Finite Group Databasebeta

← #13282365

Subgroups — #13282365

Order 1792.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89722C211yesmaximal, characteristic
2C7×#1437C211yesmaximal, characteristic
3#11729301C211yesmaximal, characteristic
4#11729300C211yesmaximal, characteristic
5#11729299C211yesmaximal, characteristic
6#11729298C211yesmaximal, characteristic
7#11729298C211yesmaximal, characteristic
8#11729289C211yesmaximal, characteristic, complemented
9#11729288C211yesmaximal, characteristic, complemented
10#11727177C211yesmaximal, characteristic, complemented
11#11727171C211yesmaximal, characteristic, complemented
12#11727165C211yesmaximal, characteristic, complemented
13#11727165C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727157C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
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#89722C418yescomplemented
52#14456—71nomaximal, Sylow
53C25×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×Dic7—41no—
61C23×Dic7—41no—
62C23×Dic7—41no—
63C23×Dic7—41no—
64C23×Dic7—41no—
65C23×Dic7—41no—
66C23×Dic7C2×C414yes—
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—41no—
80C2×C7×C22⋊C4—41no—
81C2×C7×C22⋊C4—41no—
82C2×C7×C22⋊C4C2×C414yes—
83C2×C7×C22⋊C4Q814yes—
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—41no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—41no—
91C2×C22⋊Dic7—41no—
92C2×C22⋊Dic7—41no—
93C2×C22⋊Dic7—41no—
94C2×C22⋊Dic7—41no—
95C2×C22⋊Dic7C2×C414yes—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—41no—
99C2×C4⋊Dic7—41no—
100C2×C4⋊Dic7—41no—
101C2×C4⋊Dic7—41no—
102C2×C4⋊Dic7—41no—
103C2×C4⋊Dic7C2×C414yes—
104C2×C4⋊Dic7C2×C414yes—
105C2×Dic7⋊C4—41no—
106C2×Dic7⋊C4—41no—
107C2×Dic7⋊C4—41no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—41no—
110C2×C4×Dic7—41no—
111C7×#95—22no—
112C7×#95—41no—
113C7×#95—41no—
114C7⋊#95—22no—
115C7⋊#95—22no—
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⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95C2×C414yes—
132C7⋊#95C2×C414yes—
133C2×#385—71no—
134#1445—71no—
135#1443—71no—
136#1441—71no—
137#1441—71no—
138#1439—71no—
139#1439—71no—
140#1437—71no—
141#1437D711yescharacteristic
142#1436—71no—
143C4⋊#95—71no—
144#1434—71no—
145#1434—71no—
146C22⋊#95—71no—
147C22⋊#95—71no—
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×C7—21no—
159C24×C7—21no—
160C24×C7C22×C412yes—
161C24×C7C2×Q812yes—
162C24×C7#4112yes—
163C24×C7C2411yescharacteristic
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×C7C2×Q812yes—
202C22×C4×C7C2×Q812yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
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—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—44no—
258C22×Dic7—44no—
259C22×Dic7—44no—
260C22×Dic7—44no—
261C22×Dic7—44no—
262C22×Dic7—44no—
263C22×Dic7—44no—
264C22×Dic7C22×C412yes—
265C22×Dic7C22×C412yes—
266C22×Dic7C22×C412yes—
267C22×Dic7C22×C412yes—
268C22×Dic7#4112yes—
269C7×C22⋊C4—28no—
270C7×C22⋊C4—44no—
271C7×C22⋊C4—44no—
272C42×C7—44no—
273C22⋊Dic7—44no—
274C22⋊Dic7—44no—
275C22⋊Dic7—44no—
276C4⋊Dic7—44no—
277C4⋊Dic7—44no—
278C4⋊Dic7—44no—
279Dic7⋊C4—44no—
280C4×Dic7—44no—
281C24×C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4C2×D711yescharacteristic
290C22×C22⋊C4C2×D711yescharacteristic
291C22×C22⋊C4C2×D711yescharacteristic
292C22×C42—71no—
293C22×C42C2×D711yescharacteristic
294#385—78no—
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×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95C2×D711yescharacteristic
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
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—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
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—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7C4×Q814yes—
352C23×C7C23×C411yescharacteristic
353C23×C7C22×Q811yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7C2×#4111yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7H(5,𝔽2)11yescharacteristic
360C23×C7H(5,𝔽2)11yescharacteristic
361C23×C7H(5,𝔽2)11yescharacteristic
362C23×C7H(5,𝔽2)11yescharacteristic
363C23×C7H(5,𝔽2)11yescharacteristic
364C23×C7H(5,𝔽2)11yescharacteristic
365C23×C7H(5,𝔽2)11yescharacteristic
366C23×C72−1+411yescharacteristic
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
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—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#11714yes—
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—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C25C22×D711yescharacteristic
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—74no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—281no—
477C23×C4—281no—
478C23×C4—281no—
479C23×C4—281no—
480C23×C4—281no—
481C23×C4—281no—
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—142no—
491C2×C4⋊C4—142no—
492C2×C4⋊C4—281no—
493C2×C4⋊C4—281no—
494C2×C4⋊C4—281no—
495C2×C4⋊C4—281no—
496C2×C4⋊C4—281no—
497C2×C4⋊C4—281no—
498C2×C4⋊C4—281no—
499C2×C4⋊C4—281no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—142no—
509C2×C22⋊C4—142no—
510C2×C22⋊C4—142no—
511C2×C22⋊C4—281no—
512C2×C22⋊C4—281no—
513C2×C22⋊C4—281no—
514C2×C22⋊C4—281no—
515C2×C22⋊C4—281no—
516C2×C22⋊C4Dic1414yes—
517C2×C22⋊C4C4×D714yes—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—41no—
521C2×C42—142no—
522C2×C42—281no—
523C2×C42—281no—
524#95—22no—
525#95—41no—
526#95—41no—
527#95—74no—
528#95—74no—
529#95—142no—
530#95—142no—
531#95—281no—
532#95—281no—
533#95—281no—
534#95—281no—
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—
546C22×C7—24no—
547C22×C7—24no—
548C22×C7—24no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
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×C7C2×#11711yescharacteristic
562C22×C7C2×C4×Q811yescharacteristic
563C22×C7C4×#4111yescharacteristic
564C22×C7#51811yescharacteristic
565C22×C7#51811yescharacteristic
566C22×C7#51811yescharacteristic
567C22×C7#52011yescharacteristic
568C22×C7#53811yescharacteristic
569C22×C7#53811yescharacteristic
570C22×C7#53911yescharacteristic
571C22×C7#53911yescharacteristic
572C22×C7#54011yescharacteristic
573C22×C7#54011yescharacteristic
574C22×C7#54011yescharacteristic
575C22×C7#54211yescharacteristic
576C22×C7#54211yescharacteristic
577C22×C7#54211yescharacteristic
578C22×C7#54311yescharacteristic
579C22×C7#54411yescharacteristic
580C22×C7#55111yescharacteristic
581C22×C7#55111yescharacteristic
582C22×C7#55111yescharacteristic
583C22×C7#55111yescharacteristic
584C22×C7#55311yescharacteristic
585C22×C7#55311yescharacteristic
586C22×C7#55311yescharacteristic
587C22×C7#55311yescharacteristic
588C22×C7#55411yescharacteristic
589C22×C7#55411yescharacteristic
590C22×C7#55411yescharacteristic
591C22×C7#55411yescharacteristic
592C22×C7#56011yescharacteristic
593C22×C7#56011yescharacteristic
594C22×C7#56011yescharacteristic
595C22×C7H(3,𝔽4)11yescharacteristic
596C4×C7—24no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600C4×C7—42no—
601C4×C7—81no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606Dic7—42no—
607Dic7—81no—
608Dic7—81no—
609Dic7—81no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24C2×Dic1412yes—
623C24C2×C4×D712yes—
624C24#115712yes—
625C24C23×D711yescharacteristic
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—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
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—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—284no—
718C22×C4—284no—
719C22×C4—284no—
720C22×C4—284no—
721C22×C4—284no—
722C22×C4—284no—
723C22×C4—284no—
724C22×C4C2×Dic1412yes—
725C22×C4C2×Dic1412yes—
726C22×C4C2×C4×D712yes—
727C22×C4C2×C4×D712yes—
728C22×C4#115912yes—
729C22×C4#115912yes—
730C22×C4#115912yes—
731C4⋊C4—284no—
732C4⋊C4—284no—
733C4⋊C4—284no—
734C4⋊C4—284no—
735C22⋊C4—28no—
736C22⋊C4—44no—
737C22⋊C4—44no—
738C22⋊C4—284no—
739C22⋊C4—284no—
740C22⋊C4—284no—
741C42—44no—
742C42—284no—
743C2×C7—44no—
744C2×C7#231911yescharacteristic
745C2×C7#232911yescharacteristic
746C2×C7#233511yescharacteristic
747C2×C7#234511yescharacteristic
748C2×C7#235311yescharacteristic
749C2×C7#236811yescharacteristic
750C2×C7#237511yescharacteristic
751C2×C7#274611yescharacteristic
752C2×C7#274811yescharacteristic
753C2×C7#274911yescharacteristic
754C2×C7#275311yescharacteristic
755C2×C7#275711yescharacteristic
756C2×C7#276311yescharacteristic
757C2×C7#278011yescharacteristic
758C2×C7#279011yescharacteristic
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
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—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23C4×Dic1414yes—
794C23C22×Dic1411yescharacteristic
795C23C22×C4×D711yescharacteristic
796C23C2×#115711yescharacteristic
797C23C2×#115911yescharacteristic
798C23C2×#115911yescharacteristic
799C23C2×#115911yescharacteristic
800C23#654811yescharacteristic
801C23#654811yescharacteristic
802C23#654811yescharacteristic
803C23D7×#4111yescharacteristic
804C23#655311yescharacteristic
805C23#655311yescharacteristic
806C23#655311yescharacteristic
807C23#655311yescharacteristic
808C23#655411yescharacteristic
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
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—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—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—142no—
861C2×C4—142no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—142no—
865C2×C4—2816no—
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—
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#644014yes—
908C7#1445611yescharacteristic, complemented, Sylow
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22C2×C4×Dic1411yescharacteristic
925C22C2×#644011yescharacteristic
926C22#9017411yescharacteristic
927C22#9018611yescharacteristic
928C22#9021011yescharacteristic
929C22#9021211yescharacteristic
930C22#9021811yescharacteristic
931C22C4×#115911yescharacteristic
932C22#9023011yescharacteristic
933C22#9023411yescharacteristic
934C22#9023411yescharacteristic
935C22#9023411yescharacteristic
936C22#9023611yescharacteristic
937C22#9023611yescharacteristic
938C22#9023711yescharacteristic
939C22#9025111yescharacteristic
940C22#9025511yescharacteristic
941C22#9025611yescharacteristic
942C22#9025611yescharacteristic
943C22#9027811yescharacteristic
944C22#9029211yescharacteristic
945C22#9029411yescharacteristic
946C22#9030911yescharacteristic
947C22#9031011yescharacteristic
948C22#9031011yescharacteristic
949C22#9031111yescharacteristic
950C22#9034911yescharacteristic
951C22#9035611yescharacteristic
952C22#9035711yescharacteristic
953C22#9036911yescharacteristic
954C22#9037311yescharacteristic
955C22#9037411yescharacteristic
956C22#9040111yescharacteristic
957C22#9040211yescharacteristic
958C22#9041011yescharacteristic
959C4—24no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—81no—
965C4—282no—
966C4—282no—
967C4—282no—
968C4—282no—
969C4—282no—
970C4—561no—
971C4—561no—
972C4—561no—
973C2—44no—
974C2#1173089211yescharacteristic
975C2#1173090211yescharacteristic
976C2#1173091911yescharacteristic
977C2#1173211911yescharacteristic
978C2#1173228111yescharacteristic
979C2#1173228311yescharacteristic
980C2#1173291411yescharacteristic
981C2#1173318811yescharacteristic
982C2#1173319311yescharacteristic
983C2#1173323211yescharacteristic
984C2#1173328511yescharacteristic
985C2#1173338711yescharacteristic
986C2#1173374011yescharacteristic
987C2#1173385411yescharacteristic
988C2#1173385811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1437C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1437D7
hypocenterC7#14456
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
8. #11729289C2semidirect
9. #11729288C2semidirect
10. #11727177C2semidirect
11. #11727171C2semidirect
12. #11727165C2semidirect
13. #11727165C2semidirect
14. #11727161C2semidirect
15. #11727157C2semidirect
51. #89722C4semidirect
908. C7#14456semidirect

Maximal subgroups

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

subgroupindex
C2×#897222
C7×#14372
#117293012
#117293002
#117292992
#117292982
#117292892
#117292882
#117271772
#117271712
#117271652
#117271612
#117271572
#144567