Finite Group Databasebeta

← #13282122

Subgroups — #13282122

Order 1792.

1506 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×#388C211yesmaximal, characteristic
2C2×#89753C211yesmaximal, characteristic, complemented
3C2×#89722C211yesmaximal, characteristic
4#11729319C211yesmaximal, characteristic, complemented
5#11729302C211yesmaximal, characteristic
6#11729300C211yesmaximal, characteristic
7#11729299C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11729289C211yesmaximal, characteristic, complemented
11#11729288C211yesmaximal, characteristic, complemented
12#11727170C211yesmaximal, characteristic, complemented
13#11727166C211yesmaximal, characteristic, complemented
14#11727166C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C7×#388C418yescomplemented
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7⋊#95C2211yescharacteristic
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
52#89753—24no—
53#89722—24no—
54#14433—71nomaximal, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—22no—
63C23×Dic7—22no—
64C23×Dic7—22no—
65C23×Dic7—41no—
66C23×Dic7—41no—
67C23×Dic7—41no—
68C23×Dic7—41no—
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⋊C4C2×C414yescomplemented
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—41no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4C2×C414yes—
87C2×C7×C22⋊C4C2×C414yes—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C42×C7—41no—
90C2×C42×C7—41no—
91C2×C42×C7C2×C414yescomplemented
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—22no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—41no—
107C2×C4⋊Dic7—41no—
108C2×C4⋊Dic7—41no—
109C2×C4⋊Dic7—41no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—41no—
113C7×#95C2×C414yescomplemented
114C7×#95C2×C414yescomplemented
115C7⋊#95—22no—
116C7⋊#95—22no—
117C7⋊#95—22no—
118C7⋊#95—22no—
119C7⋊#95—22no—
120C7⋊#95—22no—
121C7⋊#95—41no—
122C7⋊#95—41no—
123C7⋊#95—41no—
124C7⋊#95—41no—
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⋊#95D414yes—
135C2×#388D711yescharacteristic
136C2×#387—71no—
137C2×#385—71no—
138#1443—71no—
139#1442—71no—
140#1442—71no—
141#1441—71no—
142#1440—71no—
143#1439—71no—
144#1437—71no—
145C4⋊#95—71no—
146#1434—71no—
147#1434—71no—
148C22⋊#95—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×C7C22×C412yes—
201C22×C4×C7C22×C412yes—
202C22×C4×C7C22×C412yes—
203C22×C4×C7C22×C412yes—
204C22×C4×C7C22×C412yes—
205C22×C4×C7C22×C412yes—
206C22×C4×C7C2×D412yes—
207C22×C4×C7#4112yes—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
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—44no—
261C22×Dic7—44no—
262C22×Dic7—44no—
263C22×Dic7—44no—
264C22×Dic7—44no—
265C22×Dic7—44no—
266C22×Dic7—44no—
267C22×Dic7C2×D412yes—
268C22×Dic7C2×D412yes—
269C22×Dic7#4112yes—
270C22×Dic7#4112yes—
271C7×C4⋊C4—28no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—44no—
275C42×C7—44no—
276C22⋊Dic7—44no—
277C22⋊Dic7—44no—
278C22⋊Dic7—44no—
279C4⋊Dic7—44no—
280C4⋊Dic7—44no—
281C4⋊Dic7—44no—
282C4×Dic7—44no—
283C24×C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4C2×D711yescharacteristic
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4C2×D711yescharacteristic
292C22×C22⋊C4C2×D711yescharacteristic
293C22×C22⋊C4C2×D711yescharacteristic
294C22×C42—71no—
295C22×C42C2×D711yescharacteristic
296#388Dic718yescomplemented
297#387—144no—
298#385—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—41no—
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×C7C4×D414yes—
413C2×Dic7—22no—
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—416no—
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—71no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—142no—
480C23×C4—142no—
481C23×C4—142no—
482C23×C4—281no—
483C23×C4—281no—
484C23×C4—281no—
485C23×C4—281no—
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—142no—
495C2×C4⋊C4—142no—
496C2×C4⋊C4—142no—
497C2×C4⋊C4—142no—
498C2×C4⋊C4—142no—
499C2×C4⋊C4—281no—
500C2×C4⋊C4—281no—
501C2×C4⋊C4—281no—
502C2×C4⋊C4—281no—
503C2×C4⋊C4C2×Dic714yescomplemented
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—142no—
511C2×C22⋊C4—142no—
512C2×C22⋊C4—142no—
513C2×C22⋊C4—142no—
514C2×C22⋊C4—142no—
515C2×C22⋊C4—281no—
516C2×C22⋊C4—281no—
517C2×C22⋊C4—281no—
518C2×C22⋊C4—281no—
519C2×C22⋊C4C2×Dic714yes—
520C2×C22⋊C4C2×Dic714yes—
521C2×C22⋊C4C2×Dic714yes—
522C2×C42—41no—
523C2×C42—41no—
524C2×C42—142no—
525C2×C42—142no—
526C2×C42—281no—
527C2×C42C2×Dic714yescomplemented
528#95—74no—
529#95—142no—
530#95—142no—
531#95—142no—
532#95—142no—
533#95—142no—
534#95—142no—
535#95—281no—
536#95—281no—
537#95—281no—
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×Dic714yescomplemented
549#95C2×Dic714yescomplemented
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#52011yescharacteristic
570C22×C7#52011yescharacteristic
571C22×C7#52011yescharacteristic
572C22×C7#53511yescharacteristic
573C22×C7#53611yescharacteristic
574C22×C7#53811yescharacteristic
575C22×C7#53811yescharacteristic
576C22×C7#53811yescharacteristic
577C22×C7#53911yescharacteristic
578C22×C7#53911yescharacteristic
579C22×C7#53911yescharacteristic
580C22×C7#54111yescharacteristic
581C22×C7#54211yescharacteristic
582C22×C7#54211yescharacteristic
583C22×C7#54211yescharacteristic
584C22×C7#54611yescharacteristic
585C22×C7#54611yescharacteristic
586C22×C7#54611yescharacteristic
587C22×C7#54811yescharacteristic
588C22×C7#55111yescharacteristic
589C22×C7#55111yescharacteristic
590C22×C7#55211yescharacteristic
591C22×C7#55211yescharacteristic
592C22×C7#55211yescharacteristic
593C22×C7#55311yescharacteristic
594C22×C7#55311yescharacteristic
595C22×C7#55311yescharacteristic
596C22×C7#56011yescharacteristic
597C22×C7#56211yescharacteristic
598C22×C7#56211yescharacteristic
599C22×C7#56311yescharacteristic
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—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—141no—
669C22×C4—141no—
670C22×C4—141no—
671C22×C4—141no—
672C22×C4—141no—
673C22×C4—141no—
674C22×C4—141no—
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—284no—
721C22×C4—284no—
722C22×C4—284no—
723C22×C4—284no—
724C22×C4—284no—
725C22×C4—284no—
726C22×C4—284no—
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—284no—
737C4⋊C4—284no—
738C4⋊C4—284no—
739C22⋊C4—28no—
740C22⋊C4—28no—
741C22⋊C4—44no—
742C22⋊C4—284no—
743C22⋊C4—284no—
744C22⋊C4—284no—
745C42—44no—
746C42—284no—
747C2×C7—44no—
748C2×C7#231811yescharacteristic
749C2×C7#232611yescharacteristic
750C2×C7#233411yescharacteristic
751C2×C7#234311yescharacteristic
752C2×C7#235211yescharacteristic
753C2×C7#236411yescharacteristic
754C2×C7#237611yescharacteristic
755C2×C7#268511yescharacteristic
756C2×C7#268711yescharacteristic
757C2×C7#269011yescharacteristic
758C2×C7#269611yescharacteristic
759C2×C7#273911yescharacteristic
760C2×C7#275711yescharacteristic
761C2×C7#276511yescharacteristic
762C2×C7#277911yescharacteristic
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
804C23D7×#4111yescharacteristic
805C23D7×#4111yescharacteristic
806C23#655311yescharacteristic
807C23#655311yescharacteristic
808C23#655311yescharacteristic
809C23#655411yescharacteristic
810C23#655411yescharacteristic
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—41no—
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—142no—
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—2816no—
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#1443311yescharacteristic, 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#9021811yescharacteristic
929C22#9021811yescharacteristic
930C22#9022211yescharacteristic
931C22#9022211yescharacteristic
932C22#9023211yescharacteristic
933C22#9024111yescharacteristic
934C22#9024311yescharacteristic
935C22#9025111yescharacteristic
936C22#9025111yescharacteristic
937C22#9025511yescharacteristic
938C22#9025511yescharacteristic
939C22#9025611yescharacteristic
940C22#9029211yescharacteristic
941C22#9029211yescharacteristic
942C22#9030111yescharacteristic
943C22#9030111yescharacteristic
944C22#9034211yescharacteristic
945C22#9035711yescharacteristic
946C22#9035811yescharacteristic
947C22#9035811yescharacteristic
948C22#9036511yescharacteristic
949C22#9036611yescharacteristic
950C22#9037311yescharacteristic
951C22#9037311yescharacteristic
952C22#9039211yescharacteristic
953C22#9039511yescharacteristic
954C22#9039811yescharacteristic
955C22#9040111yescharacteristic
956C22C2×#648911yescharacteristic
957C22C2×D4×Dic711yescharacteristic
958C22#9048911yescharacteristic
959C22#41×Dic711yescharacteristic
960C22#9051811yescharacteristic
961C22#9051811yescharacteristic
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#1173311811yescharacteristic
979C2#1173312211yescharacteristic
980C2#1173316111yescharacteristic
981C2#1173318811yescharacteristic
982C2#1173319511yescharacteristic
983C2#1173321611yescharacteristic
984C2#1173336411yescharacteristic
985C2#1173336711yescharacteristic
986C2#1173968211yescharacteristic
987C2#1173976911yescharacteristic
988C2#1173978011yescharacteristic
989C2#1174008311yescharacteristic
990C2#1174028511yescharacteristic
991C2#1174039811yescharacteristic
992C2#1174051911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#14433
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#89753C2semidirect
4. #11729319C2semidirect
10. #11729289C2semidirect
11. #11729288C2semidirect
12. #11727170C2semidirect
13. #11727166C2semidirect
14. #11727166C2semidirect
15. #11727155C2semidirect
29. C7×#388C4semidirect
79. C2×C7×C4⋊C4C2×C4semidirect
91. C2×C42×C7C2×C4semidirect
113. C7×#95C2×C4semidirect
114. C7×#95C2×C4semidirect
296. #388Dic7semidirect
503. C2×C4⋊C4C2×Dic7semidirect
527. C2×C42C2×Dic7semidirect
548. #95C2×Dic7semidirect
549. #95C2×Dic7semidirect
912. C7#14433semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×#897532
C2×#897222
#117293192
#117293022
#117293002
#117292992
#117292982
#117292892
#117292882
#117271702
#117271662
#117271552
#144337