Finite Group Databasebeta

← #13277936

Subgroups — #13277936

Order 1792.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#385C211yesmaximal, characteristic
2C2×C4×C22⋊Dic7C211yesmaximal, characteristic
3C2×#89753C211yesmaximal, characteristic, complemented
4#11729881C211yesmaximal, characteristic
5#11729319C211yesmaximal, characteristic, complemented
6#11729318C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729300C211yesmaximal, characteristic
9#11729300C211yesmaximal, characteristic
10#11729299C211yesmaximal, characteristic
11#11729299C211yesmaximal, characteristic
12#11727170C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14#11727155C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C7×#385C418yescomplemented
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C4×C22⋊Dic7—24no—
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89753—24no—
54#14075—71nomaximal, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—41no—
59C23×C4×C7—41no—
60C23×C4×C7—41no—
61C23×C4×C7—41no—
62C23×C4×C7C2×C414yes—
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—41no—
80C2×C7×C4⋊C4—41no—
81C2×C7×C4⋊C4C2×C414yes—
82C2×C7×C4⋊C4C2×C414yes—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4—41no—
87C2×C7×C22⋊C4C2×C414yes—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—41no—
99C2×C22⋊Dic7—41no—
100C2×C22⋊Dic7Q814yes—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—22no—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—41no—
105C2×C4⋊Dic7—41no—
106C2×C4⋊Dic7—41no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—41no—
113C2×C4×Dic7—41no—
114C2×C4×Dic7—41no—
115C2×C4×Dic7—41no—
116C2×C4×Dic7—41no—
117C2×C4×Dic7—41no—
118C2×C4×Dic7D414yes—
119C7×#95C2×C414yes—
120C7×#95C2×C414yes—
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C2×#387—71no—
140C2×#385D711yescharacteristic
141C2×C4×C22⋊C4—71no—
142#1443—71no—
143#1441—71no—
144#1439—71no—
145#1439—71no—
146#1437—71no—
147#1437—71no—
148#1436—71no—
149#1436—71no—
150C4⋊#95—71no—
151#1434—71no—
152C22⋊#95—71no—
153C4×#95—71no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7C22×C412yes—
167C24×C7C2×Q812yes—
168C24×C7#4112yes—
169C24×C7C2411yescharacteristic
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—28no—
203C22×C4×C7—44no—
204C22×C4×C7—44no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7#4112yes—
217C22×C4×C7#4112yes—
218C22×C4×C7#4112yes—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7C2×D412yes—
268C22×Dic7C2×D412yes—
269C22×Dic7C2×Q812yes—
270C22×Dic7C2×Q812yes—
271C22×Dic7#4112yes—
272C22×Dic7#4112yes—
273C22×Dic7#4112yes—
274C22×Dic7#4112yes—
275C7×C4⋊C4—28no—
276C7×C4⋊C4—44no—
277C7×C22⋊C4—28no—
278C7×C22⋊C4—44no—
279C22⋊Dic7—28no—
280C22⋊Dic7—28no—
281C22⋊Dic7—44no—
282C22⋊Dic7—44no—
283C4⋊Dic7—44no—
284C4⋊Dic7—44no—
285C4×Dic7—44no—
286C4×Dic7—44no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C24×C4C2×D711yescharacteristic
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4C2×D711yescharacteristic
293C22×C4⋊C4C2×D711yescharacteristic
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C42—71no—
301C22×C42—71no—
302C22×C42—71no—
303C22×C42—71no—
304#387—144no—
305#385Dic718yescomplemented
306C4×C22⋊C4—144no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7C4×Q814yes—
362C23×C7C23×C411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C22×Q811yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7H(5,𝔽2)11yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C7H(5,𝔽2)11yescharacteristic
376C23×C7H(5,𝔽2)11yescharacteristic
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—416no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7#11714yes—
419C2×C4×C7C4×D414yes—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—41no—
445C2×Dic7—41no—
446C2×Dic7—41no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—41no—
450C2×Dic7—41no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7C22⋊Q814yes—
476C25C22×D711yescharacteristic
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—41no—
480C23×C4—41no—
481C23×C4—41no—
482C23×C4—41no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4C2×Dic714yes—
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—142no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—281no—
506C2×C4⋊C4—281no—
507C2×C4⋊C4—281no—
508C2×C4⋊C4C2×Dic714yes—
509C2×C4⋊C4C2×Dic714yes—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—142no—
516C2×C22⋊C4—142no—
517C2×C22⋊C4—142no—
518C2×C22⋊C4—142no—
519C2×C22⋊C4—142no—
520C2×C22⋊C4—142no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—142no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—281no—
525C2×C22⋊C4—281no—
526C2×C22⋊C4C2×Dic714yes—
527C2×C22⋊C4C2×Dic714yes—
528C2×C42—74no—
529C2×C42—142no—
530C2×C42—142no—
531C2×C42—142no—
532C2×C42—142no—
533C2×C42—142no—
534C2×C42—281no—
535C2×C42—281no—
536C2×C42—281no—
537C2×C42—281no—
538C2×C42—281no—
539C2×C42—281no—
540#95—142no—
541#95—142no—
542#95—142no—
543#95—142no—
544#95—142no—
545#95—142no—
546#95—142no—
547#95—142no—
548#95—142no—
549#95—142no—
550#95—142no—
551#95—142no—
552#95—142no—
553#95—281no—
554#95—281no—
555#95—281no—
556#95—281no—
557#95—281no—
558#95C2×Dic714yes—
559#95C2×Dic714yes—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—24no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7C2×#11711yescharacteristic
576C22×C7C2×C4×D411yescharacteristic
577C22×C7C2×C4×Q811yescharacteristic
578C22×C7C4×#4111yescharacteristic
579C22×C7C4×#4111yescharacteristic
580C22×C7#51811yescharacteristic
581C22×C7#51811yescharacteristic
582C22×C7C2×C22⋊Q811yescharacteristic
583C22×C7#52511yescharacteristic
584C22×C7#52911yescharacteristic
585C22×C7#52911yescharacteristic
586C22×C7#52911yescharacteristic
587C22×C7#53211yescharacteristic
588C22×C7#53211yescharacteristic
589C22×C7#53311yescharacteristic
590C22×C7#53411yescharacteristic
591C22×C7#53511yescharacteristic
592C22×C7#53811yescharacteristic
593C22×C7#53811yescharacteristic
594C22×C7#55111yescharacteristic
595C22×C7#55111yescharacteristic
596C22×C7#55111yescharacteristic
597C22×C7#55111yescharacteristic
598C22×C7#55111yescharacteristic
599C22×C7#55311yescharacteristic
600C22×C7#55311yescharacteristic
601C22×C7#55311yescharacteristic
602C22×C7#55311yescharacteristic
603C22×C7#55311yescharacteristic
604C22×C7#55311yescharacteristic
605C22×C7#55411yescharacteristic
606C22×C7#55411yescharacteristic
607C22×C7#55411yescharacteristic
608C22×C7#55411yescharacteristic
609C22×C7#55911yescharacteristic
610C4×C7—24no—
611C4×C7—24no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7—42no—
615C4×C7—42no—
616Dic7—24no—
617Dic7—42no—
618Dic7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—81no—
623Dic7—81no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24Q8×D712yes—
637C24#116112yes—
638C24C22×Dic712yes—
639C24C23×D711yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—28no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—72no—
680C22×C4—72no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4#115712yes—
736C22×C4#115712yes—
737C22×C4D4×D712yes—
738C22×C4#115912yes—
739C22×C4C22×Dic712yes—
740C22×C4C22×Dic712yes—
741C22×C4C22×Dic712yes—
742C22×C4C22×Dic712yes—
743C22×C4C22×Dic712yes—
744C22×C4C22×Dic712yes—
745C4⋊C4—28no—
746C4⋊C4—44no—
747C4⋊C4—284no—
748C4⋊C4—284no—
749C22⋊C4—28no—
750C22⋊C4—44no—
751C22⋊C4—148no—
752C22⋊C4—148no—
753C22⋊C4—284no—
754C22⋊C4—284no—
755C42—284no—
756C42—284no—
757C42—284no—
758C42—284no—
759C2×C7—44no—
760C2×C7#229311yescharacteristic
761C2×C7C4×C22⋊Q811yescharacteristic
762C2×C7#232111yescharacteristic
763C2×C7#234511yescharacteristic
764C2×C7#235311yescharacteristic
765C2×C7#236811yescharacteristic
766C2×C7#237411yescharacteristic
767C2×C7#256411yescharacteristic
768C2×C7#256611yescharacteristic
769C2×C7#257611yescharacteristic
770C2×C7#257811yescharacteristic
771C2×C7#258711yescharacteristic
772C2×C7#258911yescharacteristic
773C2×C7#260211yescharacteristic
774C2×C7#260311yescharacteristic
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23Q8×Dic714yes—
810C23C2×#115711yescharacteristic
811C23C2×#115711yescharacteristic
812C23C2×D4×D711yescharacteristic
813C23C2×#115911yescharacteristic
814C23#654811yescharacteristic
815C23#654811yescharacteristic
816C23#654811yescharacteristic
817C23#654811yescharacteristic
818C23C2×Q8×D711yescharacteristic
819C23C2×#116111yescharacteristic
820C23D7×#4111yescharacteristic
821C23D7×#4111yescharacteristic
822C23D7×#4111yescharacteristic
823C23D7×#4111yescharacteristic
824C23C23×Dic711yescharacteristic
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—416no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—74no—
867C2×C4—142no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—281no—
889C2×C4—281no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—281no—
893C2×C4—281no—
894C2×C4—281no—
895C2×C4—281no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4#648914yes—
923C2×C4D4×Dic714yes—
924C7#1407511yescharacteristic, complemented, Sylow
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22#9020211yescharacteristic
941C22#9020211yescharacteristic
942C22#9020511yescharacteristic
943C22#9020511yescharacteristic
944C22#9023111yescharacteristic
945C22#9023111yescharacteristic
946C22#9023911yescharacteristic
947C22#9023911yescharacteristic
948C22#9024711yescharacteristic
949C22#9024711yescharacteristic
950C22#9024811yescharacteristic
951C22#9024811yescharacteristic
952C22#9028011yescharacteristic
953C22#9028311yescharacteristic
954C22#9028411yescharacteristic
955C22#9028411yescharacteristic
956C22#9031311yescharacteristic
957C22#9031511yescharacteristic
958C22D7×C22⋊Q811yescharacteristic
959C22#9031811yescharacteristic
960C22#9032711yescharacteristic
961C22#9032711yescharacteristic
962C22#9032811yescharacteristic
963C22#9032811yescharacteristic
964C22#9035011yescharacteristic
965C22#9035211yescharacteristic
966C22#9035211yescharacteristic
967C22#9035511yescharacteristic
968C22C2×#648911yescharacteristic
969C22C2×D4×Dic711yescharacteristic
970C22#9048911yescharacteristic
971C22#9048911yescharacteristic
972C22C2×Q8×Dic711yescharacteristic
973C22#41×Dic711yescharacteristic
974C22#41×Dic711yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—144no—
982C4—282no—
983C4—282no—
984C4—282no—
985C4—282no—
986C4—282no—
987C4—561no—
988C4—561no—
989C2—44no—
990C2#1173192211yescharacteristic
991C2#1173192711yescharacteristic
992C2#1173192911yescharacteristic
993C2#1173193611yescharacteristic
994C2#1173193811yescharacteristic
995C2#1173194411yescharacteristic
996C2#1173206011yescharacteristic
997C2#1173206311yescharacteristic
998C2#1173960511yescharacteristic
999C2#1173976411yescharacteristic
1000C2#1173978111yescharacteristic
1001C2#1174002311yescharacteristic
1002C2Dic7×C22⋊Q811yescharacteristic
1003C2#1174019411yescharacteristic
1004C2#1174028411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#385C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7#14075
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×#89753C2semidirect
5. #11729319C2semidirect
6. #11729318C2semidirect
7. #11729317C2semidirect
12. #11727170C2semidirect
13. #11727161C2semidirect
14. #11727155C2semidirect
15. Dic7×#95C2semidirect
31. C7×#385C4semidirect
305. #385Dic7semidirect
924. C7#14075semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3852
C2×C4×C22⋊Dic72
C2×#897532
#117298812
#117293192
#117293182
#117293172
#117293002
#117292992
#117271702
#117271612
#117271552
Dic7×#952
#140757