Finite Group Databasebeta

← #13283907

Subgroups — #13283907

Order 1792.

1498 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×#89725C211yesmaximal, characteristic
2C2×#89717C211yesmaximal, characteristic
3C2×#89716C211yesmaximal, characteristic
4C7×#1439C211yesmaximal, characteristic
5#11729322C211yesmaximal, characteristic, complemented
6#11729318C211yesmaximal, characteristic, complemented
7#11729298C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11727171C211yesmaximal, characteristic, complemented
11#11727171C211yesmaximal, characteristic, complemented
12#11727165C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727157C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
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
51#89725C418yescomplemented
52#89717—24no—
53#89716—24no—
54#14576—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—41no—
79C2×C7×C4⋊C4—41no—
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⋊C4—41no—
87C2×C7×C22⋊C4—41no—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—41no—
94C2×C22⋊Dic7—41no—
95C2×C22⋊Dic7C2×C414yes—
96C2×C22⋊Dic7C2×C414yes—
97C2×C22⋊Dic7D414yes—
98C2×C4⋊Dic7—41no—
99C2×C4⋊Dic7—41no—
100C2×C4⋊Dic7C2×C414yescomplemented
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—41no—
105C2×Dic7⋊C4—41no—
106C2×Dic7⋊C4—41no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—41no—
111C2×C4×Dic7—41no—
112C2×C4×Dic7—41no—
113C7×#95—22no—
114C7×#95—41no—
115C7×#95—41no—
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—41no—
125C7⋊#95—41no—
126C7⋊#95—41no—
127C7⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95C2×C414yescomplemented
133C7⋊#95C2×C414yescomplemented
134C7⋊#95C2×C414yescomplemented
135C2×#397—71no—
136C2×#388—71no—
137C2×#388—71no—
138#1444—71no—
139#1443—71no—
140#1443—71no—
141#1441—71no—
142#1439D711yescharacteristic
143#1436—71no—
144#1436—71no—
145#1436—71no—
146#1434—71no—
147C22⋊#95—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×C7C2×D412yes—
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—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7C22×C412yes—
205C22×C4×C7C22×C412yes—
206C22×C4×C7#4112yes—
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—44no—
257C22×Dic7—44no—
258C22×Dic7—44no—
259C22×Dic7—44no—
260C22×Dic7—44no—
261C22×Dic7—44no—
262C22×Dic7—44no—
263C22×Dic7C22×C412yes—
264C22×Dic7C22×C412yes—
265C22×Dic7C22×C412yes—
266C22×Dic7C22×C412yes—
267C22×Dic7C2×D412yes—
268C22×Dic7C2×D412yes—
269C22×Dic7#4112yes—
270C22×Dic7#4112yes—
271C7×C4⋊C4—44no—
272C7×C22⋊C4—44no—
273C7×C22⋊C4—44no—
274C7×C22⋊C4—44no—
275C22⋊Dic7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—44no—
278C4⋊Dic7—44no—
279Dic7⋊C4—44no—
280Dic7⋊C4—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×C42—71no—
296#397—78no—
297#388—144no—
298#388—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×#95C2×D711yescharacteristic
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×C7C4×D414yes—
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—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
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×C7—41no—
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—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—416no—
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—41no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—74no—
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⋊C4—281no—
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—41no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—142no—
516C2×C22⋊C4—142no—
517C2×C22⋊C4—142no—
518C2×C22⋊C4—142no—
519C2×C22⋊C4—281no—
520C2×C22⋊C4—281no—
521C2×C22⋊C4C4×D714yes—
522C2×C42—142no—
523C2×C42—142no—
524C2×C42—142no—
525C2×C42—281no—
526C2×C42—281no—
527C2×C42—281no—
528#95—22no—
529#95—41no—
530#95—41no—
531#95—74no—
532#95—74no—
533#95—74no—
534#95—142no—
535#95—142no—
536#95—142no—
537#95—142no—
538#95—142no—
539#95—142no—
540#95—142no—
541#95—142no—
542#95—281no—
543#95—281no—
544#95—281no—
545#95—281no—
546#95—281no—
547#95—281no—
548#95—281no—
549#95—281no—
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×C4×D411yescharacteristic
566C22×C7C4×#4111yescharacteristic
567C22×C7C4×#4111yescharacteristic
568C22×C7#51811yescharacteristic
569C22×C7#52011yescharacteristic
570C22×C7#52011yescharacteristic
571C22×C7#52011yescharacteristic
572C22×C7#53411yescharacteristic
573C22×C7#53711yescharacteristic
574C22×C7#53811yescharacteristic
575C22×C7#53811yescharacteristic
576C22×C7#53811yescharacteristic
577C22×C7#53811yescharacteristic
578C22×C7#53911yescharacteristic
579C22×C7#53911yescharacteristic
580C22×C7#54011yescharacteristic
581C22×C7#54211yescharacteristic
582C22×C7#54211yescharacteristic
583C22×C7#54211yescharacteristic
584C22×C7#54611yescharacteristic
585C22×C7#54611yescharacteristic
586C22×C7#54711yescharacteristic
587C22×C7#54711yescharacteristic
588C22×C7#55111yescharacteristic
589C22×C7#55111yescharacteristic
590C22×C7#55111yescharacteristic
591C22×C7#55211yescharacteristic
592C22×C7#55211yescharacteristic
593C22×C7#55211yescharacteristic
594C22×C7#55311yescharacteristic
595C22×C7#55611yescharacteristic
596C22×C7#56011yescharacteristic
597C22×C7#56311yescharacteristic
598C22×C7#56311yescharacteristic
599C22×C7#56311yescharacteristic
600C4×C7—42no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—81no—
605C4×C7—81no—
606Dic7—42no—
607Dic7—42no—
608Dic7—42no—
609Dic7—42no—
610Dic7—42no—
611Dic7—42no—
612Dic7—42no—
613Dic7—42no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C2×C4×D712yes—
627C24D4×D712yes—
628C24#116112yes—
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—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—72no—
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—284no—
725C22×C4—284no—
726C22×C4—284no—
727C22×C4—284no—
728C22×C4—284no—
729C22×C4—284no—
730C22×C4—284no—
731C22×C4C2×C4×D712yes—
732C22×C4C2×C4×D712yes—
733C22×C4#115912yes—
734C22×C4#115912yes—
735C4⋊C4—44no—
736C4⋊C4—284no—
737C4⋊C4—284no—
738C4⋊C4—284no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—148no—
743C22⋊C4—148no—
744C22⋊C4—284no—
745C42—284no—
746C42—284no—
747C2×C7—44no—
748C2×C7#232511yescharacteristic
749C2×C7#233511yescharacteristic
750C2×C7#233711yescharacteristic
751C2×C7#235911yescharacteristic
752C2×C7#235911yescharacteristic
753C2×C7#237311yescharacteristic
754C2×C7#238311yescharacteristic
755C2×C7#268811yescharacteristic
756C2×C7#269511yescharacteristic
757C2×C7#271511yescharacteristic
758C2×C7#271711yescharacteristic
759C2×C7#273511yescharacteristic
760C2×C7#273811yescharacteristic
761C2×C7#274511yescharacteristic
762C2×C7#276511yescharacteristic
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#645614yes—
798C23C22×C4×D711yescharacteristic
799C23C2×D4×D711yescharacteristic
800C23C2×#115911yescharacteristic
801C23C2×#115911yescharacteristic
802C23#654811yescharacteristic
803C23#654811yescharacteristic
804C23#654811yescharacteristic
805C23#654811yescharacteristic
806C23C2×#116111yescharacteristic
807C23D7×#4111yescharacteristic
808C23D7×#4111yescharacteristic
809C23#655311yescharacteristic
810C23#655411yescharacteristic
811C23#655411yescharacteristic
812C23#655411yescharacteristic
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—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
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—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—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—2816no—
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×C4—281no—
912C7#1457611yescharacteristic, 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#9017711yescharacteristic
929C22C2×#645611yescharacteristic
930C22#9021411yescharacteristic
931C22C4×#115911yescharacteristic
932C22C4×#115911yescharacteristic
933C22#9023711yescharacteristic
934C22#9023711yescharacteristic
935C22#9028211yescharacteristic
936C22#9028211yescharacteristic
937C22#9028411yescharacteristic
938C22#9028811yescharacteristic
939C22#9029311yescharacteristic
940C22#9029411yescharacteristic
941C22#9029611yescharacteristic
942C22#9030411yescharacteristic
943C22#9030411yescharacteristic
944C22#9030911yescharacteristic
945C22#9031111yescharacteristic
946C22#9032811yescharacteristic
947C22#9032811yescharacteristic
948C22#9033311yescharacteristic
949C22#9033311yescharacteristic
950C22#9033511yescharacteristic
951C22#9033611yescharacteristic
952C22#9034111yescharacteristic
953C22#9034211yescharacteristic
954C22#9034611yescharacteristic
955C22#9034611yescharacteristic
956C22#9035311yescharacteristic
957C22#9036011yescharacteristic
958C22#9036211yescharacteristic
959C22#9036311yescharacteristic
960C22#9039611yescharacteristic
961C22#9040311yescharacteristic
962C22#9041011yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—282no—
970C4—282no—
971C4—282no—
972C4—282no—
973C4—282no—
974C4—282no—
975C4—282no—
976C4—282no—
977C2—44no—
978C2#1173131811yescharacteristic
979C2#1173184011yescharacteristic
980C2#1173184011yescharacteristic
981C2#1173211611yescharacteristic
982C2#1173293111yescharacteristic
983C2#1173293911yescharacteristic
984C2#1173374511yescharacteristic
985C2#1173421811yescharacteristic
986C2#1173428211yescharacteristic
987C2#1173446111yescharacteristic
988C2#1173448311yescharacteristic
989C2#1173482711yescharacteristic
990C2#1173488711yescharacteristic
991C2#1173514711yescharacteristic
992C2#1173551911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1439C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1439D7
hypocenterC7#14576
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
5. #11729322C2semidirect
6. #11729318C2semidirect
10. #11727171C2semidirect
11. #11727171C2semidirect
12. #11727165C2semidirect
13. #11727161C2semidirect
14. #11727160C2semidirect
15. #11727157C2semidirect
51. #89725C4semidirect
100. C2×C4⋊Dic7C2×C4semidirect
132. C7⋊#95C2×C4semidirect
133. C7⋊#95C2×C4semidirect
134. C7⋊#95C2×C4semidirect
912. C7#14576semidirect

Maximal subgroups

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

subgroupindex
C2×#897252
C2×#897172
C2×#897162
C7×#14392
#117293222
#117293182
#117292982
#117271712
#117271652
#117271612
#117271602
#117271572
#145767