Finite Group Databasebeta

← #13275984

Subgroups — #13275984

Order 1792.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C2×#89992C212yesmaximal
3C2×#89984C211yesmaximal, characteristic, complemented
4C22×C7⋊#95C211yesmaximal, characteristic, complemented
5C2×#89722C212yesmaximal, complemented
6#11729881C211yesmaximal, characteristic, complemented
7#11729881C211yesmaximal, characteristic, complemented
8#11729319C212yesmaximal, complemented
9#11729300C212yesmaximal, complemented
10#11729289C211yesmaximal, characteristic, complemented
11#11729288C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×Dic7C2212yes—
16C2×C4×C7×D4—28no—
17C2×C4×C7×D4C418yescomplemented
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C22⋊Dic7C2212yes—
23C22×C22⋊Dic7C2212yes—
24C22×C22⋊Dic7C2212yes—
25C22×C4⋊Dic7C2212yes—
26C22×C4⋊Dic7C2212yes—
27#89992—28no—
28#89984—24no—
29C2×C7⋊#95—24no—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2211yescharacteristic
40#89722—28no—
41#13899—71nomaximal, Sylow
42C25×C7C2311yescharacteristic
43C25×C7C2311yescharacteristic
44C22×C7×D4—24no—
45C22×C7×D4—24no—
46C22×C7×D4C2×C414yes—
47C22×C7×D4D414yes—
48C22×C7×D4Q814yes—
49C23×C4×C7—24no—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7—24no—
53C23×C4×C7—22no—
54C23×C4×C7—22no—
55C23×C4×C7—42no—
56C23×C4×C7—42no—
57C23×C4×C7C2×C414yes—
58C23×C4×C7C2×C414yescomplemented
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7—24no—
65C23×Dic7—24no—
66C23×Dic7—24no—
67C23×Dic7—24no—
68C23×Dic7—24no—
69C23×Dic7—42no—
70C23×Dic7—42no—
71C23×Dic7C2312yes—
72C23×Dic7C2312yes—
73C23×Dic7C2312yes—
74C23×Dic7C2312yes—
75C4×C7×D4—232no—
76C2×C7×C4⋊C4—24no—
77C2×C7×C4⋊C4C2×C414yescomplemented
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4C2×C414yes—
80C2×C7×C22⋊C4C2×C414yescomplemented
81C2×C7×C22⋊C4D418yes—
82C2×C42×C7—24no—
83C2×C42×C7C2×C414yescomplemented
84C2×C22⋊Dic7—24no—
85C2×C22⋊Dic7—24no—
86C2×C22⋊Dic7—24no—
87C2×C22⋊Dic7—24no—
88C2×C22⋊Dic7—24no—
89C2×C22⋊Dic7—24no—
90C2×C22⋊Dic7—24no—
91C2×C22⋊Dic7—42no—
92C2×C22⋊Dic7—42no—
93C2×C4⋊Dic7—24no—
94C2×C4⋊Dic7—24no—
95C2×C4⋊Dic7—24no—
96C2×C4⋊Dic7—24no—
97C2×C4⋊Dic7—42no—
98C2×C4⋊Dic7—42no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—22no—
102C7⋊#95—22no—
103C7⋊#95—24no—
104C7⋊#95—24no—
105C7⋊#95—22no—
106C7⋊#95—24no—
107C7⋊#95—42no—
108C7⋊#95D414yescomplemented
109C22×C4×D4D711yescharacteristic
110C2×#386—72no—
111C2×#385—72no—
112C2×#380—71no—
113C22×#95—71no—
114#1441—72no—
115#1439—72no—
116C4⋊#95—71no—
117#1434—71no—
118C22⋊#95—71no—
119C22⋊#95—71no—
120C24×C7—21no—
121C24×C7—22no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—22no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—21no—
130C24×C7—22no—
131C24×C7—21no—
132C24×C7—22no—
133C24×C7—21no—
134C24×C7C22×C412yes—
135C24×C7C22×C412yes—
136C24×C7C2×D412yes—
137C24×C7C2×D414yes—
138C24×C7C2×D412yes—
139C24×C7C2×Q812yes—
140C24×C7C2×Q812yes—
141C24×C7#4114yes—
142C24×C7C2411yescharacteristic
143C2×C7×D4—28no—
144C2×C7×D4—28no—
145C2×C7×D4—216no—
146C2×C7×D4—216no—
147C2×C7×D4C4⋊C4116yescomplemented
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—28no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—21no—
162C22×C4×C7—22no—
163C22×C4×C7—28no—
164C22×C4×C7—28no—
165C22×C4×C7—28no—
166C22×C4×C7—44no—
167C22×C4×C7—44no—
168C22×C4×C7—48no—
169C22×C4×C7—48no—
170C22×C4×C7—48no—
171C22×C4×C7—48no—
172C22×C4×C7C22×C412yes—
173C22×C4×C7C22×C412yes—
174C22×C4×C7C22×C412yes—
175C22×C4×C7C22×C412yes—
176C22×C4×C7C22×C412yes—
177C22×C4×C7C2×D414yes—
178C22×C4×C7C2×D414yes—
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×Q812yes—
182C22×C4×C7#4112yes—
183C22×Dic7—216no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—48no—
211C22×Dic7—48no—
212C22×Dic7—48no—
213C22×Dic7—48no—
214C22×Dic7—48no—
215C22×Dic7—48no—
216C22×Dic7C2×D414yes—
217C22×Dic7#4114yes—
218C7×C4⋊C4—28no—
219C7×C22⋊C4—28no—
220C7×C22⋊C4C22⋊C4116yescomplemented
221C42×C7—28no—
222C22⋊Dic7—48no—
223C22⋊Dic7—48no—
224C22⋊Dic7—48no—
225C4⋊Dic7—48no—
226C4⋊Dic7—48no—
227C23×D4C2×D711yescharacteristic
228C24×C4—72no—
229C24×C4C2×D711yescharacteristic
230C24×C4C2×D711yescharacteristic
231C2×C4×D4—28no—
232C2×C4×D4Dic718yescomplemented
233C22×C4⋊C4—72no—
234C22×C4⋊C4—72no—
235C22×C4⋊C4C2×D711yescharacteristic
236C22×C22⋊C4—72no—
237C22×C22⋊C4—72no—
238C22×C22⋊C4—72no—
239C22×C22⋊C4C2×D711yescharacteristic
240C22×C22⋊C4C2×D711yescharacteristic
241C22×C42C2×D711yescharacteristic
242#386—148no—
243#385—148no—
244#380—144no—
245C2×#95—71no—
246C2×#95—71no—
247C2×#95—71no—
248C2×#95—71no—
249C2×#95—72no—
250C2×#95—72no—
251C2×#95—72no—
252C2×#95—72no—
253C2×#95—72no—
254C2×#95—72no—
255C2×#95—144no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—22no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—22no—
270C23×C7—24no—
271C23×C7—22no—
272C23×C7—24no—
273C23×C7—22no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—24no—
281C23×C7—24no—
282C23×C7—22no—
283C23×C7—24no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—24no—
287C23×C7—22no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7C2×C22⋊C414yes—
297C23×C7C2×C4⋊C414yes—
298C23×C7C2×C4⋊C414yes—
299C23×C7#11714yes—
300C23×C7#12118yes—
301C23×C7C22⋊Q818yes—
302C23×C7C23×C411yescharacteristic
303C23×C7C22×D411yescharacteristic
304C23×C7C22×D411yescharacteristic
305C23×C7C22×D412yes—
306C23×C7C22×Q811yescharacteristic
307C23×C7C2×#4112yes—
308C23×C7C2×#4111yescharacteristic
309C23×C7C2×#4112yes—
310C23×C7H(5,𝔽2)12yes—
311C23×C7H(5,𝔽2)11yescharacteristic
312C23×C72−1+411yescharacteristic
313C7×D4—232no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—24no—
327C2×C4×C7—24no—
328C2×C4×C7—24no—
329C2×C4×C7—24no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—416no—
334C2×C4×C7—416no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7C2×C22⋊C414yes—
338C2×C4×C7C2×C22⋊C414yes—
339C2×C4×C7C2×C4⋊C414yes—
340C2×C4×C7C4×D414yes—
341C2×Dic7—24no—
342C2×Dic7—24no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—24no—
347C2×Dic7—432no—
348C2×Dic7—42no—
349C2×Dic7—42no—
350C2×Dic7—42no—
351C2×Dic7—42no—
352C2×Dic7—42no—
353C2×Dic7—42no—
354C2×Dic7—42no—
355C2×Dic7—42no—
356C2×Dic7—42no—
357C2×Dic7—42no—
358C2×Dic7—42no—
359C2×Dic7—42no—
360C2×Dic7—42no—
361C2×Dic7—42no—
362C2×Dic7—42no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C25C22×D711yescharacteristic
371C25C22×D711yescharacteristic
372C22×D4—24no—
373C22×D4—24no—
374C22×D4Dic1414yes—
375C22×D4D2814yes—
376C22×D4C2×Dic714yes—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—72no—
386C23×C4—72no—
387C23×C4—72no—
388C23×C4—72no—
389C23×C4—144no—
390C23×C4—144no—
391C23×C4—144no—
392C23×C4—144no—
393C23×C4—144no—
394C23×C4—282no—
395C23×C4—282no—
396C23×C4C2×Dic714yes—
397C23×C4C2×Dic714yescomplemented
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D711yescharacteristic
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C4×D4—232no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—144no—
406C2×C4⋊C4—144no—
407C2×C4⋊C4—144no—
408C2×C4⋊C4—144no—
409C2×C4⋊C4—282no—
410C2×C4⋊C4—282no—
411C2×C4⋊C4C2×Dic714yescomplemented
412C2×C22⋊C4—24no—
413C2×C22⋊C4—144no—
414C2×C22⋊C4—144no—
415C2×C22⋊C4—144no—
416C2×C22⋊C4—144no—
417C2×C22⋊C4—144no—
418C2×C22⋊C4—144no—
419C2×C22⋊C4—144no—
420C2×C22⋊C4—282no—
421C2×C22⋊C4—282no—
422C2×C22⋊C4C2×Dic714yes—
423C2×C22⋊C4C2×Dic714yescomplemented
424C2×C22⋊C4C22⋊D718yes—
425C2×C42—24no—
426C2×C42C2×Dic714yescomplemented
427#95—74no—
428#95—144no—
429#95—144no—
430#95—144no—
431#95—142no—
432#95—142no—
433#95—142no—
434#95—144no—
435#95—144no—
436#95—282no—
437C22×C7—24no—
438C22×C7—24no—
439C22×C7—24no—
440C22×C7—24no—
441C22×C7—24no—
442C22×C7—28no—
443C22×C7—28no—
444C22×C7—28no—
445C22×C7—28no—
446C22×C7—24no—
447C22×C7—24no—
448C22×C7—24no—
449C22×C7—24no—
450C22×C7—42no—
451C22×C7—42no—
452C22×C7—42no—
453C22×C7—44no—
454C22×C7—44no—
455C22×C7—44no—
456C22×C7—44no—
457C22×C7—42no—
458C22×C7#38018yescomplemented
459C22×C7C22×C22⋊C411yescharacteristic
460C22×C7C22×C4⋊C411yescharacteristic
461C22×C7C2×#11711yescharacteristic
462C22×C7C2×C4×D411yescharacteristic
463C22×C7C4×#4111yescharacteristic
464C22×C7#51811yescharacteristic
465C22×C7#52011yescharacteristic
466C22×C7C2×#12112yes—
467C22×C7C2×C22⋊Q812yes—
468C22×C7#52512yes—
469C22×C7#52912yes—
470C22×C7#53812yes—
471C22×C7#53912yes—
472C22×C7D4212yes—
473C22×C7D4211yescharacteristic
474C22×C7#54612yes—
475C22×C7#54612yes—
476C22×C7#54612yes—
477C22×C7#54711yescharacteristic
478C22×C7#54712yes—
479C22×C7D4×Q811yescharacteristic
480C22×C7#55412yes—
481C22×C7#55411yescharacteristic
482C4×C7—24no—
483C4×C7—24no—
484C4×C7—24no—
485C4×C7—24no—
486C4×C7—42no—
487Dic7—44no—
488Dic7—44no—
489Dic7—82no—
490Dic7—82no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—21no—
504C24—22no—
505C24C2×Dic1412yes—
506C24C2×Dic1412yes—
507C24C2×D2812yes—
508C24C2×D2812yes—
509C24#115714yes—
510C24C22×Dic712yes—
511C24C22×Dic712yes—
512C24C2×C22⋊D714yes—
513C24C23×D711yescharacteristic
514C2×D4—216no—
515C2×D4—28no—
516C2×D4—216no—
517C2×D4—28no—
518C2×D4C4⋊Dic7116yescomplemented
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—28no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—74no—
544C22×C4—74no—
545C22×C4—1416no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—288no—
573C22×C4—288no—
574C22×C4—288no—
575C22×C4—288no—
576C22×C4—288no—
577C22×C4—288no—
578C22×C4C2×Dic1412yes—
579C22×C4C2×D2812yes—
580C22×C4D4×D712yes—
581C22×C4#115912yes—
582C22×C4C22×Dic712yes—
583C22×C4C22×Dic712yes—
584C22×C4C22×Dic712yes—
585C22×C4C22×Dic712yes—
586C22×C4C22×Dic712yes—
587C22×C4C2×C22⋊D714yes—
588C22×C4C2×C22⋊D714yes—
589C4⋊C4—28no—
590C4⋊C4—288no—
591C4⋊C4—288no—
592C22⋊C4—28no—
593C22⋊C4—288no—
594C22⋊C4—288no—
595C22⋊C4—288no—
596C22⋊C4C22⋊Dic7116yescomplemented
597C42—28no—
598C2×C7—28no—
599C2×C7—44no—
600C2×C7C2×#38011yescharacteristic
601C2×C7#229011yescharacteristic
602C2×C7#231811yescharacteristic
603C2×C7D4×C22⋊C411yescharacteristic
604C2×C7#233911yescharacteristic
605C2×C7D4×C4⋊C411yescharacteristic
606C2×C7#234911yescharacteristic
607C2×C7#242412yes—
608C2×C7#242512yes—
609C2×C7#244912yes—
610C2×C7#245012yes—
611C23—22no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—24no—
632C23—22no—
633C23—24no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23#648718yes—
652C23C2×C4⋊Dic714yes—
653C23C2×C4⋊Dic714yes—
654C23#648914yes—
655C23#649318yes—
656C23C2×C22⋊Dic714yes—
657C23C22×Dic1411yescharacteristic
658C23C22×D2811yescharacteristic
659C23C2×#115712yes—
660C23C2×D4×D711yescharacteristic
661C23C2×#115911yescharacteristic
662C23#654812yes—
663C23D7×#4112yes—
664C23#655311yescharacteristic
665C23#655411yescharacteristic
666C23C23×Dic711yescharacteristic
667C23C22×C22⋊D712yes—
668D4—232no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—416no—
689C2×C4—416no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—144no—
693C2×C4—144no—
694C2×C4—144no—
695C2×C4—144no—
696C2×C4—144no—
697C2×C4—144no—
698C2×C4—2832no—
699C2×C4—282no—
700C2×C4—282no—
701C2×C4—282no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—282no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—282no—
711C2×C4—282no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4—282no—
719C2×C4—282no—
720C2×C4—282no—
721C2×C4C2×C4⋊Dic714yes—
722C2×C4D4×Dic714yes—
723C2×C4C2×C22⋊Dic714yes—
724C2×C4C2×C22⋊Dic714yes—
725C7#1389911yescharacteristic, complemented, Sylow
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—28no—
733C22—28no—
734C22—28no—
735C22—28no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22#8998418yescomplemented
748C22D4×Dic1411yescharacteristic
749C22#9022912yes—
750C22#9023012yes—
751C22#9023411yescharacteristic
752C22#9023812yes—
753C22D4×D2811yescharacteristic
754C22#9024512yes—
755C22#9024611yescharacteristic
756C22#9025112yes—
757C22#9025512yes—
758C22C2×#648712yes—
759C22C22×C4⋊Dic711yescharacteristic
760C22C2×#648911yescharacteristic
761C22C2×#649312yes—
762C22C2×D4×Dic711yescharacteristic
763C22#9048911yescharacteristic
764C22D4×C22⋊D712yes—
765C22#9049712yes—
766C22#9051512yes—
767C22#41×Dic711yescharacteristic
768C22#9051811yescharacteristic
769C22#9052012yes—
770C22C22×C22⋊Dic711yescharacteristic
771C4—24no—
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—284no—
777C4—284no—
778C4—562no—
779C4—562no—
780C2—28no—
781C2—44no—
782C2#1173976311yescharacteristic
783C2#1173976911yescharacteristic
784C2D4×C4⋊Dic711yescharacteristic
785C2#1173977811yescharacteristic
786C2#1173980012yes—
787C2#1173980512yes—
788C2#1173980612yes—
789C2#1173985212yes—
790C2C2×#8998411yescharacteristic
791C2D4×C22⋊Dic711yescharacteristic
792C2#1174153311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C4×C7×D4C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC22×C4×D4D7
hypocenterC7#13899
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#89984C2semidirect
4. C22×C7⋊#95C2semidirect
5. C2×#89722C2semidirect
6. #11729881C2semidirect
7. #11729881C2semidirect
8. #11729319C2semidirect
9. #11729300C2semidirect
10. #11729289C2semidirect
11. #11729288C2semidirect
17. C2×C4×C7×D4C4semidirect
58. C23×C4×C7C2×C4semidirect
77. C2×C7×C4⋊C4C2×C4semidirect
80. C2×C7×C22⋊C4C2×C4semidirect
83. C2×C42×C7C2×C4semidirect
108. C7⋊#95D4semidirect
147. C2×C7×D4C4⋊C4semidirect
220. C7×C22⋊C4C22⋊C4semidirect
232. C2×C4×D4Dic7semidirect
397. C23×C4C2×Dic7semidirect
411. C2×C4⋊C4C2×Dic7semidirect
423. C2×C22⋊C4C2×Dic7semidirect
426. C2×C42C2×Dic7semidirect
458. C22×C7#380semidirect
518. C2×D4C4⋊Dic7semidirect
596. C22⋊C4C22⋊Dic7semidirect
725. C7#13899semidirect
747. C22#89984semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C2×#899922
C2×#899842
C22×C7⋊#952
C2×#897222
#117298812
#117293192
#117293002
#117292892
#117292882
#138997