Finite Group Databasebeta

← #13282296

Subgroups — #13282296

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6441C211yesmaximal, characteristic
2C2×#89701C211yesmaximal, characteristic, complemented
3C2×#89418C211yesmaximal, characteristic, complemented
4C7×#1437C211yesmaximal, characteristic
5#11729301C211yesmaximal, characteristic
6#11729300C211yesmaximal, characteristic
7#11729299C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11729290C211yesmaximal, characteristic, complemented
11#11727175C211yesmaximal, characteristic, complemented
12#11727175C211yesmaximal, characteristic, complemented
13#11727165C211yesmaximal, characteristic, complemented
14#11727164C211yesmaximal, characteristic, complemented
15#11727161C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C23×Dic14C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×#6441—24no—
32C2×#6441—24no—
33C2×#6441C418yescomplemented
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
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89701—24no—
55#89418—24no—
56#14449—71nomaximal, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—41no—
67C23×Dic7—41no—
68C23×Dic7—41no—
69C23×Dic7—41no—
70C23×Dic7C2×C414yes—
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C22×Dic14—41no—
80C22×Dic14—41no—
81C22×Dic14—41no—
82C22×Dic14—41no—
83C22×Dic14C2×C414yes—
84C22×Dic14D414yes—
85C22×Dic14D414yes—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—41no—
91C2×C7×C22⋊C4—41no—
92C2×C7×C22⋊C4—41no—
93C2×C7×C22⋊C4C2×C414yes—
94C2×C7×C22⋊C4Q814yescomplemented
95C2×C42×C7—22no—
96C2×C42×C7—41no—
97C2×C42×C7—41no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—22no—
100C2×C22⋊Dic7—22no—
101C2×C22⋊Dic7—22no—
102C2×C22⋊Dic7—22no—
103C2×C22⋊Dic7—41no—
104C2×C22⋊Dic7—41no—
105C2×C22⋊Dic7—41no—
106C2×C22⋊Dic7C2×C414yes—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—41no—
111C2×C4⋊Dic7—41no—
112C2×C4⋊Dic7C2×C414yes—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—41no—
119C2×Dic7⋊C4—41no—
120C2×Dic7⋊C4C2×C414yes—
121C2×Dic7⋊C4C2×C414yes—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—41no—
124C2×C4×Dic7—41no—
125#6441—232no—
126C7×#95—22no—
127C7×#95—22no—
128C7×#95—41no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95—41no—
145C7⋊#95—41no—
146C22×C22⋊Q8—71no—
147C2×#391—71no—
148C2×#391—71no—
149#1445—71no—
150#1445—71no—
151#1441—71no—
152#1441—71no—
153#1439—71no—
154#1439—71no—
155#1437—71no—
156#1437D711yescharacteristic
157#1436—71no—
158#1436—71no—
159C22⋊#95—71no—
160C22⋊#95—71no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7C22×C412yes—
174C24×C7C2×Q812yes—
175C24×C7#4112yes—
176C24×C7C2411yescharacteristic
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×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×Q812yes—
217C22×C4×C7C2×Q812yes—
218C22×C4×C7#4112yes—
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—28no—
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—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—44no—
268C22×Dic7—44no—
269C22×Dic7—44no—
270C22×Dic7—44no—
271C22×Dic7—44no—
272C22×Dic7—44no—
273C22×Dic7C22×C412yes—
274C22×Dic7C22×C412yes—
275C22×Dic7C22×C412yes—
276C22×Dic7C22×C412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7C2×D412yes—
280C22×Dic7C2×D412yes—
281C22×Dic7#4112yes—
282C2×Dic14—44no—
283C2×Dic14—44no—
284C2×Dic14—44no—
285C2×Dic14—44no—
286C2×Dic14—44no—
287C2×Dic14—44no—
288C2×Dic14C22⋊C4116yescomplemented
289C7×C22⋊C4—28no—
290C7×C22⋊C4—44no—
291C7×C22⋊C4—44no—
292C42×C7—44no—
293C22⋊Dic7—28no—
294C22⋊Dic7—44no—
295C22⋊Dic7—44no—
296C4⋊Dic7—28no—
297C4⋊Dic7—44no—
298Dic7⋊C4—28no—
299Dic7⋊C4—28no—
300Dic7⋊C4—44no—
301C4×Dic7—44no—
302C23×Q8—71no—
303C24×C4—71no—
304C2×C22⋊Q8—78no—
305C2×C22⋊Q8—144no—
306C2×C22⋊Q8—144no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320#391—144no—
321#391—144no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—41no—
373C23×C7—41no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7C4×Q814yes—
377C23×C7C23×C411yescharacteristic
378C23×C7C22×D411yescharacteristic
379C23×C7C22×D411yescharacteristic
380C23×C7C22×Q811yescharacteristic
381C23×C7C2×#4111yescharacteristic
382C23×C7C2×#4111yescharacteristic
383C23×C7C2×#4111yescharacteristic
384C23×C7H(5,𝔽2)11yescharacteristic
385C23×C7H(5,𝔽2)11yescharacteristic
386C23×C7H(5,𝔽2)11yescharacteristic
387C23×C7H(5,𝔽2)11yescharacteristic
388C23×C7H(5,𝔽2)11yescharacteristic
389C23×C72−1+411yescharacteristic
390C23×C72−1+411yescharacteristic
391C23×C72−1+411yescharacteristic
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7C2×C22⋊C414yes—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—416no—
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—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7C2×C22⋊C414yes—
490C2×Dic7C2×C22⋊C414yes—
491Dic14—416no—
492C25C22×D711yescharacteristic
493C22×Q8—74no—
494C22×Q8—74no—
495C22×Q8—74no—
496C22×Q8—281no—
497C22×Q8—281no—
498C22×Q8—281no—
499C22×Q8—281no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—74no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—71no—
509C23×C4—142no—
510C23×C4—142no—
511C23×C4—281no—
512C23×C4—281no—
513C23×C4—281no—
514C23×C4—281no—
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C23×C4C22×D711yescharacteristic
519C23×C4C22×D711yescharacteristic
520C23×C4C22×D711yescharacteristic
521C22⋊Q8—1432no—
522C2×C4⋊C4—74no—
523C2×C4⋊C4—74no—
524C2×C4⋊C4—74no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—142no—
530C2×C4⋊C4—142no—
531C2×C4⋊C4—142no—
532C2×C4⋊C4—142no—
533C2×C4⋊C4—281no—
534C2×C4⋊C4—281no—
535C2×C4⋊C4—281no—
536C2×C4⋊C4—281no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—74no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—142no—
547C2×C22⋊C4—142no—
548C2×C22⋊C4—142no—
549C2×C22⋊C4—142no—
550C2×C22⋊C4—281no—
551C2×C22⋊C4—281no—
552C2×C22⋊C4—281no—
553C2×C22⋊C4Dic1414yescomplemented
554C2×C22⋊C4C4×D714yes—
555C2×C42—22no—
556C2×C42—41no—
557C2×C42—41no—
558C2×C42—142no—
559C2×C42—281no—
560C2×C42—281no—
561#95—22no—
562#95—22no—
563#95—41no—
564#95—142no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—142no—
570#95—142no—
571#95—142no—
572#95—142no—
573#95—142no—
574#95—281no—
575#95—281no—
576#95—281no—
577#95—281no—
578#95—281no—
579#95—281no—
580#95—281no—
581C22×C7—24no—
582C22×C7—24no—
583C22×C7—24no—
584C22×C7—42no—
585C22×C7—42no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7—42no—
590C22×C7—42no—
591C22×C7—42no—
592C22×C7—42no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7—42no—
596C22×C7C22×C22⋊C411yescharacteristic
597C22×C7C2×C4×Q811yescharacteristic
598C22×C7C4×#4111yescharacteristic
599C22×C7#51811yescharacteristic
600C22×C7#51811yescharacteristic
601C22×C7#51911yescharacteristic
602C22×C7#52011yescharacteristic
603C22×C7#53411yescharacteristic
604C22×C7#53411yescharacteristic
605C22×C7#53411yescharacteristic
606C22×C7#53411yescharacteristic
607C22×C7#53811yescharacteristic
608C22×C7#53911yescharacteristic
609C22×C7#53911yescharacteristic
610C22×C7#53911yescharacteristic
611C22×C7#54211yescharacteristic
612C22×C7#54211yescharacteristic
613C22×C7#54311yescharacteristic
614C22×C7#54411yescharacteristic
615C22×C7#54811yescharacteristic
616C22×C7#54811yescharacteristic
617C22×C7#54811yescharacteristic
618C22×C7#54811yescharacteristic
619C22×C7D4×Q811yescharacteristic
620C22×C7D4×Q811yescharacteristic
621C22×C7#55011yescharacteristic
622C22×C7#55011yescharacteristic
623C22×C7#55111yescharacteristic
624C22×C7#55111yescharacteristic
625C22×C7#55411yescharacteristic
626C22×C7#55411yescharacteristic
627C22×C7#56211yescharacteristic
628C22×C7#56211yescharacteristic
629C22×C7#56311yescharacteristic
630C22×C7#56311yescharacteristic
631C4×C7—24no—
632C4×C7—42no—
633C4×C7—42no—
634C4×C7—42no—
635C4×C7—42no—
636C4×C7—81no—
637Dic7—24no—
638Dic7—24no—
639Dic7—42no—
640Dic7—42no—
641Dic7—42no—
642Dic7—81no—
643Dic7—81no—
644Dic7—81no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24C2×Dic1412yes—
658C24C2×C4×D712yes—
659C24#115712yes—
660C24C23×D711yescharacteristic
661C2×Q8—716no—
662C2×Q8—284no—
663C2×Q8—284no—
664C2×Q8—284no—
665C2×Q8—284no—
666C2×Q8—284no—
667C2×Q8—284no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—72no—
704C22×C4—72no—
705C22×C4—72no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—72no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—148no—
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—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—141no—
760C22×C4—284no—
761C22×C4—284no—
762C22×C4—284no—
763C22×C4—284no—
764C22×C4—284no—
765C22×C4—284no—
766C22×C4C2×Dic1412yes—
767C22×C4C2×Dic1412yes—
768C22×C4C2×C4×D712yes—
769C22×C4C2×C4×D712yes—
770C22×C4D4×D712yes—
771C22×C4D4×D712yes—
772C22×C4#115912yes—
773C4⋊C4—148no—
774C4⋊C4—148no—
775C4⋊C4—148no—
776C4⋊C4—284no—
777C4⋊C4—284no—
778C22⋊C4—28no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—148no—
782C22⋊C4—284no—
783C22⋊C4—284no—
784C42—44no—
785C42—284no—
786C2×C7—44no—
787C2×C7#230811yescharacteristic
788C2×C7#232911yescharacteristic
789C2×C7#233211yescharacteristic
790C2×C7Q8×C22⋊C411yescharacteristic
791C2×C7#234111yescharacteristic
792C2×C7#236811yescharacteristic
793C2×C7#237811yescharacteristic
794C2×C7#272811yescharacteristic
795C2×C7#272811yescharacteristic
796C2×C7#272911yescharacteristic
797C2×C7#272911yescharacteristic
798C2×C7#273011yescharacteristic
799C2×C7#273011yescharacteristic
800C2×C7#273211yescharacteristic
801C2×C7#273211yescharacteristic
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23C4×Dic1414yes—
837C23C22×Dic1411yescharacteristic
838C23C22×C4×D711yescharacteristic
839C23C2×#115711yescharacteristic
840C23C2×D4×D711yescharacteristic
841C23C2×D4×D711yescharacteristic
842C23C2×#115911yescharacteristic
843C23#654811yescharacteristic
844C23#654811yescharacteristic
845C23#654811yescharacteristic
846C23D7×#4111yescharacteristic
847C23#655311yescharacteristic
848C23#655311yescharacteristic
849C23#655411yescharacteristic
850C23#655411yescharacteristic
851C23#655411yescharacteristic
852Q8—2816no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—74no—
895C2×C4—74no—
896C2×C4—142no—
897C2×C4—142no—
898C2×C4—142no—
899C2×C4—142no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—142no—
917C2×C4—2816no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4—281no—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4—281no—
927C2×C4—281no—
928C2×C4—281no—
929C2×C4—281no—
930C2×C4—281no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4—281no—
939C2×C4—281no—
940C2×C4—281no—
941C2×C4—281no—
942C2×C4—281no—
943C2×C4—281no—
944C2×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4—281no—
950C2×C4—281no—
951C2×C4D7×C22⋊C414yes—
952C7#1444911yescharacteristic, complemented, Sylow
953C22—24no—
954C22—24no—
955C22—24no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22C2×C4×Dic1411yescharacteristic
969C22#9017411yescharacteristic
970C22C2×D7×C22⋊C411yescharacteristic
971C22#9018611yescharacteristic
972C22#9020711yescharacteristic
973C22#9021011yescharacteristic
974C22#9021811yescharacteristic
975C22C4×#115911yescharacteristic
976C22D4×Dic1411yescharacteristic
977C22D4×Dic1411yescharacteristic
978C22#9023011yescharacteristic
979C22#9023411yescharacteristic
980C22#9023611yescharacteristic
981C22#9023611yescharacteristic
982C22#9023711yescharacteristic
983C22#9024311yescharacteristic
984C22#9024311yescharacteristic
985C22#9025111yescharacteristic
986C22#9025511yescharacteristic
987C22#9028011yescharacteristic
988C22#9028911yescharacteristic
989C22#9029011yescharacteristic
990C22#9029311yescharacteristic
991C22#9029611yescharacteristic
992C22#9029611yescharacteristic
993C22#9031211yescharacteristic
994C22#9034211yescharacteristic
995C22#9034411yescharacteristic
996C22#9035111yescharacteristic
997C22#9036811yescharacteristic
998C22#9037311yescharacteristic
999C22#9037511yescharacteristic
1000C22#9040111yescharacteristic
1001C22#9040311yescharacteristic
1002C22#9040911yescharacteristic
1003C4—24no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—81no—
1009C4—144no—
1010C4—144no—
1011C4—282no—
1012C4—282no—
1013C4—282no—
1014C4—561no—
1015C4—561no—
1016C4—561no—
1017C2—44no—
1018C2#1173089211yescharacteristic
1019C2C22⋊C4×Dic1411yescharacteristic
1020C2#1173091911yescharacteristic
1021C2#1173227211yescharacteristic
1022C2#1173227511yescharacteristic
1023C2#1173231911yescharacteristic
1024C2#1173290811yescharacteristic
1025C2#1173293711yescharacteristic
1026C2#1173315011yescharacteristic
1027C2#1173315111yescharacteristic
1028C2#1173315211yescharacteristic
1029C2#1173315311yescharacteristic
1030C2#1173374611yescharacteristic
1031C2#1173384511yescharacteristic
1032C2#1173384611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1437C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1437D7
hypocenterC7#14449
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#89701C2semidirect
3. C2×#89418C2semidirect
10. #11729290C2semidirect
11. #11727175C2semidirect
12. #11727175C2semidirect
13. #11727165C2semidirect
14. #11727164C2semidirect
15. #11727161C2semidirect
33. C2×#6441C4semidirect
94. C2×C7×C22⋊C4Q8semidirect
288. C2×Dic14C22⋊C4semidirect
553. C2×C22⋊C4Dic14semidirect
952. C7#14449semidirect

Maximal subgroups

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

subgroupindex
C22×#64412
C2×#897012
C2×#894182
C7×#14372
#117293012
#117293002
#117292992
#117292982
#117292902
#117271752
#117271652
#117271642
#117271612
#144497