Finite Group Databasebeta

← #13282947

Subgroups — #13282947

Order 1792.

1298 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89717C211yesmaximal, characteristic
2C7×#1437C211yesmaximal, characteristic
3#11729303C211yesmaximal, characteristic
4#11729302C211yesmaximal, characteristic
5#11729301C211yesmaximal, characteristic
6#11729301C211yesmaximal, characteristic
7#11729299C211yesmaximal, characteristic
8#11729290C211yesmaximal, characteristic, complemented
9#11729288C211yesmaximal, characteristic, complemented
10#11727175C211yesmaximal, characteristic, complemented
11#11727172C211yesmaximal, characteristic, complemented
12#11727160C211yesmaximal, characteristic, complemented
13#11727160C211yesmaximal, characteristic, complemented
14Dic7⋊#95C211yesmaximal, characteristic, complemented
15#11727156C211yesmaximal, characteristic, complemented
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
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#89717C418yescomplemented
52#14504—71nomaximal, Sylow
53C25×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×Dic7C2311yescharacteristic
61C23×Dic7C2311yescharacteristic
62C23×Dic7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C2×C7×C22⋊C4—22no—
69C2×C7×C22⋊C4—22no—
70C2×C7×C22⋊C4—22no—
71C2×C7×C22⋊C4—41no—
72C2×C7×C22⋊C4—41no—
73C2×C7×C22⋊C4—41no—
74C2×C7×C22⋊C4—41no—
75C2×C7×C22⋊C4—41no—
76C2×C7×C22⋊C4C2×C414yes—
77C2×C42×C7—22no—
78C2×C42×C7—41no—
79C2×C42×C7—41no—
80C2×C22⋊Dic7—22no—
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7—41no—
84C2×C22⋊Dic7—41no—
85C2×C22⋊Dic7—41no—
86C2×C22⋊Dic7—41no—
87C2×C22⋊Dic7—41no—
88C2×C22⋊Dic7—41no—
89C2×C22⋊Dic7—41no—
90C2×C22⋊Dic7C2×C414yes—
91C2×C22⋊Dic7C2×C414yes—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—41no—
97C2×Dic7⋊C4—41no—
98C2×Dic7⋊C4—41no—
99C2×Dic7⋊C4—41no—
100C2×Dic7⋊C4C2×C414yes—
101C2×C4×Dic7—41no—
102C2×C4×Dic7—41no—
103C2×C4×Dic7—41no—
104C2×C4×Dic7—41no—
105C2×C4×Dic7—41no—
106C2×C4×Dic7C2×C414yes—
107C7×#95—41no—
108C7×#95—41no—
109C7×#95—41no—
110C7⋊#95—22no—
111C7⋊#95—22no—
112C7⋊#95—22no—
113C7⋊#95—22no—
114C7⋊#95—22no—
115C7⋊#95—22no—
116C7⋊#95—22no—
117C7⋊#95—41no—
118C7⋊#95—41no—
119C7⋊#95—41no—
120C7⋊#95—41no—
121C7⋊#95—41no—
122C7⋊#95—41no—
123C7⋊#95—41no—
124C7⋊#95—41no—
125C7⋊#95—41no—
126C7⋊#95—41no—
127C7⋊#95C2×C414yes—
128C7⋊#95C2×C414yes—
129C2×#388—71no—
130#1445—71no—
131#1443—71no—
132#1440—71no—
133#1440—71no—
134#1439—71no—
135#1439—71no—
136#1437—71no—
137#1437D711yescharacteristic
138#1436—71no—
139#1436—71no—
140#1436—71no—
141C4⋊#95—71no—
142#1434—71no—
143#1434—71no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
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×C7C22×C412yes—
159C24×C7C2411yescharacteristic
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
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×C7C22×C412yes—
198C22×C4×C7C22×C412yes—
199C22×C4×C7#4112yes—
200C22×C4×C7#4112yes—
201C22×C4×C7#4112yes—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
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×Dic7C22×C412yes—
252C22×Dic7C22×C412yes—
253C22×Dic7C22×C412yes—
254C22×Dic7C22×C412yes—
255C22×Dic7#4112yes—
256C22×Dic7#4112yes—
257C22×Dic7#4112yes—
258C7×C22⋊C4—44no—
259C7×C22⋊C4—44no—
260C7×C22⋊C4—44no—
261C42×C7—44no—
262C22⋊Dic7—28no—
263C22⋊Dic7—44no—
264C22⋊Dic7—44no—
265C22⋊Dic7—44no—
266Dic7⋊C4—44no—
267Dic7⋊C4—44no—
268Dic7⋊C4—44no—
269C4×Dic7—44no—
270C4×Dic7—44no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4—71no—
273C22×C4⋊C4—71no—
274C22×C22⋊C4—71no—
275C22×C22⋊C4—71no—
276C22×C22⋊C4—71no—
277C22×C22⋊C4—71no—
278C22×C22⋊C4C2×D711yescharacteristic
279C22×C22⋊C4C2×D711yescharacteristic
280C22×C22⋊C4C2×D711yescharacteristic
281C22×C42—71no—
282C22×C42—71no—
283C22×C42C2×D711yescharacteristic
284#388—78no—
285C2×#95—71no—
286C2×#95—71no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95C2×D711yescharacteristic
305C2×#95C2×D711yescharacteristic
306C2×#95C2×D711yescharacteristic
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7C23×C411yescharacteristic
343C23×C7C2×#4111yescharacteristic
344C23×C7C2×#4111yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C7H(5,𝔽2)11yescharacteristic
352C23×C7H(5,𝔽2)11yescharacteristic
353C23×C7H(5,𝔽2)11yescharacteristic
354C23×C7H(5,𝔽2)11yescharacteristic
355C23×C72−1+411yescharacteristic
356C23×C72−1+411yescharacteristic
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
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×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—41no—
418C2×Dic7—41no—
419C2×Dic7—41no—
420C2×Dic7—41no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7—41no—
424C2×Dic7—41no—
425C2×Dic7—41no—
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#11714yes—
455C25C22×D711yescharacteristic
456C23×C4—71no—
457C23×C4—71no—
458C23×C4—71no—
459C23×C4—71no—
460C23×C4—71no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4C22×D711yescharacteristic
465C23×C4C22×D711yescharacteristic
466C23×C4C22×D711yescharacteristic
467C23×C4C22×D711yescharacteristic
468C23×C4C22×D711yescharacteristic
469C23×C4C22×D711yescharacteristic
470C2×C4⋊C4—74no—
471C2×C4⋊C4—142no—
472C2×C4⋊C4—142no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—142no—
475C2×C4⋊C4—281no—
476C2×C4⋊C4—281no—
477C2×C4⋊C4—281no—
478C2×C4⋊C4—281no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—41no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—41no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—74no—
488C2×C22⋊C4—74no—
489C2×C22⋊C4—142no—
490C2×C22⋊C4—142no—
491C2×C22⋊C4—142no—
492C2×C22⋊C4—281no—
493C2×C22⋊C4—281no—
494C2×C22⋊C4—281no—
495C2×C22⋊C4—281no—
496C2×C22⋊C4—281no—
497C2×C22⋊C4—281no—
498C2×C22⋊C4—281no—
499C2×C22⋊C4C4×D714yes—
500C2×C42—22no—
501C2×C42—41no—
502C2×C42—41no—
503C2×C42—74no—
504C2×C42—281no—
505C2×C42—281no—
506C2×C42—281no—
507C2×C42—281no—
508C2×C42—281no—
509#95—41no—
510#95—41no—
511#95—41no—
512#95—74no—
513#95—74no—
514#95—142no—
515#95—142no—
516#95—142no—
517#95—142no—
518#95—142no—
519#95—142no—
520#95—142no—
521#95—281no—
522#95—281no—
523#95—281no—
524#95—281no—
525#95—281no—
526#95—281no—
527#95—281no—
528#95—281no—
529#95—281no—
530#95—281no—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—81no—
539C22×C7—81no—
540C22×C7—81no—
541C22×C7—81no—
542C22×C7—81no—
543C22×C7—81no—
544C22×C7—81no—
545C22×C7—81no—
546C22×C7C2×#11711yescharacteristic
547C22×C7C4×#4111yescharacteristic
548C22×C7C4×#4111yescharacteristic
549C22×C7#51811yescharacteristic
550C22×C7#51811yescharacteristic
551C22×C7#52011yescharacteristic
552C22×C7#52011yescharacteristic
553C22×C7#53811yescharacteristic
554C22×C7#53811yescharacteristic
555C22×C7#53811yescharacteristic
556C22×C7#53911yescharacteristic
557C22×C7#54011yescharacteristic
558C22×C7#54011yescharacteristic
559C22×C7#54111yescharacteristic
560C22×C7#54211yescharacteristic
561C22×C7#54211yescharacteristic
562C22×C7#54211yescharacteristic
563C22×C7#54211yescharacteristic
564C22×C7#54211yescharacteristic
565C22×C7#55111yescharacteristic
566C22×C7#55111yescharacteristic
567C22×C7#55111yescharacteristic
568C22×C7#55211yescharacteristic
569C22×C7#55311yescharacteristic
570C22×C7#55311yescharacteristic
571C22×C7#55311yescharacteristic
572C22×C7#55311yescharacteristic
573C22×C7#55311yescharacteristic
574C22×C7#55611yescharacteristic
575C22×C7#55911yescharacteristic
576C22×C7#55911yescharacteristic
577C22×C7#56011yescharacteristic
578C22×C7#56011yescharacteristic
579C22×C7#56211yescharacteristic
580C22×C7#56211yescharacteristic
581C4×C7—42no—
582C4×C7—42no—
583C4×C7—42no—
584C4×C7—42no—
585C4×C7—42no—
586C4×C7—81no—
587Dic7—24no—
588Dic7—42no—
589Dic7—42no—
590Dic7—42no—
591Dic7—42no—
592Dic7—81no—
593Dic7—81no—
594Dic7—81no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24C2×C4×D712yes—
610C24C23×D711yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
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—72no—
649C22×C4—72no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—72no—
655C22×C4—141no—
656C22×C4—141no—
657C22×C4—141no—
658C22×C4—141no—
659C22×C4—141no—
660C22×C4—141no—
661C22×C4—141no—
662C22×C4—141no—
663C22×C4—141no—
664C22×C4—141no—
665C22×C4—141no—
666C22×C4—141no—
667C22×C4—141no—
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×C4C2×C4×D712yes—
705C22×C4C2×C4×D712yes—
706C22×C4#115712yes—
707C22×C4#115712yes—
708C22×C4#115912yes—
709C4⋊C4—284no—
710C4⋊C4—284no—
711C4⋊C4—284no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4—148no—
716C22⋊C4—284no—
717C22⋊C4—284no—
718C22⋊C4—284no—
719C42—44no—
720C42—284no—
721C42—284no—
722C2×C7—82no—
723C2×C7#231411yescharacteristic
724C2×C7#233511yescharacteristic
725C2×C7#233711yescharacteristic
726C2×C7#235311yescharacteristic
727C2×C7#235711yescharacteristic
728C2×C7#237311yescharacteristic
729C2×C7#237711yescharacteristic
730C2×C7#275211yescharacteristic
731C2×C7#275411yescharacteristic
732C2×C7#275711yescharacteristic
733C2×C7#277911yescharacteristic
734C2×C7#279711yescharacteristic
735C2×C7#279811yescharacteristic
736C2×C7#280011yescharacteristic
737C2×C7#280111yescharacteristic
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23C22×C4×D711yescharacteristic
774C23C2×#115711yescharacteristic
775C23C2×#115711yescharacteristic
776C23C2×#115911yescharacteristic
777C23#654811yescharacteristic
778C23#654811yescharacteristic
779C23#654811yescharacteristic
780C23#654811yescharacteristic
781C23#654811yescharacteristic
782C23D7×#4111yescharacteristic
783C23D7×#4111yescharacteristic
784C23D7×#4111yescharacteristic
785C23#655311yescharacteristic
786C23#655411yescharacteristic
787C23#655411yescharacteristic
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—74no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—142no—
834C2×C4—142no—
835C2×C4—142no—
836C2×C4—142no—
837C2×C4—142no—
838C2×C4—142no—
839C2×C4—142no—
840C2×C4—142no—
841C2×C4—142no—
842C2×C4—142no—
843C2×C4—142no—
844C2×C4—142no—
845C2×C4—142no—
846C2×C4—142no—
847C2×C4—142no—
848C2×C4—142no—
849C2×C4—281no—
850C2×C4—281no—
851C2×C4—281no—
852C2×C4—281no—
853C2×C4—281no—
854C2×C4—281no—
855C2×C4—281no—
856C2×C4—281no—
857C2×C4—281no—
858C2×C4—281no—
859C2×C4—281no—
860C2×C4—281no—
861C2×C4—281no—
862C2×C4—281no—
863C2×C4—281no—
864C2×C4—281no—
865C2×C4—281no—
866C2×C4—281no—
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—
886C7#1450411yescharacteristic, complemented, Sylow
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22C4×#115711yescharacteristic
903C22#9017711yescharacteristic
904C22#9018511yescharacteristic
905C22#9018611yescharacteristic
906C22D7×#11711yescharacteristic
907C22#9022411yescharacteristic
908C22#9022511yescharacteristic
909C22C4×#115911yescharacteristic
910C22#9023111yescharacteristic
911C22#9023111yescharacteristic
912C22#9023211yescharacteristic
913C22#9023611yescharacteristic
914C22#9023711yescharacteristic
915C22#9023711yescharacteristic
916C22#9024911yescharacteristic
917C22#9025011yescharacteristic
918C22#9025011yescharacteristic
919C22#9025311yescharacteristic
920C22#9025511yescharacteristic
921C22#9028411yescharacteristic
922C22#9029411yescharacteristic
923C22#9030411yescharacteristic
924C22#9030511yescharacteristic
925C22#9030611yescharacteristic
926C22#9031111yescharacteristic
927C22#9031211yescharacteristic
928C22#9034911yescharacteristic
929C22#9035311yescharacteristic
930C22#9035311yescharacteristic
931C22#9036011yescharacteristic
932C22#9037011yescharacteristic
933C22#9037511yescharacteristic
934C22#9039211yescharacteristic
935C22#9040011yescharacteristic
936C22#9041111yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—81no—
943C4—144no—
944C4—282no—
945C4—282no—
946C4—282no—
947C4—282no—
948C4—561no—
949C4—561no—
950C4—561no—
951C2—82no—
952C2#1173090811yescharacteristic
953C2#1173092111yescharacteristic
954C2#1173101611yescharacteristic
955C2#1173211611yescharacteristic
956C2#1173229011yescharacteristic
957C2#1173230111yescharacteristic
958C2#1173290111yescharacteristic
959C2#1173318111yescharacteristic
960C2#1173324311yescharacteristic
961C2#1173324811yescharacteristic
962C2#1173325011yescharacteristic
963C2#1173328011yescharacteristic
964C2#1173375511yescharacteristic
965C2#1173385611yescharacteristic
966C2#1173391611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1437C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1437D7
hypocenterC7#14504
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
8. #11729290C2semidirect
9. #11729288C2semidirect
10. #11727175C2semidirect
11. #11727172C2semidirect
12. #11727160C2semidirect
13. #11727160C2semidirect
14. Dic7⋊#95C2semidirect
15. #11727156C2semidirect
51. #89717C4semidirect
886. C7#14504semidirect

Maximal subgroups

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

subgroupindex
C2×#897172
C7×#14372
#117293032
#117293022
#117293012
#117292992
#117292902
#117292882
#117271752
#117271722
#117271602
Dic7⋊#952
#117271562
#145047