Finite Group Databasebeta

← #13282997

Subgroups — #13282997

Order 1792.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89717C211yesmaximal, characteristic
2C7×#1439C211yesmaximal, characteristic
3#11729321C211yesmaximal, characteristic, complemented
4#11729318C211yesmaximal, characteristic, complemented
5#11729303C211yesmaximal, characteristic
6#11729299C211yesmaximal, characteristic
7#11729298C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11727175C211yesmaximal, characteristic, complemented
11#11727172C211yesmaximal, characteristic, complemented
12#11727171C211yesmaximal, characteristic, complemented
13#11727160C211yesmaximal, characteristic, complemented
14#11727157C211yesmaximal, characteristic, complemented
15#11727156C211yesmaximal, 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×Dic7⋊C4C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
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#14509—71nomaximal, Sylow
53C25×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×Dic7—22no—
61C23×Dic7—22no—
62C23×Dic7—22no—
63C23×Dic7—41no—
64C23×Dic7—41no—
65C23×Dic7—41no—
66C23×Dic7—41no—
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—41no—
77C2×C7×C4⋊C4—41no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—41no—
82C2×C7×C22⋊C4—41no—
83C2×C7×C22⋊C4—41no—
84C2×C7×C22⋊C4—41no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4C2×C414yes—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—41no—
92C2×C22⋊Dic7—41no—
93C2×C22⋊Dic7—41no—
94C2×C22⋊Dic7C2×C414yes—
95C2×C22⋊Dic7C2×C414yes—
96C2×Dic7⋊C4—41no—
97C2×Dic7⋊C4—41no—
98C2×Dic7⋊C4C2×C414yescomplemented
99C2×C4×Dic7—41no—
100C2×C4×Dic7—41no—
101C2×C4×Dic7—41no—
102C2×C4×Dic7—41no—
103C2×C4×Dic7—41no—
104C2×C4×Dic7C2×C414yescomplemented
105C7×#95—41no—
106C7×#95—41no—
107C7×#95—41no—
108C7⋊#95—22no—
109C7⋊#95—22no—
110C7⋊#95—22no—
111C7⋊#95—22no—
112C7⋊#95—22no—
113C7⋊#95—22no—
114C7⋊#95—22no—
115C7⋊#95—41no—
116C7⋊#95—41no—
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×C414yescomplemented
128C7⋊#95C2×C414yescomplemented
129C2×#388—71no—
130#1445—71no—
131#1443—71no—
132#1443—71no—
133#1442—71no—
134#1440—71no—
135#1439D711yescharacteristic
136#1437—71no—
137#1436—71no—
138#1436—71no—
139#1434—71no—
140#1434—71no—
141C22⋊#95—71no—
142C22⋊#95—71no—
143C22⋊#95—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×C7C22×C412yes—
157C24×C7#4112yes—
158C24×C7#4112yes—
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×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7C22×C412yes—
200C22×C4×C7C22×C412yes—
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×Dic7—44no—
252C22×Dic7—44no—
253C22×Dic7—44no—
254C22×Dic7—44no—
255C22×Dic7—44no—
256C22×Dic7—44no—
257C22×Dic7—44no—
258C22×Dic7C22×C412yes—
259C22×Dic7C22×C412yes—
260C22×Dic7C22×C412yes—
261C22×Dic7C22×C412yes—
262C22×Dic7#4112yes—
263C22×Dic7#4112yes—
264C22×Dic7#4112yes—
265C7×C4⋊C4—44no—
266C7×C22⋊C4—44no—
267C7×C22⋊C4—44no—
268C7×C22⋊C4—44no—
269C22⋊Dic7—28no—
270C22⋊Dic7—44no—
271C22⋊Dic7—44no—
272Dic7⋊C4—44no—
273C4×Dic7—44no—
274C4×Dic7—44no—
275C24×C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4C2×D711yescharacteristic
278C22×C22⋊C4—71no—
279C22×C22⋊C4—71no—
280C22×C22⋊C4—71no—
281C22×C22⋊C4C2×D711yescharacteristic
282C22×C22⋊C4C2×D711yescharacteristic
283C22×C22⋊C4C2×D711yescharacteristic
284C22×C42—71no—
285C22×C42—71no—
286#388—78no—
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×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95C2×D711yescharacteristic
309C2×#95C2×D711yescharacteristic
310C2×#95C2×D711yescharacteristic
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
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—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×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7#11714yes—
346C23×C7C23×C411yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7C2×#4111yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7C2×#4111yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7H(5,𝔽2)11yescharacteristic
354C23×C7H(5,𝔽2)11yescharacteristic
355C23×C7H(5,𝔽2)11yescharacteristic
356C23×C7H(5,𝔽2)11yescharacteristic
357C23×C7H(5,𝔽2)11yescharacteristic
358C23×C7H(5,𝔽2)11yescharacteristic
359C23×C72−1+411yescharacteristic
360C23×C72−1+411yescharacteristic
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—41no—
371C2×C4×C7—41no—
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×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
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—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—416no—
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—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C25C22×D711yescharacteristic
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—142no—
470C23×C4—142no—
471C23×C4—142no—
472C23×C4—281no—
473C23×C4—281no—
474C23×C4—281no—
475C23×C4—281no—
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C2×C4⋊C4—22no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—281no—
487C2×C4⋊C4—281no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—41no—
495C2×C22⋊C4—41no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—142no—
499C2×C22⋊C4—142no—
500C2×C22⋊C4—142no—
501C2×C22⋊C4—142no—
502C2×C22⋊C4—281no—
503C2×C22⋊C4—281no—
504C2×C22⋊C4—281no—
505C2×C22⋊C4C4×D714yes—
506C2×C42—74no—
507C2×C42—281no—
508C2×C42—281no—
509C2×C42—281no—
510C2×C42—281no—
511C2×C42—281no—
512#95—41no—
513#95—41no—
514#95—41no—
515#95—74no—
516#95—74no—
517#95—142no—
518#95—142no—
519#95—142no—
520#95—142no—
521#95—142no—
522#95—142no—
523#95—142no—
524#95—281no—
525#95—281no—
526#95—281no—
527#95—281no—
528#95—281no—
529#95—281no—
530#95—281no—
531#95—281no—
532#95—281no—
533#95—281no—
534#95—281no—
535#95—281no—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7C2×#11711yescharacteristic
552C22×C7C4×#4111yescharacteristic
553C22×C7C4×#4111yescharacteristic
554C22×C7#51811yescharacteristic
555C22×C7#51811yescharacteristic
556C22×C7#52011yescharacteristic
557C22×C7#52011yescharacteristic
558C22×C7#53811yescharacteristic
559C22×C7#53811yescharacteristic
560C22×C7#53811yescharacteristic
561C22×C7#53811yescharacteristic
562C22×C7#53811yescharacteristic
563C22×C7#53911yescharacteristic
564C22×C7#53911yescharacteristic
565C22×C7#53911yescharacteristic
566C22×C7#54111yescharacteristic
567C22×C7#54211yescharacteristic
568C22×C7#54211yescharacteristic
569C22×C7#54211yescharacteristic
570C22×C7#55111yescharacteristic
571C22×C7#55111yescharacteristic
572C22×C7#55111yescharacteristic
573C22×C7#55111yescharacteristic
574C22×C7#55111yescharacteristic
575C22×C7#55211yescharacteristic
576C22×C7#55211yescharacteristic
577C22×C7#55311yescharacteristic
578C22×C7#55311yescharacteristic
579C22×C7#55311yescharacteristic
580C22×C7#55311yescharacteristic
581C22×C7#55911yescharacteristic
582C22×C7#56011yescharacteristic
583C22×C7#56011yescharacteristic
584C22×C7#56211yescharacteristic
585C22×C7#56211yescharacteristic
586C4×C7—42no—
587C4×C7—42no—
588C4×C7—42no—
589C4×C7—81no—
590C4×C7—81no—
591C4×C7—81no—
592Dic7—42no—
593Dic7—42no—
594Dic7—42no—
595Dic7—42no—
596Dic7—42no—
597Dic7—42no—
598Dic7—42no—
599Dic7—81no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24C2×C4×D712yes—
613C24#115912yes—
614C24#116112yes—
615C24C23×D711yescharacteristic
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—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—72no—
656C22×C4—72no—
657C22×C4—72no—
658C22×C4—72no—
659C22×C4—72no—
660C22×C4—72no—
661C22×C4—72no—
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×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—284no—
712C22×C4—284no—
713C22×C4—284no—
714C22×C4—284no—
715C22×C4—284no—
716C22×C4—284no—
717C22×C4—284no—
718C22×C4C2×C4×D712yes—
719C22×C4C2×C4×D712yes—
720C22×C4#115912yes—
721C4⋊C4—44no—
722C4⋊C4—284no—
723C22⋊C4—44no—
724C22⋊C4—44no—
725C22⋊C4—44no—
726C22⋊C4—148no—
727C22⋊C4—284no—
728C22⋊C4—284no—
729C42—284no—
730C42—284no—
731C2×C7—44no—
732C2×C7#231811yescharacteristic
733C2×C7#233411yescharacteristic
734C2×C7#233711yescharacteristic
735C2×C7#234311yescharacteristic
736C2×C7#235311yescharacteristic
737C2×C7#237411yescharacteristic
738C2×C7#237711yescharacteristic
739C2×C7#273511yescharacteristic
740C2×C7#273911yescharacteristic
741C2×C7#274611yescharacteristic
742C2×C7#274711yescharacteristic
743C2×C7#275111yescharacteristic
744C2×C7#277811yescharacteristic
745C2×C7#277911yescharacteristic
746C2×C7#279611yescharacteristic
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#645514yes—
782C23C22×C4×D711yescharacteristic
783C23C2×#115911yescharacteristic
784C23C2×#115911yescharacteristic
785C23#654811yescharacteristic
786C23#654811yescharacteristic
787C23#654811yescharacteristic
788C23#654811yescharacteristic
789C23#654811yescharacteristic
790C23C2×#116111yescharacteristic
791C23D7×#4111yescharacteristic
792C23D7×#4111yescharacteristic
793C23D7×#4111yescharacteristic
794C23#655311yescharacteristic
795C23#655411yescharacteristic
796C23#655411yescharacteristic
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
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—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—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—142no—
850C2×C4—142no—
851C2×C4—142no—
852C2×C4—142no—
853C2×C4—142no—
854C2×C4—142no—
855C2×C4—142no—
856C2×C4—142no—
857C2×C4—142no—
858C2×C4—142no—
859C2×C4—142no—
860C2×C4—2816no—
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—
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—
896C7#1450911yescharacteristic, complemented, Sylow
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22#9017711yescharacteristic
913C22C2×#645511yescharacteristic
914C22#9021311yescharacteristic
915C22C4×#115911yescharacteristic
916C22#9023611yescharacteristic
917C22#9023711yescharacteristic
918C22#9023711yescharacteristic
919C22#9027811yescharacteristic
920C22#9028411yescharacteristic
921C22#9028411yescharacteristic
922C22#9029211yescharacteristic
923C22#9029211yescharacteristic
924C22#9029211yescharacteristic
925C22#9029411yescharacteristic
926C22#9030411yescharacteristic
927C22#9030411yescharacteristic
928C22#9031111yescharacteristic
929C22#9031211yescharacteristic
930C22#9032811yescharacteristic
931C22#9032811yescharacteristic
932C22#9032811yescharacteristic
933C22#9033311yescharacteristic
934C22#9033511yescharacteristic
935C22#9033611yescharacteristic
936C22#9034111yescharacteristic
937C22#9035111yescharacteristic
938C22#9035211yescharacteristic
939C22#9035311yescharacteristic
940C22#9035611yescharacteristic
941C22#9036011yescharacteristic
942C22#9037211yescharacteristic
943C22#9037511yescharacteristic
944C22#9039211yescharacteristic
945C22#9039611yescharacteristic
946C22#9041111yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—81no—
951C4—81no—
952C4—81no—
953C4—282no—
954C4—282no—
955C4—282no—
956C4—282no—
957C4—282no—
958C4—282no—
959C4—282no—
960C4—561no—
961C2—44no—
962C2#1173132911yescharacteristic
963C2#1173182811yescharacteristic
964C2#1173183711yescharacteristic
965C2#1173211611yescharacteristic
966C2#1173291011yescharacteristic
967C2#1173293211yescharacteristic
968C2#1173375511yescharacteristic
969C2#1173418311yescharacteristic
970C2#1173428311yescharacteristic
971C2#1173451111yescharacteristic
972C2#1173451911yescharacteristic
973C2#1173481811yescharacteristic
974C2#1173488711yescharacteristic
975C2#1173504711yescharacteristic
976C2#1173552211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1439C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1439D7
hypocenterC7#14509
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. #11729321C2semidirect
4. #11729318C2semidirect
10. #11727175C2semidirect
11. #11727172C2semidirect
12. #11727171C2semidirect
13. #11727160C2semidirect
14. #11727157C2semidirect
15. #11727156C2semidirect
51. #89717C4semidirect
98. C2×Dic7⋊C4C2×C4semidirect
104. C2×C4×Dic7C2×C4semidirect
127. C7⋊#95C2×C4semidirect
128. C7⋊#95C2×C4semidirect
896. C7#14509semidirect

Maximal subgroups

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

subgroupindex
C2×#897172
C7×#14392
#117293212
#117293182
#117293032
#117292992
#117292982
#117271752
#117271722
#117271712
#117271602
#117271572
#117271562
#145097