Finite Group Databasebeta

← #13275736

Subgroups — #13275736

Order 1792.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C2×#89984C211yesmaximal, characteristic
4C2×#89708C211yesmaximal, characteristic, complemented
5C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
6#11729302C212yesmaximal
7#11729299C212yesmaximal
8#11729289C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727170C212yesmaximal, complemented
11#11727155C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C22⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2212yes—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4×Dic7C2212yes—
24C4×C7×C22⋊C4C418yescomplemented
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27#89984—24no—
28#89984—24no—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89708—24no—
39C4×C4⋊Dic7—24no—
40#13875—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7C2×C414yes—
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×Dic7C2312yes—
56C23×Dic7C2312yes—
57C23×Dic7C2312yes—
58C23×Dic7C2312yes—
59C2×C7×C22⋊C4—22no—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4—22no—
62C2×C7×C22⋊C4—22no—
63C2×C7×C22⋊C4C2×C414yes—
64C2×C7×C22⋊C4C2×C414yes—
65C2×C42×C7—22no—
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7—22no—
69C2×C42×C7C2×C414yes—
70C2×C42×C7C2×C414yes—
71C2×C22⋊Dic7—24no—
72C2×C22⋊Dic7—24no—
73C2×C22⋊Dic7—24no—
74C2×C22⋊Dic7—24no—
75C2×C22⋊Dic7—42no—
76C2×C22⋊Dic7—42no—
77C2×C4⋊Dic7—22no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7D414yes—
88C2×C4⋊Dic7D414yes—
89C2×C4×Dic7—24no—
90C2×C4×Dic7—24no—
91C2×C4×Dic7—42no—
92C7×#95C2×C414yes—
93C7×#95C2×C414yes—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—42no—
101C7⋊#95—42no—
102C7⋊#95—42no—
103C2×#382—71no—
104C2×#380—71no—
105C2×#380—71no—
106C2×C4×C4⋊C4—71no—
107C2×C4×C22⋊C4D711yescharacteristic
108#1443—72no—
109#1440—72no—
110#1437—72no—
111C4⋊#95—71no—
112C4⋊#95—71no—
113#1434—72no—
114C24×C7—21no—
115C24×C7—21no—
116C24×C7—21no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7C22×C412yes—
127C24×C7#4112yes—
128C24×C7#4112yes—
129C24×C7C2411yescharacteristic
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—28no—
159C22×C4×C7—28no—
160C22×C4×C7—28no—
161C22×C4×C7—44no—
162C22×C4×C7—44no—
163C22×C4×C7—44no—
164C22×C4×C7—44no—
165C22×C4×C7C22×C412yes—
166C22×C4×C7C22×C412yes—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C22×C412yes—
170C22×C4×C7C22×C412yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D412yes—
173C22×C4×C7#4112yes—
174C22×C4×C7#4112yes—
175C22×C4×C7#4112yes—
176C22×C4×C7#4112yes—
177C22×C4×C7#4112yes—
178C22×C4×C7#4112yes—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
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×Dic7C2×D414yes—
206C22×Dic7C2×D414yes—
207C7×C22⋊C4—28no—
208C7×C22⋊C4—28no—
209C42×C7—28no—
210C42×C7—28no—
211C22⋊Dic7—48no—
212C22⋊Dic7—48no—
213C4⋊Dic7—28no—
214C4⋊Dic7—28no—
215C4⋊Dic7—44no—
216C4⋊Dic7—44no—
217C4×Dic7—48no—
218C24×C4C2×D711yescharacteristic
219C22×C4⋊C4—71no—
220C22×C4⋊C4—71no—
221C22×C4⋊C4—71no—
222C22×C4⋊C4—71no—
223C22×C22⋊C4—72no—
224C22×C22⋊C4—72no—
225C22×C22⋊C4C2×D711yescharacteristic
226C22×C22⋊C4C2×D711yescharacteristic
227C22×C42—72no—
228C22×C42C2×D711yescharacteristic
229C22×C42C2×D711yescharacteristic
230#382—144no—
231#380—144no—
232#380—144no—
233C4×C4⋊C4—144no—
234C4×C22⋊C4Dic718yescomplemented
235C2×#95—72no—
236C2×#95—72no—
237C2×#95—72no—
238C2×#95—72no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95C2×D711yescharacteristic
245C2×#95C2×D711yescharacteristic
246C23×C7—22no—
247C23×C7—22no—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—41no—
265C23×C7—41no—
266C23×C7—41no—
267C23×C7—41no—
268C23×C7—41no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7#11714yes—
281C23×C7C23×C411yescharacteristic
282C23×C7C22×D411yescharacteristic
283C23×C7C22×D411yescharacteristic
284C23×C7C2×#4111yescharacteristic
285C23×C7C2×#4111yescharacteristic
286C23×C7C2×#4111yescharacteristic
287C23×C7C2×#4111yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7H(5,𝔽2)11yescharacteristic
293C23×C7H(5,𝔽2)11yescharacteristic
294C23×C72−1+411yescharacteristic
295C23×C72−1+411yescharacteristic
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—416no—
331C2×C4×C7#11714yes—
332C2×C4×C7#11714yes—
333C2×C4×C7C4×D414yes—
334C2×C4×C7C4×D414yes—
335C2×C4×C7#12114yes—
336C2×C4×C7#12314yes—
337C2×C4×C7#12414yes—
338C2×C4×C7#12614yes—
339C2×Dic7—24no—
340C2×Dic7—24no—
341C2×Dic7—24no—
342C2×Dic7—24no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—42no—
346C2×Dic7—42no—
347C2×Dic7—42no—
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—
367C25C22×D711yescharacteristic
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—72no—
375C23×C4—72no—
376C23×C4—72no—
377C23×C4—72no—
378C23×C4C2×Dic714yes—
379C23×C4C22×D711yescharacteristic
380C23×C4C22×D711yescharacteristic
381C23×C4C22×D711yescharacteristic
382C23×C4C22×D711yescharacteristic
383C23×C4C22×D711yescharacteristic
384C23×C4C22×D711yescharacteristic
385C2×C4⋊C4—74no—
386C2×C4⋊C4—74no—
387C2×C4⋊C4—142no—
388C2×C4⋊C4—142no—
389C2×C4⋊C4—142no—
390C2×C4⋊C4—142no—
391C2×C4⋊C4—142no—
392C2×C4⋊C4—142no—
393C2×C4⋊C4—142no—
394C2×C4⋊C4—142no—
395C2×C4⋊C4—142no—
396C2×C4⋊C4—142no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—144no—
402C2×C22⋊C4—144no—
403C2×C22⋊C4—144no—
404C2×C22⋊C4—144no—
405C2×C22⋊C4—282no—
406C2×C22⋊C4—282no—
407C2×C22⋊C4C2×Dic714yes—
408C2×C22⋊C4C2×Dic714yes—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—144no—
414C2×C42—144no—
415C2×C42—282no—
416C2×C42C2×Dic714yes—
417C2×C42C2×Dic714yes—
418#95—144no—
419#95—144no—
420#95—144no—
421#95—144no—
422#95—144no—
423#95—144no—
424#95—282no—
425#95—282no—
426#95—282no—
427#95C2×Dic714yes—
428#95C2×Dic714yes—
429C22×C7—24no—
430C22×C7—24no—
431C22×C7—24no—
432C22×C7—42no—
433C22×C7—42no—
434C22×C7—42no—
435C22×C7—42no—
436C22×C7—42no—
437C22×C7—42no—
438C22×C7—42no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—42no—
443C22×C7—42no—
444C22×C7C2×#11711yescharacteristic
445C22×C7C2×#11711yescharacteristic
446C22×C7C2×#11711yescharacteristic
447C22×C7C2×C4×D411yescharacteristic
448C22×C7C2×C4×D411yescharacteristic
449C22×C7#52011yescharacteristic
450C22×C7#52011yescharacteristic
451C22×C7C2×#12111yescharacteristic
452C22×C7C2×#12311yescharacteristic
453C22×C7C2×#12411yescharacteristic
454C22×C7C2×#12611yescharacteristic
455C22×C7#52911yescharacteristic
456C22×C7#52911yescharacteristic
457C22×C7#52911yescharacteristic
458C22×C7#52911yescharacteristic
459C22×C7#54011yescharacteristic
460C22×C7#54111yescharacteristic
461C22×C7#54211yescharacteristic
462C22×C7#54211yescharacteristic
463C22×C7#54611yescharacteristic
464C22×C7#54611yescharacteristic
465C22×C7#54611yescharacteristic
466C22×C7#54711yescharacteristic
467C22×C7#54811yescharacteristic
468C22×C7#54811yescharacteristic
469C22×C7#54811yescharacteristic
470C22×C7#55011yescharacteristic
471C22×C7#55211yescharacteristic
472C22×C7#55211yescharacteristic
473C22×C7#55211yescharacteristic
474C22×C7#55311yescharacteristic
475C22×C7#55311yescharacteristic
476C22×C7#55311yescharacteristic
477C22×C7#55511yescharacteristic
478C22×C7#55611yescharacteristic
479C4×C7—24no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—42no—
483C4×C7—42no—
484C4×C7#38818yes—
485Dic7—44no—
486Dic7—44no—
487Dic7—82no—
488Dic7—82no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24#115712yes—
502C24#115712yes—
503C24C22×Dic712yes—
504C24C23×D711yescharacteristic
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—74no—
541C22×C4—74no—
542C22×C4—142no—
543C22×C4—142no—
544C22×C4—142no—
545C22×C4—142no—
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#115712yes—
569C22×C4#115712yes—
570C22×C4#115712yes—
571C22×C4#115712yes—
572C22×C4D4×D712yes—
573C22×C4D4×D712yes—
574C22×C4#115912yes—
575C22×C4#115912yes—
576C22×C4C22×Dic712yes—
577C22×C4C22×Dic712yes—
578C22×C4C22×Dic712yes—
579C22×C4C22×Dic712yes—
580C22×C4C22×Dic712yes—
581C22×C4C22×Dic712yes—
582C4⋊C4—148no—
583C4⋊C4—148no—
584C4⋊C4—284no—
585C4⋊C4—284no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—288no—
589C22⋊C4—288no—
590C42—28no—
591C42—28no—
592C42—288no—
593C2×C7—44no—
594C2×C7#228311yescharacteristic
595C2×C7C2×#38811yescharacteristic
596C2×C7#231411yescharacteristic
597C2×C7#235211yescharacteristic
598C2×C7#235211yescharacteristic
599C2×C7#235211yescharacteristic
600C2×C7#235411yescharacteristic
601C2×C7#242011yescharacteristic
602C2×C7#242111yescharacteristic
603C2×C7#242611yescharacteristic
604C2×C7#242711yescharacteristic
605C2×C7#248911yescharacteristic
606C2×C7#249011yescharacteristic
607C2×C7#249411yescharacteristic
608C2×C7#249511yescharacteristic
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23#648914yes—
644C23C2×#115711yescharacteristic
645C23C2×#115711yescharacteristic
646C23C2×#115711yescharacteristic
647C23C2×#115711yescharacteristic
648C23C2×#115711yescharacteristic
649C23C2×#115711yescharacteristic
650C23C2×D4×D711yescharacteristic
651C23C2×D4×D711yescharacteristic
652C23C2×#115911yescharacteristic
653C23C2×#115911yescharacteristic
654C23#655311yescharacteristic
655C23#655311yescharacteristic
656C23#655411yescharacteristic
657C23#655411yescharacteristic
658C23C23×Dic711yescharacteristic
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—416no—
694C2×C4—144no—
695C2×C4—144no—
696C2×C4—144no—
697C2×C4—144no—
698C2×C4—144no—
699C2×C4—144no—
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×C4—282no—
722C2×C4#644214yes—
723C2×C4#644614yes—
724C2×C4#644714yes—
725C2×C4#644814yes—
726C2×C4#648914yes—
727C2×C4#648914yes—
728C2×C4D4×Dic714yes—
729C2×C4D4×Dic714yes—
730C7#1387511yescharacteristic, complemented, Sylow
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22#9017011yescharacteristic
747C22#9017011yescharacteristic
748C22#9017011yescharacteristic
749C22#9017011yescharacteristic
750C22C2×#644211yescharacteristic
751C22C2×#644611yescharacteristic
752C22C2×#644711yescharacteristic
753C22C2×#644811yescharacteristic
754C22#9020911yescharacteristic
755C22#9022511yescharacteristic
756C22#9022511yescharacteristic
757C22#9022611yescharacteristic
758C22#9023211yescharacteristic
759C22#9023211yescharacteristic
760C22#9023211yescharacteristic
761C22#9023311yescharacteristic
762C22#9024111yescharacteristic
763C22#9024111yescharacteristic
764C22#9024111yescharacteristic
765C22#9024211yescharacteristic
766C22#9024311yescharacteristic
767C22#9024311yescharacteristic
768C22#9024311yescharacteristic
769C22#9024411yescharacteristic
770C22#9025411yescharacteristic
771C22#9025611yescharacteristic
772C22#9025611yescharacteristic
773C22#9025611yescharacteristic
774C22C2×#648911yescharacteristic
775C22C2×#648911yescharacteristic
776C22C2×#648911yescharacteristic
777C22C2×D4×Dic711yescharacteristic
778C22C2×D4×Dic711yescharacteristic
779C22#9051811yescharacteristic
780C22#9051811yescharacteristic
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—284no—
787C4—284no—
788C4—562no—
789C4—562no—
790C4#8972318yes—
791C2—44no—
792C2#1173092811yescharacteristic
793C2#1173093011yescharacteristic
794C2#1173093111yescharacteristic
795C2#1173095011yescharacteristic
796C2#1173095111yescharacteristic
797C2#1173095511yescharacteristic
798C2#1173095611yescharacteristic
799C2#1173102911yescharacteristic
800C2#1173950511yescharacteristic
801C2C2×#8972311yescharacteristic
802C2#1173967611yescharacteristic
803C2#1173978011yescharacteristic
804C2#1173978011yescharacteristic
805C2#1173978011yescharacteristic
806C2#1173978211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#13875
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#89708C2semidirect
5. C2×C4×C4⋊Dic7C2semidirect
8. #11729289C2semidirect
9. #11729289C2semidirect
10. #11727170C2semidirect
11. #11727155C2semidirect
24. C4×C7×C22⋊C4C4semidirect
234. C4×C22⋊C4Dic7semidirect
730. C7#13875semidirect

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×#899842
C2×#897082
C2×C4×C4⋊Dic72
#117293022
#117292992
#117292892
#117271702
#117271552
#138757