Finite Group Databasebeta

← #13280286

Subgroups — #13280286

Order 1792.

1522 conjugacy classes of subgroups.

The subgroup lattice has 994 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#11729323C211yesmaximal, characteristic, complemented
6#11729319C211yesmaximal, characteristic, complemented
7#11729318C211yesmaximal, characteristic, complemented
8#11729302C211yesmaximal, characteristic
9#11729302C211yesmaximal, characteristic
10#11729300C211yesmaximal, characteristic
11#11729300C211yesmaximal, characteristic
12#11727170C211yesmaximal, characteristic, complemented
13#11727166C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, 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
29C7×#385C418yescomplemented
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C4×C22⋊Dic7—24no—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
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#14269—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—41no—
98C2×C22⋊Dic7—41no—
99C2×C22⋊Dic7—41no—
100C2×C22⋊Dic7—41no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—22no—
103C2×C4⋊Dic7—41no—
104C2×C4⋊Dic7—41no—
105C2×C4⋊Dic7—41no—
106C2×C4⋊Dic7—41no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—41no—
109C2×C4×Dic7—41no—
110C2×C4×Dic7—41no—
111C2×C4×Dic7—41no—
112C2×C4×Dic7D414yes—
113C7×#95C2×C414yes—
114C7×#95C2×C414yes—
115C7⋊#95—22no—
116C7⋊#95—22no—
117C7⋊#95—22no—
118C7⋊#95—22no—
119C7⋊#95—22no—
120C7⋊#95—22no—
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—41no—
126C7⋊#95—41no—
127C7⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95—41no—
134C7⋊#95—41no—
135C2×#387—71no—
136C2×#385D711yescharacteristic
137C2×C4×C22⋊C4—71no—
138#1445—71no—
139#1443—71no—
140#1442—71no—
141#1441—71no—
142#1440—71no—
143#1440—71no—
144#1439—71no—
145#1439—71no—
146#1436—71no—
147#1436—71no—
148#1434—71no—
149C22⋊#95—71no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
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×C7C22×C412yes—
163C24×C7#4112yes—
164C24×C7#4112yes—
165C24×C7C2411yescharacteristic
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
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—28no—
201C22×C4×C7—44no—
202C22×C4×C7—44no—
203C22×C4×C7—44no—
204C22×C4×C7—44no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7C22×C412yes—
208C22×C4×C7C22×C412yes—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7#4112yes—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
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×Dic7#4112yes—
270C22×Dic7#4112yes—
271C7×C4⋊C4—28no—
272C7×C4⋊C4—44no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—44no—
275C22⋊Dic7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—44no—
278C22⋊Dic7—44no—
279C4⋊Dic7—44no—
280C4⋊Dic7—44no—
281C4×Dic7—44no—
282C4×Dic7—44no—
283C24×C4C2×D711yescharacteristic
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4C2×D711yescharacteristic
287C22×C4⋊C4C2×D711yescharacteristic
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4C2×D711yescharacteristic
293C22×C22⋊C4C2×D711yescharacteristic
294C22×C42—71no—
295C22×C42—71no—
296#387—144no—
297#385Dic718yescomplemented
298C4×C22⋊C4—144no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
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×#95C2×D711yescharacteristic
320C2×#95C2×D711yescharacteristic
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
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—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
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#11714yes—
356C23×C7C23×C411yescharacteristic
357C23×C7C22×D411yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7C2×#4111yescharacteristic
363C23×C7H(5,𝔽2)11yescharacteristic
364C23×C7H(5,𝔽2)11yescharacteristic
365C23×C7H(5,𝔽2)11yescharacteristic
366C23×C7H(5,𝔽2)11yescharacteristic
367C23×C7H(5,𝔽2)11yescharacteristic
368C23×C72−1+411yescharacteristic
369C23×C72−1+411yescharacteristic
370C23×C72−1+411yescharacteristic
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
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—416no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
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×C7C4×D414yes—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—41no—
427C2×Dic7—41no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—41no—
440C2×Dic7—41no—
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—
470C25C22×D711yescharacteristic
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—41no—
474C23×C4—41no—
475C23×C4—41no—
476C23×C4—41no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4C2×Dic714yes—
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C23×C4C22×D711yescharacteristic
489C23×C4C22×D711yescharacteristic
490C23×C4C22×D711yescharacteristic
491C23×C4C22×D711yescharacteristic
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—142no—
497C2×C4⋊C4—142no—
498C2×C4⋊C4—281no—
499C2×C4⋊C4—281no—
500C2×C4⋊C4—281no—
501C2×C4⋊C4—281no—
502C2×C4⋊C4C2×Dic714yes—
503C2×C4⋊C4C2×Dic714yes—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—142no—
509C2×C22⋊C4—142no—
510C2×C22⋊C4—142no—
511C2×C22⋊C4—142no—
512C2×C22⋊C4—142no—
513C2×C22⋊C4—142no—
514C2×C22⋊C4—142no—
515C2×C22⋊C4—142no—
516C2×C22⋊C4—281no—
517C2×C22⋊C4—281no—
518C2×C22⋊C4—281no—
519C2×C22⋊C4—281no—
520C2×C22⋊C4C2×Dic714yes—
521C2×C22⋊C4C2×Dic714yes—
522C2×C42—74no—
523C2×C42—142no—
524C2×C42—281no—
525C2×C42—281no—
526C2×C42—281no—
527C2×C42—281no—
528#95—142no—
529#95—142no—
530#95—142no—
531#95—142no—
532#95—142no—
533#95—142no—
534#95—142no—
535#95—142no—
536#95—142no—
537#95—142no—
538#95—281no—
539#95—281no—
540#95—281no—
541#95—281no—
542#95—281no—
543#95—281no—
544#95—281no—
545#95—281no—
546#95—281no—
547#95—281no—
548#95C2×Dic714yes—
549#95C2×Dic714yes—
550C22×C7—24no—
551C22×C7—24no—
552C22×C7—24no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7C2×#11711yescharacteristic
566C22×C7C2×C4×D411yescharacteristic
567C22×C7C4×#4111yescharacteristic
568C22×C7#51811yescharacteristic
569C22×C7#51811yescharacteristic
570C22×C7#51911yescharacteristic
571C22×C7#52011yescharacteristic
572C22×C7#52511yescharacteristic
573C22×C7#52511yescharacteristic
574C22×C7#52911yescharacteristic
575C22×C7#52911yescharacteristic
576C22×C7#53411yescharacteristic
577C22×C7#53511yescharacteristic
578C22×C7#53611yescharacteristic
579C22×C7#53711yescharacteristic
580C22×C7#53811yescharacteristic
581C22×C7#53811yescharacteristic
582C22×C7#53811yescharacteristic
583C22×C7#53811yescharacteristic
584C22×C7#53811yescharacteristic
585C22×C7#53911yescharacteristic
586C22×C7#53911yescharacteristic
587C22×C7#53911yescharacteristic
588C22×C7#53911yescharacteristic
589C22×C7#53911yescharacteristic
590C22×C7#53911yescharacteristic
591C22×C7#53911yescharacteristic
592C22×C7#53911yescharacteristic
593C22×C7#53911yescharacteristic
594C22×C7#54011yescharacteristic
595C22×C7#54111yescharacteristic
596C22×C7#54211yescharacteristic
597C22×C7#54211yescharacteristic
598C22×C7#54211yescharacteristic
599C22×C7#54211yescharacteristic
600C4×C7—24no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7—42no—
606Dic7—42no—
607Dic7—42no—
608Dic7—42no—
609Dic7—42no—
610Dic7—81no—
611Dic7—81no—
612Dic7—81no—
613Dic7—81no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24#115712yes—
627C24#115712yes—
628C24C22×Dic712yes—
629C24C23×D711yescharacteristic
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
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—28no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
678C22×C4—141no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4—141no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—141no—
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×C4D4×D712yes—
728C22×C4#115912yes—
729C22×C4C22×Dic712yes—
730C22×C4C22×Dic712yes—
731C22×C4C22×Dic712yes—
732C22×C4C22×Dic712yes—
733C22×C4C22×Dic712yes—
734C22×C4C22×Dic712yes—
735C4⋊C4—28no—
736C4⋊C4—44no—
737C4⋊C4—284no—
738C4⋊C4—284no—
739C22⋊C4—28no—
740C22⋊C4—44no—
741C22⋊C4—148no—
742C22⋊C4—148no—
743C22⋊C4—284no—
744C22⋊C4—284no—
745C42—284no—
746C42—284no—
747C2×C7—44no—
748C2×C7#229011yescharacteristic
749C2×C7#231311yescharacteristic
750C2×C7#231811yescharacteristic
751C2×C7#232111yescharacteristic
752C2×C7#232311yescharacteristic
753C2×C7#233211yescharacteristic
754C2×C7#233511yescharacteristic
755C2×C7#263011yescharacteristic
756C2×C7#263311yescharacteristic
757C2×C7#263611yescharacteristic
758C2×C7#263811yescharacteristic
759C2×C7#264911yescharacteristic
760C2×C7#265211yescharacteristic
761C2×C7#265211yescharacteristic
762C2×C7#265311yescharacteristic
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23#648914yes—
798C23C2×#115711yescharacteristic
799C23C2×#115711yescharacteristic
800C23C2×D4×D711yescharacteristic
801C23C2×#115911yescharacteristic
802C23#654811yescharacteristic
803C23#654811yescharacteristic
804C23#654811yescharacteristic
805C23#654811yescharacteristic
806C23#655111yescharacteristic
807C23#655111yescharacteristic
808C23D7×#4111yescharacteristic
809C23D7×#4111yescharacteristic
810C23#655311yescharacteristic
811C23#655411yescharacteristic
812C23C23×Dic711yescharacteristic
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
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—416no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—142no—
856C2×C4—142no—
857C2×C4—142no—
858C2×C4—142no—
859C2×C4—142no—
860C2×C4—142no—
861C2×C4—142no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—142no—
865C2×C4—142no—
866C2×C4—142no—
867C2×C4—281no—
868C2×C4—281no—
869C2×C4—281no—
870C2×C4—281no—
871C2×C4—281no—
872C2×C4—281no—
873C2×C4—281no—
874C2×C4—281no—
875C2×C4—281no—
876C2×C4—281no—
877C2×C4—281no—
878C2×C4—281no—
879C2×C4—281no—
880C2×C4—281no—
881C2×C4—281no—
882C2×C4—281no—
883C2×C4—281no—
884C2×C4—281no—
885C2×C4—281no—
886C2×C4—281no—
887C2×C4—281no—
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×C4D4×Dic714yes—
912C7#1426911yescharacteristic, complemented, Sylow
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22#9020611yescharacteristic
929C22#9020611yescharacteristic
930C22#9020611yescharacteristic
931C22#9020611yescharacteristic
932C22#9022911yescharacteristic
933C22#9022911yescharacteristic
934C22#9023811yescharacteristic
935C22#9023811yescharacteristic
936C22#9025111yescharacteristic
937C22#9025111yescharacteristic
938C22#9025511yescharacteristic
939C22#9025511yescharacteristic
940C22#9028011yescharacteristic
941C22#9028311yescharacteristic
942C22#9028411yescharacteristic
943C22#9028411yescharacteristic
944C22#9031611yescharacteristic
945C22#9031911yescharacteristic
946C22#9032011yescharacteristic
947C22#9032911yescharacteristic
948C22#9032911yescharacteristic
949C22#9033111yescharacteristic
950C22#9033111yescharacteristic
951C22#9033411yescharacteristic
952C22#9034811yescharacteristic
953C22#9035111yescharacteristic
954C22#9035311yescharacteristic
955C22#9035411yescharacteristic
956C22C2×#648911yescharacteristic
957C22C2×D4×Dic711yescharacteristic
958C22#9048911yescharacteristic
959C22#9048911yescharacteristic
960C22#9050311yescharacteristic
961C22#41×Dic711yescharacteristic
962C22#9051811yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—282no—
970C4—282no—
971C4—282no—
972C4—282no—
973C4—561no—
974C4—561no—
975C4—561no—
976C4—561no—
977C2—44no—
978C2#1173194811yescharacteristic
979C2#1173195011yescharacteristic
980C2#1173195111yescharacteristic
981C2#1173195211yescharacteristic
982C2#1173206711yescharacteristic
983C2#1173206811yescharacteristic
984C2#1173206911yescharacteristic
985C2#1173207111yescharacteristic
986C2#1173960011yescharacteristic
987C2#1173976311yescharacteristic
988C2#1173976911yescharacteristic
989C2#1174002311yescharacteristic
990C2#1174018911yescharacteristic
991C2#1174019111yescharacteristic
992C2#1174028211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#385C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7#14269
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. #11729323C2semidirect
6. #11729319C2semidirect
7. #11729318C2semidirect
12. #11727170C2semidirect
13. #11727166C2semidirect
14. #11727161C2semidirect
15. #11727155C2semidirect
29. C7×#385C4semidirect
297. #385Dic7semidirect
912. C7#14269semidirect

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
#117293232
#117293192
#117293182
#117293022
#117293002
#117271702
#117271662
#117271612
#117271552
#142697