Finite Group Databasebeta

← C7×#14534 #13191750

Subgroups — C7×#14534 #13191750

Order 1792.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#392C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic, complemented
3C2×C7×#390C211yesmaximal, characteristic, complemented
4C2×C7×#388C211yesmaximal, characteristic, complemented
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C2×C7×#386C211yesmaximal, characteristic, complemented
7C2×C7×#385C211yesmaximal, 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×#1436C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊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×C42×C7C2211yescharacteristic
38C22×C42×C7C2211yescharacteristic
39C7×#392C418yescomplemented
40C7×#390—24no—
41C7×#390—24no—
42C7×#388—24no—
43C7×#386—24no—
44C7×#386—24no—
45C7×#385—24no—
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
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
58#14534C711yesmaximal, characteristic, direct product factor, Sylow
59C25×C7C2311yescharacteristic
60C25×C7C2311yescharacteristic
61C25×C7C2311yescharacteristic
62C22×C7×D4—22no—
63C22×C7×D4—22no—
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—41no—
71C22×C7×D4—41no—
72C22×C7×D4—41no—
73C22×C7×D4—41no—
74C22×C7×D4—41no—
75C22×C7×D4—41no—
76C22×C7×D4—41no—
77C22×C7×D4—41no—
78C22×C7×D4—41no—
79C22×C7×D4—41no—
80C22×C7×D4C2×C414yes—
81C22×C7×D4C2×C414yes—
82C22×C7×D4C2×C414yescomplemented
83C23×C4×C7—22no—
84C23×C4×C7—22no—
85C23×C4×C7—22no—
86C23×C4×C7—41no—
87C23×C4×C7—41no—
88C23×C4×C7—41no—
89C23×C4×C7—41no—
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2311yescharacteristic
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2311yescharacteristic
95C23×C4×C7C2311yescharacteristic
96C23×C4×C7C2311yescharacteristic
97C23×C4×C7C2311yescharacteristic
98C23×C4×C7C2311yescharacteristic
99C23×C4×C7C2311yescharacteristic
100C23×C4×C7C2311yescharacteristic
101C23×C4×C7C2311yescharacteristic
102C2×C7×C4⋊C4—22no—
103C2×C7×C4⋊C4—22no—
104C2×C7×C4⋊C4—22no—
105C2×C7×C4⋊C4—22no—
106C2×C7×C4⋊C4—41no—
107C2×C7×C4⋊C4—41no—
108C2×C7×C4⋊C4—41no—
109C2×C7×C4⋊C4—41no—
110C2×C7×C4⋊C4D414yescomplemented
111C2×C7×C22⋊C4—22no—
112C2×C7×C22⋊C4—22no—
113C2×C7×C22⋊C4—22no—
114C2×C7×C22⋊C4—22no—
115C2×C7×C22⋊C4—22no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—22no—
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—41no—
132C2×C7×C22⋊C4—41no—
133C2×C7×C22⋊C4—41no—
134C2×C7×C22⋊C4—41no—
135C2×C7×C22⋊C4—41no—
136C2×C7×C22⋊C4—41no—
137C2×C7×C22⋊C4—41no—
138C2×C7×C22⋊C4—41no—
139C2×C7×C22⋊C4—41no—
140C2×C7×C22⋊C4—41no—
141C2×C7×C22⋊C4—41no—
142C2×C7×C22⋊C4—41no—
143C2×C7×C22⋊C4—41no—
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⋊C4C2×C414yes—
150C2×C7×C22⋊C4C2×C414yescomplemented
151C2×C7×C22⋊C4C2×C414yescomplemented
152C2×C7×C22⋊C4D414yescomplemented
153C2×C42×C7—22no—
154C2×C42×C7—22no—
155C2×C42×C7—22no—
156C2×C42×C7—41no—
157C2×C42×C7—41no—
158C2×C42×C7—41no—
159C7×#95—22no—
160C7×#95—22no—
161C7×#95—22no—
162C7×#95—22no—
163C7×#95—22no—
164C7×#95—22no—
165C7×#95—22no—
166C7×#95—41no—
167C7×#95—41no—
168C7×#95—41no—
169C7×#95C2×C414yescomplemented
170C7×#95D414yescomplemented
171C2×#392C2×C711yescharacteristic
172C2×#390C2×C711yescharacteristic, complemented
173C2×#390C2×C711yescharacteristic, complemented
174C2×#388C2×C711yescharacteristic, complemented
175C2×#386C2×C711yescharacteristic, complemented
176C2×#386C2×C711yescharacteristic, complemented
177C2×#385C2×C711yescharacteristic, complemented
178#1440C2×C711yescharacteristic, complemented
179#1439C2×C711yescharacteristic, complemented
180#1439C2×C711yescharacteristic, complemented
181#1438C2×C711yescharacteristic, complemented
182#1438C2×C711yescharacteristic, complemented
183#1437C2×C711yescharacteristic, complemented
184#1436C2×C711yescharacteristic, complemented
185#1436C2×C711yescharacteristic, complemented
186C24×C7—21no—
187C24×C7—21no—
188C24×C7—21no—
189C24×C7—21no—
190C24×C7—21no—
191C24×C7—21no—
192C24×C7—21no—
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×C7C22×C412yes—
227C24×C7C22×C412yes—
228C24×C7C22×C412yes—
229C24×C7C2×D412yes—
230C24×C7#4112yes—
231C24×C7C2411yescharacteristic
232C2×C7×D4—28no—
233C2×C7×D4—28no—
234C2×C7×D4—28no—
235C2×C7×D4—28no—
236C2×C7×D4—44no—
237C2×C7×D4—44no—
238C2×C7×D4—44no—
239C2×C7×D4—44no—
240C2×C7×D4—44no—
241C2×C7×D4—44no—
242C2×C7×D4—44no—
243C2×C7×D4—44no—
244C2×C7×D4—44no—
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—
253C22×C4×C7—21no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—21no—
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—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—21no—
321C22×C4×C7—21no—
322C22×C4×C7—21no—
323C22×C4×C7—44no—
324C22×C4×C7—44no—
325C22×C4×C7—44no—
326C22×C4×C7—44no—
327C22×C4×C7—44no—
328C22×C4×C7—44no—
329C22×C4×C7—44no—
330C22×C4×C7C22×C412yes—
331C22×C4×C7C22×C412yes—
332C22×C4×C7C22×C412yes—
333C22×C4×C7C22×C412yes—
334C22×C4×C7C2×D412yes—
335C22×C4×C7C2×D412yes—
336C22×C4×C7C2×D412yes—
337C22×C4×C7C2×D412yes—
338C22×C4×C7C2×D412yes—
339C22×C4×C7C2×D412yes—
340C22×C4×C7C2×D412yes—
341C22×C4×C7C2×D412yes—
342C22×C4×C7#4112yes—
343C22×C4×C7#4112yes—
344C7×C4⋊C4—44no—
345C7×C4⋊C4—44no—
346C7×C4⋊C4—44no—
347C7×C22⋊C4—28no—
348C7×C22⋊C4—28no—
349C7×C22⋊C4—44no—
350C7×C22⋊C4—44no—
351C7×C22⋊C4—44no—
352C7×C22⋊C4—44no—
353C7×C22⋊C4—44no—
354C7×C22⋊C4—44no—
355C7×C22⋊C4—44no—
356C7×C22⋊C4—44no—
357C7×C22⋊C4—44no—
358C7×C22⋊C4—44no—
359C7×C22⋊C4—44no—
360C7×C22⋊C4—44no—
361C42×C7—44no—
362C42×C7—44no—
363C23×D4C22×C711yescharacteristic
364C23×D4C22×C711yescharacteristic
365C23×D4C22×C711yescharacteristic
366C24×C4C22×C711yescharacteristic
367C22×C4⋊C4C22×C711yescharacteristic
368C22×C4⋊C4C22×C711yescharacteristic
369C22×C4⋊C4C22×C711yescharacteristic
370C22×C22⋊C4C22×C711yescharacteristic
371C22×C22⋊C4C22×C711yescharacteristic
372C22×C22⋊C4C22×C711yescharacteristic
373C22×C22⋊C4C22×C711yescharacteristic
374C22×C22⋊C4C22×C711yescharacteristic
375C22×C22⋊C4C22×C711yescharacteristic
376C22×C22⋊C4C22×C711yescharacteristic
377C22×C22⋊C4C22×C711yescharacteristic
378C22×C22⋊C4C22×C711yescharacteristic
379C22×C22⋊C4C22×C711yescharacteristic
380C22×C22⋊C4C22×C711yescharacteristic
381C22×C22⋊C4C22×C711yescharacteristic
382C22×C22⋊C4C22×C711yescharacteristic
383C22×C22⋊C4C22×C711yescharacteristic
384C22×C42C22×C711yescharacteristic
385C22×C42C22×C711yescharacteristic
386#392C4×C718yescomplemented
387#390—24no—
388#390—24no—
389#388—24no—
390#386—24no—
391#386—24no—
392#385—24no—
393C2×#95C22×C711yescharacteristic
394C2×#95C22×C711yescharacteristic
395C2×#95C22×C711yescharacteristic
396C2×#95C22×C711yescharacteristic
397C2×#95C22×C711yescharacteristic
398C2×#95C22×C711yescharacteristic
399C2×#95C22×C711yescharacteristic
400C2×#95C22×C711yescharacteristic
401C2×#95C22×C711yescharacteristic
402C2×#95C22×C711yescharacteristic
403C2×#95C22×C711yescharacteristic
404C2×#95C22×C711yescharacteristic
405C23×C7—22no—
406C23×C7—22no—
407C23×C7—22no—
408C23×C7—22no—
409C23×C7—22no—
410C23×C7—22no—
411C23×C7—22no—
412C23×C7—22no—
413C23×C7—22no—
414C23×C7—22no—
415C23×C7—22no—
416C23×C7—22no—
417C23×C7—22no—
418C23×C7—22no—
419C23×C7—22no—
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—41no—
438C23×C7—41no—
439C23×C7—41no—
440C23×C7—41no—
441C23×C7—41no—
442C23×C7—41no—
443C23×C7—41no—
444C23×C7—41no—
445C23×C7—41no—
446C23×C7—41no—
447C23×C7—41no—
448C23×C7—41no—
449C23×C7—41no—
450C23×C7—41no—
451C23×C7—41no—
452C23×C7—41no—
453C23×C7—41no—
454C23×C7—41no—
455C23×C7—41no—
456C23×C7—41no—
457C23×C7—41no—
458C23×C7—41no—
459C23×C7—41no—
460C23×C7—41no—
461C23×C7—41no—
462C23×C7—41no—
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×C7C4×D414yes—
510C23×C7C23×C411yescharacteristic
511C23×C7C22×D411yescharacteristic
512C23×C7C22×D411yescharacteristic
513C23×C7C22×D411yescharacteristic
514C23×C7C2×#4111yescharacteristic
515C23×C7C2×#4111yescharacteristic
516C23×C7C2×#4111yescharacteristic
517C23×C7H(5,𝔽2)11yescharacteristic
518C23×C7H(5,𝔽2)11yescharacteristic
519C23×C7H(5,𝔽2)11yescharacteristic
520C23×C7H(5,𝔽2)11yescharacteristic
521C23×C7H(5,𝔽2)11yescharacteristic
522C23×C7H(5,𝔽2)11yescharacteristic
523C23×C7H(5,𝔽2)11yescharacteristic
524C23×C72−1+411yescharacteristic
525C7×D4—416no—
526C7×D4—416no—
527C7×D4—416no—
528C2×C4×C7—22no—
529C2×C4×C7—22no—
530C2×C4×C7—22no—
531C2×C4×C7—22no—
532C2×C4×C7—22no—
533C2×C4×C7—22no—
534C2×C4×C7—22no—
535C2×C4×C7—22no—
536C2×C4×C7—22no—
537C2×C4×C7—22no—
538C2×C4×C7—22no—
539C2×C4×C7—22no—
540C2×C4×C7—22no—
541C2×C4×C7—22no—
542C2×C4×C7—22no—
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—416no—
565C2×C4×C7—41no—
566C2×C4×C7—41no—
567C2×C4×C7—41no—
568C2×C4×C7—41no—
569C2×C4×C7—41no—
570C2×C4×C7—41no—
571C2×C4×C7—41no—
572C2×C4×C7—41no—
573C2×C4×C7—41no—
574C2×C4×C7—41no—
575C2×C4×C7—41no—
576C2×C4×C7—41no—
577C2×C4×C7—41no—
578C2×C4×C7—41no—
579C2×C4×C7—41no—
580C2×C4×C7—41no—
581C2×C4×C7—41no—
582C2×C4×C7—41no—
583C2×C4×C7—41no—
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×C7C4×D414yes—
612C2×C4×C7C4×D414yes—
613C25C23×C711yescharacteristic
614C25C23×C711yescharacteristic
615C25C23×C711yescharacteristic
616C22×D4—22no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—22no—
624C22×D4—41no—
625C22×D4—41no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4—41no—
631C22×D4—41no—
632C22×D4—41no—
633C22×D4—41no—
634C22×D4C2×C4×C714yes—
635C22×D4C2×C4×C714yes—
636C22×D4C2×C4×C714yescomplemented
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—22no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4—41no—
644C23×C4C23×C711yescharacteristic
645C23×C4C23×C711yescharacteristic
646C23×C4C23×C711yescharacteristic
647C23×C4C23×C711yescharacteristic
648C23×C4C23×C711yescharacteristic
649C23×C4C23×C711yescharacteristic
650C23×C4C23×C711yescharacteristic
651C23×C4C23×C711yescharacteristic
652C23×C4C23×C711yescharacteristic
653C23×C4C23×C711yescharacteristic
654C23×C4C23×C711yescharacteristic
655C23×C4C23×C711yescharacteristic
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4C7×D414yescomplemented
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4C2×C4×C714yes—
704C2×C22⋊C4C2×C4×C714yescomplemented
705C2×C22⋊C4C2×C4×C714yescomplemented
706C2×C22⋊C4C7×D414yescomplemented
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42—41no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95C2×C4×C714yescomplemented
724#95C7×D414yescomplemented
725C22×C7—24no—
726C22×C7—24no—
727C22×C7—24no—
728C22×C7—42no—
729C22×C7—42no—
730C22×C7—42no—
731C22×C7—42no—
732C22×C7—42no—
733C22×C7—42no—
734C22×C7—42no—
735C22×C7—42no—
736C22×C7—42no—
737C22×C7—42no—
738C22×C7—42no—
739C22×C7—42no—
740C22×C7—42no—
741C22×C7—42no—
742C22×C7—42no—
743C22×C7—42no—
744C22×C7—42no—
745C22×C7—42no—
746C22×C7—42no—
747C22×C7—42no—
748C22×C7—42no—
749C22×C7—42no—
750C22×C7—42no—
751C22×C7—42no—
752C22×C7—42no—
753C22×C7—42no—
754C22×C7—81no—
755C22×C7—81no—
756C22×C7—81no—
757C22×C7—81no—
758C22×C7—81no—
759C22×C7—81no—
760C22×C7—81no—
761C22×C7—81no—
762C22×C7—81no—
763C22×C7—81no—
764C22×C7—81no—
765C22×C7—81no—
766C22×C7—81no—
767C22×C7—81no—
768C22×C7—81no—
769C22×C7—81no—
770C22×C7C2×C4×D411yescharacteristic
771C22×C7C2×C4×D411yescharacteristic
772C22×C7C2×C4×D411yescharacteristic
773C22×C7#51811yescharacteristic
774C22×C7#51811yescharacteristic
775C22×C7#51811yescharacteristic
776C22×C7#52011yescharacteristic
777C22×C7#53411yescharacteristic
778C22×C7#53411yescharacteristic
779C22×C7#53511yescharacteristic
780C22×C7#53511yescharacteristic
781C22×C7#53511yescharacteristic
782C22×C7#53711yescharacteristic
783C22×C7#53811yescharacteristic
784C22×C7#53811yescharacteristic
785C22×C7#53811yescharacteristic
786C22×C7#53811yescharacteristic
787C22×C7#54011yescharacteristic
788C22×C7#54211yescharacteristic
789C22×C7D4211yescharacteristic
790C22×C7D4211yescharacteristic
791C22×C7D4211yescharacteristic
792C22×C7#54611yescharacteristic
793C22×C7#54611yescharacteristic
794C22×C7#54711yescharacteristic
795C22×C7#54811yescharacteristic
796C22×C7#55011yescharacteristic
797C22×C7#55011yescharacteristic
798C22×C7#55111yescharacteristic
799C22×C7#55311yescharacteristic
800C22×C7#55911yescharacteristic
801C22×C7#56011yescharacteristic
802C22×C7#56011yescharacteristic
803C22×C7#56211yescharacteristic
804C22×C7#56211yescharacteristic
805C4×C7—24no—
806C4×C7—24no—
807C4×C7—42no—
808C4×C7—42no—
809C4×C7—42no—
810C4×C7—42no—
811C4×C7—42no—
812C4×C7—42no—
813C4×C7—42no—
814C4×C7—42no—
815C4×C7—81no—
816C4×C7—81no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
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—
857C24C22×C4×C712yes—
858C24C22×C4×C712yes—
859C24C22×C4×C712yes—
860C24C2×C7×D412yes—
861C24C7×#4112yes—
862C24C24×C711yescharacteristic
863C2×D4—28no—
864C2×D4—28no—
865C2×D4—28no—
866C2×D4—28no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
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—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—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4C22×C4×C712yes—
962C22×C4C22×C4×C712yes—
963C22×C4C22×C4×C712yes—
964C22×C4C22×C4×C712yes—
965C22×C4C2×C7×D412yes—
966C22×C4C2×C7×D412yes—
967C22×C4C2×C7×D412yes—
968C22×C4C2×C7×D412yes—
969C22×C4C2×C7×D412yes—
970C22×C4C2×C7×D412yes—
971C22×C4C2×C7×D412yes—
972C22×C4C2×C7×D412yes—
973C22×C4C7×#4112yes—
974C22×C4C7×#4112yes—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—44no—
981C22⋊C4—44no—
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—
992C42—44no—
993C42—44no—
994C2×C7—44no—
995C2×C7—82no—
996C2×C7—82no—
997C2×C7#232111yescharacteristic
998C2×C7#232111yescharacteristic
999C2×C7#232411yescharacteristic
1000C2×C7#235811yescharacteristic
1001C2×C7#236111yescharacteristic
1002C2×C7#236611yescharacteristic
1003C2×C7#237711yescharacteristic
1004C2×C7#266911yescharacteristic
1005C2×C7#267311yescharacteristic
1006C2×C7#267611yescharacteristic
1007C2×C7#268211yescharacteristic
1008C2×C7#271011yescharacteristic
1009C2×C7#271411yescharacteristic
1010C2×C7#273011yescharacteristic
1011C2×C7#279711yescharacteristic
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
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—
1116C23C4×C7×D414yes—
1117C23C23×C4×C711yescharacteristic
1118C23C22×C7×D411yescharacteristic
1119C23C22×C7×D411yescharacteristic
1120C23C22×C7×D411yescharacteristic
1121C23C2×C7×#4111yescharacteristic
1122C23C2×C7×#4111yescharacteristic
1123C23C2×C7×#4111yescharacteristic
1124C23C7×H(5,𝔽2)11yescharacteristic
1125C23C7×H(5,𝔽2)11yescharacteristic
1126C23C7×H(5,𝔽2)11yescharacteristic
1127C23C7×H(5,𝔽2)11yescharacteristic
1128C23C7×H(5,𝔽2)11yescharacteristic
1129C23C7×H(5,𝔽2)11yescharacteristic
1130C23C7×H(5,𝔽2)11yescharacteristic
1131C23C7×2−1+411yescharacteristic
1132D4—416no—
1133D4—416no—
1134D4—416no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
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—416no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
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×C4C4×C7×D414yes—
1219C2×C4C4×C7×D414yes—
1220C7#1453411yescharacteristic, direct product factor, Sylow
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22C2×C4×C7×D411yescharacteristic
1267C22C2×C4×C7×D411yescharacteristic
1268C22C2×C4×C7×D411yescharacteristic
1269C22C7×#51811yescharacteristic
1270C22C7×#51811yescharacteristic
1271C22C7×#51811yescharacteristic
1272C22C7×#52011yescharacteristic
1273C22C7×#53411yescharacteristic
1274C22C7×#53411yescharacteristic
1275C22C7×#53511yescharacteristic
1276C22C7×#53511yescharacteristic
1277C22C7×#53511yescharacteristic
1278C22C7×#53711yescharacteristic
1279C22C7×#53811yescharacteristic
1280C22C7×#53811yescharacteristic
1281C22C7×#53811yescharacteristic
1282C22C7×#53811yescharacteristic
1283C22C7×#54011yescharacteristic
1284C22C7×#54211yescharacteristic
1285C22C7×D4211yescharacteristic
1286C22C7×D4211yescharacteristic
1287C22C7×D4211yescharacteristic
1288C22C7×#54611yescharacteristic
1289C22C7×#54611yescharacteristic
1290C22C7×#54711yescharacteristic
1291C22C7×#54811yescharacteristic
1292C22C7×#55011yescharacteristic
1293C22C7×#55011yescharacteristic
1294C22C7×#55111yescharacteristic
1295C22C7×#55311yescharacteristic
1296C22C7×#55911yescharacteristic
1297C22C7×#56011yescharacteristic
1298C22C7×#56011yescharacteristic
1299C22C7×#56211yescharacteristic
1300C22C7×#56211yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C2—44no—
1314C2—82no—
1315C2—82no—
1316C2C7×#232111yescharacteristic
1317C2C7×#232111yescharacteristic
1318C2C7×#232411yescharacteristic
1319C2C7×#235811yescharacteristic
1320C2C7×#236111yescharacteristic
1321C2C7×#236611yescharacteristic
1322C2C7×#237711yescharacteristic
1323C2C7×#266911yescharacteristic
1324C2C7×#267311yescharacteristic
1325C2C7×#267611yescharacteristic
1326C2C7×#268211yescharacteristic
1327C2C7×#271011yescharacteristic
1328C2C7×#271411yescharacteristic
1329C2C7×#273011yescharacteristic
1330C2C7×#279711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC2×C7×#392C2
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×#390C2semidirect
4. C2×C7×#388C2semidirect
5. C2×C7×#386C2semidirect
6. C2×C7×#386C2semidirect
7. C2×C7×#385C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
11. C7×#1438C2semidirect
12. C7×#1438C2semidirect
13. C7×#1437C2semidirect
14. C7×#1436C2semidirect
15. C7×#1436C2semidirect
39. C7×#392C4semidirect
58. #14534C7direct (N × H)
82. C22×C7×D4C2×C4semidirect
110. C2×C7×C4⋊C4D4semidirect
150. C2×C7×C22⋊C4C2×C4semidirect
151. C2×C7×C22⋊C4C2×C4semidirect
152. C2×C7×C22⋊C4D4semidirect
169. C7×#95C2×C4semidirect
170. C7×#95D4semidirect
172. C2×#390C2×C7semidirect
173. C2×#390C2×C7semidirect
174. C2×#388C2×C7semidirect
175. C2×#386C2×C7semidirect
176. C2×#386C2×C7semidirect
177. C2×#385C2×C7semidirect
178. #1440C2×C7semidirect
179. #1439C2×C7semidirect
180. #1439C2×C7semidirect
181. #1438C2×C7semidirect
182. #1438C2×C7semidirect
183. #1437C2×C7semidirect
184. #1436C2×C7semidirect
185. #1436C2×C7semidirect
386. #392C4×C7semidirect
636. C22×D4C2×C4×C7semidirect
664. C2×C4⋊C4C7×D4semidirect
704. C2×C22⋊C4C2×C4×C7semidirect
705. C2×C22⋊C4C2×C4×C7semidirect
706. C2×C22⋊C4C7×D4semidirect
723. #95C2×C4×C7semidirect
724. #95C7×D4semidirect
1220. C7#14534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3922
C2×C7×#3902
C2×C7×#3882
C2×C7×#3862
C2×C7×#3852
C7×#14402
C7×#14392
C7×#14382
C7×#14372
C7×#14362
#145347