528C23×C7C22×D411yescharacteristic
529C23×C7C22×D411yescharacteristic
530C23×C7C22×D411yescharacteristic
531C23×C7C22×D411yescharacteristic
532C23×C7C22×D411yescharacteristic
533C23×C7C2×#4111yescharacteristic
534C23×C7C2×#4111yescharacteristic
535C23×C7C2×#4111yescharacteristic
536C23×C7C2×#4111yescharacteristic
537C23×C7C2×#4111yescharacteristic
538C23×C7C2×#4111yescharacteristic
539C23×C7H(5,𝔽2)11yescharacteristic
540C23×C7H(5,𝔽2)11yescharacteristic
541C23×C7H(5,𝔽2)11yescharacteristic
542C23×C72−1+411yescharacteristic
543C7×D4—232no—
544C7×D4—416no—
545C7×D4—416no—
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—416no—
583C2×C4×C7—416no—
584C2×C4×C7—41no—
585C2×C4×C7—41no—
586C2×C4×C7—41no—
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×C7—41no—
626C2×C4×C7—41no—
627C2×C4×C7—41no—
628C2×C4×C7—41no—
629C2×C4×C7—41no—
630C2×C4×C7#12014yes—
631C2×C4×C7#12314yescomplemented
632C25C23×C711yescharacteristic
633C25C23×C711yescharacteristic
634C25C23×C711yescharacteristic
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—22no—
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—41no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4—41no—
655C22×D4C7×D414yes—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—41no—
666C23×C4—41no—
667C23×C4—41no—
668C23×C4—41no—
669C23×C4C7×D414yescomplemented
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
679C23×C4C23×C711yescharacteristic
680C23×C4C23×C711yescharacteristic
681C23×C4C23×C711yescharacteristic
682#123—232no—
683C4×D4—232no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4C7×D414yescomplemented
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—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4C7×D414yescomplemented
734C2×C22⋊C4C7×D414yescomplemented
735C2×C42—22no—
736C2×C42—22no—
737C2×C42—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—41no—
748#95—41no—
749#95—41no—
750C22×C7—24no—
751C22×C7—24no—
752C22×C7—24no—
753C22×C7—24no—
754C22×C7—24no—
755C22×C7—24no—
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—42no—
784C22×C7—42no—
785C22×C7—42no—
786C22×C7—42no—
787C22×C7—81no—
788C22×C7—81no—
789C22×C7—81no—
790C22×C7—81no—
791C22×C7—81no—
792C22×C7—81no—
793C22×C7—81no—
794C22×C7—81no—
795C22×C7C2×#12011yescharacteristic
796C22×C7C2×#12011yescharacteristic
797C22×C7C2×#12311yescharacteristic
798C22×C7C2×#12311yescharacteristic
799C22×C7#52511yescharacteristic
800C22×C7#52511yescharacteristic
801C22×C7#52511yescharacteristic
802C22×C7#52511yescharacteristic
803C22×C7#52511yescharacteristic
804C22×C7#52511yescharacteristic
805C22×C7#53211yescharacteristic
806C22×C7#53211yescharacteristic
807C22×C7#53211yescharacteristic
808C22×C7#53411yescharacteristic
809C22×C7#53711yescharacteristic
810C22×C7#53811yescharacteristic
811C22×C7#53911yescharacteristic
812C22×C7#54011yescharacteristic
813C22×C7#54211yescharacteristic
814C22×C7D4211yescharacteristic
815C22×C7D4211yescharacteristic
816C22×C7D4211yescharacteristic
817C22×C7D4211yescharacteristic
818C22×C7#54611yescharacteristic
819C22×C7#54611yescharacteristic
820C22×C7#54611yescharacteristic
821C22×C7#54711yescharacteristic
822C22×C7#54711yescharacteristic
823C22×C7#54711yescharacteristic
824C22×C7#54811yescharacteristic
825C22×C7#55011yescharacteristic
826C22×C7#55111yescharacteristic
827C22×C7#55311yescharacteristic
828C22×C7#55311yescharacteristic
829C22×C7#55911yescharacteristic
830C4×C7—24no—
831C4×C7—24no—
832C4×C7—42no—
833C4×C7—42no—
834C4×C7—42no—
835C4×C7—42no—
836C4×C7—42no—
837C4×C7—42no—
838C4×C7—42no—
839C4×C7—42no—
840C4×C7—81no—
841C4×C7—81no—
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—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24C2×C7×D412yes—
881C24C2×C7×D412yes—
882C24C2×C7×D412yes—
883C24C2×C7×D412yes—
884C24C2×C7×D412yes—
885C24C7×#4112yes—
886C24C7×#4112yes—
887C24C24×C711yescharacteristic
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
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—28no—
918C22×C4—28no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
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—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—28no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4C2×C7×D412yes—
994C22×C4C2×C7×D412yes—
995C22×C4C2×C7×D412yes—
996C22×C4C2×C7×D412yes—
997C22×C4C2×C7×D412yes—
998C22×C4C2×C7×D412yes—
999C22×C4C2×C7×D412yes—
1000C22×C4C2×C7×D412yes—
1001C22×C4C2×C7×D412yes—
1002C22×C4C2×C7×D412yes—
1003C22×C4C7×#4112yes—
1004C22×C4C7×#4112yes—
1005C22×C4C7×#4112yes—
1006C22×C4C7×#4112yes—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—44no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C42—28no—
1025C2×C7—44no—
1026C2×C7—44no—
1027C2×C7—82no—
1028C2×C7#238811yescharacteristic
1029C2×C7#240311yescharacteristic
1030C2×C7#240711yescharacteristic
1031C2×C7#241811yescharacteristic
1032C2×C7#242211yescharacteristic
1033C2×C7#243011yescharacteristic
1034C2×C7#244311yescharacteristic
1035C2×C7#244511yescharacteristic
1036C2×C7#245511yescharacteristic
1037C2×C7#245611yescharacteristic
1038C2×C7#246111yescharacteristic
1039C2×C7#246411yescharacteristic
1040C2×C7#260211yescharacteristic
1041C2×C7#263011yescharacteristic
1042C2×C7#284911yescharacteristic
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—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
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—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23C7×#12014yes—
1147C23C7×#12314yescomplemented
1148C23C22×C7×D411yescharacteristic
1149C23C22×C7×D411yescharacteristic
1150C23C22×C7×D411yescharacteristic
1151C23C22×C7×D411yescharacteristic
1152C23C22×C7×D411yescharacteristic
1153C23C2×C7×#4111yescharacteristic
1154C23C2×C7×#4111yescharacteristic
1155C23C2×C7×#4111yescharacteristic
1156C23C2×C7×#4111yescharacteristic
1157C23C2×C7×#4111yescharacteristic
1158C23C2×C7×#4111yescharacteristic
1159C23C7×H(5,𝔽2)11yescharacteristic
1160C23C7×H(5,𝔽2)11yescharacteristic
1161C23C7×H(5,𝔽2)11yescharacteristic
1162C23C7×2−1+411yescharacteristic
1163D4—232no—
1164D4—416no—
1165D4—416no—
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—416no—
1203C2×C4—416no—
1204C2×C4—41no—
1205C2×C4—41no—
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×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4C7×#12014yes—
1251C2×C4C7×#12314yescomplemented
1252C7#1472111yescharacteristic, direct product factor, Sylow
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
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—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22C2×C7×#12011yescharacteristic
1299C22C2×C7×#12011yescharacteristic
1300C22C2×C7×#12311yescharacteristic
1301C22C2×C7×#12311yescharacteristic
1302C22C7×#52511yescharacteristic
1303C22C7×#52511yescharacteristic
1304C22C7×#52511yescharacteristic
1305C22C7×#52511yescharacteristic
1306C22C7×#52511yescharacteristic
1307C22C7×#52511yescharacteristic
1308C22C7×#53211yescharacteristic
1309C22C7×#53211yescharacteristic
1310C22C7×#53211yescharacteristic
1311C22C7×#53411yescharacteristic
1312C22C7×#53711yescharacteristic
1313C22C7×#53811yescharacteristic
1314C22C7×#53911yescharacteristic
1315C22C7×#54011yescharacteristic
1316C22C7×#54211yescharacteristic
1317C22C7×D4211yescharacteristic
1318C22C7×D4211yescharacteristic
1319C22C7×D4211yescharacteristic
1320C22C7×D4211yescharacteristic
1321C22C7×#54611yescharacteristic
1322C22C7×#54611yescharacteristic
1323C22C7×#54611yescharacteristic
1324C22C7×#54711yescharacteristic
1325C22C7×#54711yescharacteristic
1326C22C7×#54711yescharacteristic
1327C22C7×#54811yescharacteristic
1328C22C7×#55011yescharacteristic
1329C22C7×#55111yescharacteristic
1330C22C7×#55311yescharacteristic
1331C22C7×#55311yescharacteristic
1332C22C7×#55911yescharacteristic
1333C4—24no—
1334C4—24no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2C7×#238811yescharacteristic
1349C2C7×#240311yescharacteristic
1350C2C7×#240711yescharacteristic
1351C2C7×#241811yescharacteristic
1352C2C7×#242211yescharacteristic
1353C2C7×#243011yescharacteristic
1354C2C7×#244311yescharacteristic
1355C2C7×#244511yescharacteristic
1356C2C7×#245511yescharacteristic
1357C2C7×#245611yescharacteristic
1358C2C7×#246111yescharacteristic
1359C2C7×#246411yescharacteristic
1360C2C7×#260211yescharacteristic
1361C2C7×#263011yescharacteristic
1362C2C7×#284911yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC2×C7×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×#123C2semidirect
2. C22×C4×C7×D4C2semidirect
3. C2×C7×#394C2semidirect
5. C2×C7×#386C2semidirect
6. C2×C7×#385C2semidirect
7. C7×#1444C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
11. C7×#1438C2semidirect
12. C7×#1438C2semidirect
13. C7×#1437C2semidirect
14. C7×#1436C2semidirect
15. C7×C22⋊#95C2semidirect
61. #14721C7direct (N × H)
99. C23×C4×C7D4semidirect
125. C2×C7×C4⋊C4D4semidirect
163. C2×C7×C22⋊C4D4semidirect
164. C2×C7×C22⋊C4D4semidirect
180. C22×#123C2×C7semidirect
181. C22×C4×D4C2×C7semidirect
182. C2×#394C2×C7semidirect
184. C2×#386C2×C7semidirect
185. C2×#385C2×C7semidirect
186. #1444C2×C7semidirect
187. #1440C2×C7semidirect
188. #1439C2×C7semidirect
189. #1439C2×C7semidirect
190. #1438C2×C7semidirect
191. #1438C2×C7semidirect
192. #1437C2×C7semidirect
193. #1436C2×C7semidirect
194. C22⋊#95C2×C7semidirect
527. C23×C7#123semidirect
631. C2×C4×C7#123semidirect
669. C23×C4C7×D4semidirect
695. C2×C4⋊C4C7×D4semidirect
733. C2×C22⋊C4C7×D4semidirect
734. C2×C22⋊C4C7×D4semidirect
1147. C23C7×#123semidirect
1251. C2×C4C7×#123semidirect
1252. C7#14721direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C22×C4×C7×D42
C2×C7×#3942
C2×C7×#3922
C2×C7×#3862
C2×C7×#3852
C7×#14442
C7×#14402
C7×#14392
C7×#14382
C7×#14372
C7×#14362
C7×C22⋊#952
#147217