Finite Group Databasebeta

← #13285524

Subgroups — #13285524

Order 1792.

1578 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89982C211yesmaximal, characteristic
3C2×#89705C211yesmaximal, characteristic, complemented
4C2×#89429C211yesmaximal, characteristic, complemented
5#11729881C211yesmaximal, characteristic
6#11729301C211yesmaximal, characteristic
7#11729301C211yesmaximal, characteristic
8#11729300C211yesmaximal, characteristic
9#11729300C211yesmaximal, characteristic
10#11729290C211yesmaximal, characteristic, complemented
11#11729290C211yesmaximal, characteristic, complemented
12#11729289C211yesmaximal, characteristic, complemented
13#11727171C211yesmaximal, characteristic, complemented
14#11727168C211yesmaximal, characteristic, complemented
15#11727166C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
31C4×C7×C22⋊C4—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34#89982—24no—
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
53#89705—24no—
54#89429—24no—
55#14744—71nomaximal, Sylow
56C25×C7C2311yescharacteristic
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—41no—
63C23×C4×C7—41no—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4Q814yes—
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—41no—
89C2×C42×C7—41no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—41no—
99C2×C22⋊Dic7—41no—
100C2×C22⋊Dic7—41no—
101C2×C22⋊Dic7—41no—
102C2×C4⋊Dic7—22no—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—41no—
106C2×C4⋊Dic7—41no—
107C2×C4⋊Dic7—41no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—41no—
117C2×Dic7⋊C4—41no—
118C2×Dic7⋊C4—41no—
119C2×Dic7⋊C4D414yes—
120C7×#95—22no—
121C7×#95D414yes—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C2×#398—71no—
141C2×#387—71no—
142C2×#385—71no—
143C2×C4×C22⋊C4D711yescharacteristic
144#1443—71no—
145#1442—71no—
146#1442—71no—
147#1439—71no—
148#1439—71no—
149#1439—71no—
150#1439—71no—
151#1436—71no—
152#1436—71no—
153C4⋊#95—71no—
154C22⋊#95—71no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7C2×Q812yes—
168C24×C7#4112yes—
169C24×C7#4112yes—
170C24×C7C2411yescharacteristic
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—28no—
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—44no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7—44no—
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×Q812yes—
215C22×C4×C7C2×Q812yes—
216C22×C4×C7#4112yes—
217C22×C4×C7#4112yes—
218C22×C4×C7#4112yes—
219C22×C4×C7#4112yes—
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—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—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7C2×D412yes—
273C22×Dic7C2×D412yes—
274C22×Dic7#4112yes—
275C22×Dic7#4112yes—
276C7×C22⋊C4—28no—
277C7×C22⋊C4—28no—
278C42×C7—44no—
279C42×C7—44no—
280C22⋊Dic7—28no—
281C22⋊Dic7—44no—
282C22⋊Dic7—44no—
283C22⋊Dic7—44no—
284C4⋊Dic7—44no—
285C4⋊Dic7—44no—
286Dic7⋊C4—28no—
287Dic7⋊C4—44no—
288Dic7⋊C4—44no—
289Dic7⋊C4—44no—
290C24×C4C2×D711yescharacteristic
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4—71no—
300C22×C22⋊C4—71no—
301C22×C22⋊C4C2×D711yescharacteristic
302C22×C22⋊C4C2×D711yescharacteristic
303C22×C42C2×D711yescharacteristic
304C22×C42C2×D711yescharacteristic
305#398—144no—
306#387—144no—
307#385—144no—
308C4×C22⋊C4—24no—
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×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95C2×D711yescharacteristic
328C2×#95C2×D711yescharacteristic
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—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
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×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7#12514yes—
364C23×C7C22×D411yescharacteristic
365C23×C7C22×D411yescharacteristic
366C23×C7C22×Q811yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7H(5,𝔽2)11yescharacteristic
376C23×C7H(5,𝔽2)11yescharacteristic
377C23×C7H(5,𝔽2)11yescharacteristic
378C23×C72−1+411yescharacteristic
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—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
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—416no—
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×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×C7C22⋊Q814yes—
421C2×C4×C7#12314yes—
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—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—
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—
478C25C22×D711yescharacteristic
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C2×C4⋊C4—74no—
501C2×C4⋊C4—142no—
502C2×C4⋊C4—142no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—142no—
506C2×C4⋊C4—142no—
507C2×C4⋊C4—142no—
508C2×C4⋊C4—142no—
509C2×C4⋊C4—142no—
510C2×C4⋊C4—142no—
511C2×C4⋊C4—142no—
512C2×C4⋊C4—281no—
513C2×C4⋊C4—281no—
514C2×C4⋊C4—281no—
515C2×C4⋊C4—281no—
516C2×C4⋊C4—281no—
517C2×C4⋊C4—281no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—142no—
525C2×C22⋊C4—142no—
526C2×C22⋊C4—142no—
527C2×C22⋊C4—142no—
528C2×C22⋊C4—142no—
529C2×C22⋊C4—142no—
530C2×C22⋊C4—142no—
531C2×C22⋊C4—281no—
532C2×C22⋊C4—281no—
533C2×C22⋊C4—281no—
534C2×C22⋊C4—281no—
535C2×C22⋊C4Dic1414yes—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—41no—
541C2×C42—41no—
542#95—22no—
543#95—142no—
544#95—142no—
545#95—142no—
546#95—142no—
547#95—142no—
548#95—142no—
549#95—142no—
550#95—142no—
551#95—142no—
552#95—142no—
553#95—142no—
554#95—142no—
555#95—142no—
556#95—142no—
557#95—281no—
558#95—281no—
559#95—281no—
560#95—281no—
561#95C22⋊D714yes—
562C22×C7—24no—
563C22×C7—24no—
564C22×C7—24no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7C2×C22⋊Q811yescharacteristic
578C22×C7C2×#12311yescharacteristic
579C22×C7#52511yescharacteristic
580C22×C7#52511yescharacteristic
581C22×C7#52511yescharacteristic
582C22×C7C2×#12511yescharacteristic
583C22×C7#52911yescharacteristic
584C22×C7#52911yescharacteristic
585C22×C7#52911yescharacteristic
586C22×C7#52911yescharacteristic
587C22×C7#52911yescharacteristic
588C22×C7#53211yescharacteristic
589C22×C7#53311yescharacteristic
590C22×C7#53811yescharacteristic
591C22×C7#53811yescharacteristic
592C22×C7#53811yescharacteristic
593C22×C7#53911yescharacteristic
594C22×C7#54211yescharacteristic
595C22×C7#54211yescharacteristic
596C22×C7D4211yescharacteristic
597C22×C7#54611yescharacteristic
598C22×C7#54611yescharacteristic
599C22×C7#54611yescharacteristic
600C22×C7#54811yescharacteristic
601C22×C7D4×Q811yescharacteristic
602C22×C7#55011yescharacteristic
603C22×C7#55111yescharacteristic
604C22×C7#55111yescharacteristic
605C22×C7#55211yescharacteristic
606C22×C7#55211yescharacteristic
607C22×C7#55311yescharacteristic
608C22×C7#55311yescharacteristic
609C22×C7#55411yescharacteristic
610C22×C7#55411yescharacteristic
611C22×C7#55411yescharacteristic
612C4×C7—24no—
613C4×C7—24no—
614C4×C7—42no—
615C4×C7—42no—
616C4×C7—42no—
617C4×C7—42no—
618Dic7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—81no—
623Dic7—81no—
624Dic7—81no—
625Dic7—81no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24C2×Dic1412yes—
639C24#115712yes—
640C24#115712yes—
641C24C23×D711yescharacteristic
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—28no—
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—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
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—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×C4C2×Dic1412yes—
738C22×C4C2×Dic1412yes—
739C22×C4#115712yes—
740C22×C4#115712yes—
741C22×C4#115712yes—
742C22×C4D4×D712yes—
743C22×C4#115912yes—
744C22×C4C2×C22⋊D712yes—
745C22×C4C2×C22⋊D712yes—
746C22×C4C2×C22⋊D712yes—
747C4⋊C4—148no—
748C4⋊C4—284no—
749C4⋊C4—284no—
750C4⋊C4—284no—
751C4⋊C4—284no—
752C4⋊C4—284no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—148no—
756C22⋊C4—284no—
757C22⋊C4—284no—
758C22⋊C4—284no—
759C42—44no—
760C42—44no—
761C2×C7—44no—
762C2×C7#239511yescharacteristic
763C2×C7#241811yescharacteristic
764C2×C7#242311yescharacteristic
765C2×C7#245011yescharacteristic
766C2×C7#245211yescharacteristic
767C2×C7#245611yescharacteristic
768C2×C7#246011yescharacteristic
769C2×C7#247311yescharacteristic
770C2×C7#247711yescharacteristic
771C2×C7#250511yescharacteristic
772C2×C7#251511yescharacteristic
773C2×C7#255411yescharacteristic
774C2×C7#258711yescharacteristic
775C2×C7#265311yescharacteristic
776C2×C7#285111yescharacteristic
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23#643314yes—
812C23C22×Dic1411yescharacteristic
813C23C2×#115711yescharacteristic
814C23C2×#115711yescharacteristic
815C23C2×#115711yescharacteristic
816C23C2×#115711yescharacteristic
817C23C2×#115711yescharacteristic
818C23C2×D4×D711yescharacteristic
819C23C2×#115911yescharacteristic
820C23#654811yescharacteristic
821C23#654811yescharacteristic
822C23D7×#4111yescharacteristic
823C23D7×#4111yescharacteristic
824C23#655311yescharacteristic
825C23#655411yescharacteristic
826C23C22×C22⋊D711yescharacteristic
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
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—142no—
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—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4—281no—
924C2×C4#644614yes—
925C2×C4#648714yes—
926C7#1474411yescharacteristic, complemented, Sylow
927C22—24no—
928C22—24no—
929C22—24no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22C2×#643311yescharacteristic
943C22#9016111yescharacteristic
944C22#9017011yescharacteristic
945C22#9017011yescharacteristic
946C22C2×#644611yescharacteristic
947C22#9018111yescharacteristic
948C22#9018511yescharacteristic
949C22#9018611yescharacteristic
950C22#9021811yescharacteristic
951C22#9021911yescharacteristic
952C22#9022211yescharacteristic
953C22#9022511yescharacteristic
954C22D4×Dic1411yescharacteristic
955C22#9022911yescharacteristic
956C22#9022911yescharacteristic
957C22#9023011yescharacteristic
958C22#9023011yescharacteristic
959C22#9023111yescharacteristic
960C22#9023211yescharacteristic
961C22#9023411yescharacteristic
962C22#9023811yescharacteristic
963C22#9023911yescharacteristic
964C22#9024411yescharacteristic
965C22#9024911yescharacteristic
966C22#9025111yescharacteristic
967C22#9025111yescharacteristic
968C22#9025211yescharacteristic
969C22#9025511yescharacteristic
970C22C2×#648711yescharacteristic
971C22#9048211yescharacteristic
972C22#9048211yescharacteristic
973C22D4×C22⋊D711yescharacteristic
974C22#9049711yescharacteristic
975C22#9052011yescharacteristic
976C22#9052211yescharacteristic
977C4—24no—
978C4—24no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—282no—
984C4—282no—
985C4—282no—
986C4—282no—
987C4—561no—
988C4—561no—
989C4—561no—
990C4—561no—
991C2—44no—
992C2#1173092911yescharacteristic
993C2#1173094611yescharacteristic
994C2#1173096511yescharacteristic
995C2#1173096711yescharacteristic
996C2#1173098011yescharacteristic
997C2#1173099311yescharacteristic
998C2#1173100111yescharacteristic
999C2#1173102711yescharacteristic
1000C2#1173951911yescharacteristic
1001C2#1173957311yescharacteristic
1002C2#1173972611yescharacteristic
1003C2#1173980611yescharacteristic
1004C2#1173980711yescharacteristic
1005C2#1173980911yescharacteristic
1006C2#1173981111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutator, socle, cosocleC24×C7C24
FittingC2×C4×C7×C22⋊C4C2
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#14744
LCSG ▷ C24×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#89705C2semidirect
4. C2×#89429C2semidirect
10. #11729290C2semidirect
11. #11729290C2semidirect
12. #11729289C2semidirect
13. #11727171C2semidirect
14. #11727168C2semidirect
15. #11727166C2semidirect
926. C7#14744semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#899822
C2×#897052
C2×#894292
#117298812
#117293012
#117293002
#117292902
#117292892
#117271712
#117271682
#117271662
#147447