Finite Group Databasebeta

← #13275737

Subgroups — #13275737

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×#89759C211yesmaximal, characteristic
2C2×#89759C211yesmaximal, characteristic
3C2×#89749C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
6C7×C4⋊#95C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11727183C212yesmaximal
9#11727171C212yesmaximal, complemented
10#11727162C212yesmaximal
11#11727155C212yesmaximal, complemented
12C23×C4×D7C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×(C2×D7)⋊C4C2212yes—
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4×Dic7C2212yes—
23C22×C4×Dic7C2211yescharacteristic
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
35#89759—24no—
36#89759—24no—
37#89749—24no—
38C4×(C2×D7)⋊C4C418yescomplemented
39C4×C4⋊Dic7—24no—
40#13875—71nomaximal, Sylow
41C24×D7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2312yes—
51C23×Dic7C2312yes—
52C22×C4×D7—22no—
53C22×C4×D7—22no—
54C22×C4×D7—22no—
55C22×C4×D7—22no—
56C22×C4×D7—22no—
57C22×C4×D7—22no—
58C22×C4×D7C2×C414yes—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C42×C7—22no—
66C2×C42×C7—22no—
67C2×C42×C7C2×C414yes—
68C2×(C2×D7)⋊C4—22no—
69C2×(C2×D7)⋊C4—22no—
70C2×(C2×D7)⋊C4—22no—
71C2×(C2×D7)⋊C4—22no—
72C2×(C2×D7)⋊C4—24no—
73C2×(C2×D7)⋊C4—24no—
74C2×(C2×D7)⋊C4—24no—
75C2×(C2×D7)⋊C4—24no—
76C2×(C2×D7)⋊C4—42no—
77C2×(C2×D7)⋊C4—42no—
78C2×(C2×D7)⋊C4C2×C414yes—
79C2×(C2×D7)⋊C4C2×C414yes—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7D414yes—
85C2×C4⋊Dic7D414yes—
86C2×C4×Dic7—22no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—24no—
89C2×C4×Dic7—24no—
90C2×C4×Dic7—42no—
91C2×C4×Dic7C2×C414yes—
92C7×#95—24no—
93C7×#95—42no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—42no—
100C7⋊#95—42no—
101C7⋊#95C2×C414yes—
102C7⋊#95C2×C414yes—
103C2×#382—71no—
104C2×#380—71no—
105C2×#380—71no—
106C2×C4×C4⋊C4—71no—
107C2×C4×C22⋊C4—71no—
108#1443—72no—
109#1440—72no—
110#1437—72no—
111C4⋊#95—71no—
112C4⋊#95D711yescharacteristic, complemented
113#1434—72no—
114C24×C7C2411yescharacteristic
115C23×D7—21no—
116C23×D7—21no—
117C23×D7—21no—
118C23×D7—21no—
119C23×D7—21no—
120C23×D7—21no—
121C23×D7—21no—
122C23×D7—21no—
123C23×D7—21no—
124C23×D7—21no—
125C23×D7—21no—
126C23×D7—21no—
127C23×D7C22×C412yes—
128C23×D7#4112yes—
129C23×D7#4112yes—
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—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7C22×C412yes—
155C22×C4×C7C22×C412yes—
156C22×C4×C7C22×C412yes—
157C22×C4×C7C2×D412yes—
158C22×C4×C7C2×D412yes—
159C22×C4×C7#4112yes—
160C22×C4×C7#4112yes—
161C22×C4×C7#4112yes—
162C22×C4×C7#4112yes—
163C22×C4×C7#4112yes—
164C22×C4×C7#4112yes—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—22no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—22no—
195C22×Dic7C22×C412yes—
196C22×Dic7C22×C412yes—
197C22×Dic7C22×C412yes—
198C22×Dic7C2×D414yes—
199C22×Dic7C2×D414yes—
200C2×C4×D7—28no—
201C2×C4×D7—28no—
202C2×C4×D7—28no—
203C2×C4×D7—44no—
204C2×C4×D7—44no—
205C2×C4×D7—44no—
206C2×C4×D7—44no—
207C7×C4⋊C4—44no—
208C7×C4⋊C4—44no—
209C42×C7—28no—
210(C2×D7)⋊C4—28no—
211(C2×D7)⋊C4—28no—
212(C2×D7)⋊C4—48no—
213(C2×D7)⋊C4—48no—
214C4⋊Dic7—28no—
215C4⋊Dic7—28no—
216C4×Dic7—28no—
217C4×Dic7—48no—
218C24×C4—71no—
219C22×C4⋊C4—71no—
220C22×C4⋊C4—71no—
221C22×C4⋊C4C2×D711yescharacteristic
222C22×C4⋊C4C2×D711yescharacteristic
223C22×C22⋊C4—71no—
224C22×C22⋊C4—71no—
225C22×C22⋊C4—72no—
226C22×C22⋊C4—72no—
227C22×C42—71no—
228C22×C42—72no—
229C22×C42C2×D711yescharacteristic
230#382—144no—
231#380—144no—
232#380—144no—
233C4×C4⋊C4—144no—
234C4×C22⋊C4—78no—
235C2×#95—71no—
236C2×#95—71no—
237C2×#95—72no—
238C2×#95—72no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95C2×D712yes—
245C2×#95C2×D712yes—
246C23×C7C23×C411yescharacteristic
247C23×C7C22×D411yescharacteristic
248C23×C7C22×D411yescharacteristic
249C23×C7C2×#4111yescharacteristic
250C23×C7C2×#4111yescharacteristic
251C23×C7C2×#4111yescharacteristic
252C23×C7C2×#4111yescharacteristic
253C23×C7C2×#4111yescharacteristic
254C23×C7C2×#4111yescharacteristic
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4111yescharacteristic
257C23×C7H(5,𝔽2)11yescharacteristic
258C23×C7H(5,𝔽2)11yescharacteristic
259C23×C72−1+411yescharacteristic
260C23×C72−1+411yescharacteristic
261C22×D7—22no—
262C22×D7—22no—
263C22×D7—22no—
264C22×D7—22no—
265C22×D7—22no—
266C22×D7—22no—
267C22×D7—22no—
268C22×D7—22no—
269C22×D7—22no—
270C22×D7—22no—
271C22×D7—22no—
272C22×D7—22no—
273C22×D7—22no—
274C22×D7—22no—
275C22×D7—22no—
276C22×D7—22no—
277C22×D7—22no—
278C22×D7—22no—
279C22×D7—41no—
280C22×D7—41no—
281C22×D7—41no—
282C22×D7—41no—
283C22×D7—41no—
284C22×D7—41no—
285C22×D7—41no—
286C22×D7—41no—
287C22×D7—41no—
288C22×D7—41no—
289C22×D7—41no—
290C22×D7—41no—
291C22×D7—41no—
292C22×D7—41no—
293C22×D7—41no—
294C22×D7—41no—
295C22×D7#11714yes—
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—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7#11714yes—
324C2×C4×C7#11714yes—
325C2×C4×C7C4×D414yes—
326C2×C4×C7C4×D414yes—
327C2×C4×C7#12114yes—
328C2×C4×C7#12314yes—
329C2×C4×C7#12414yes—
330C2×C4×C7#12614yes—
331C2×Dic7—22no—
332C2×Dic7—22no—
333C2×Dic7—22no—
334C2×Dic7—22no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—24no—
341C2×Dic7—24no—
342C2×Dic7—24no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—41no—
347C2×Dic7—41no—
348C2×Dic7—41no—
349C2×Dic7—41no—
350C2×Dic7—42no—
351C2×Dic7—42no—
352C2×Dic7—42no—
353C2×Dic7—42no—
354C2×Dic7—42no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—42no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—42no—
363C2×Dic7—41no—
364C2×Dic7—42no—
365C2×Dic7—41no—
366C4×D7—416no—
367C25—71no—
368C23×C4—72no—
369C23×C4—72no—
370C23×C4—71no—
371C23×C4—71no—
372C23×C4—71no—
373C23×C4—74no—
374C23×C4—142no—
375C23×C4—142no—
376C23×C4—142no—
377C23×C4—142no—
378C23×C4—142no—
379C23×C4—142no—
380C23×C4C22×D712yes—
381C23×C4C22×D712yes—
382C23×C4C22×D711yescharacteristic
383C23×C4C22×D711yescharacteristic
384C23×C4C22×D711yescharacteristic
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—74no—
392C2×C4⋊C4—74no—
393C2×C4⋊C4—142no—
394C2×C4⋊C4—142no—
395C2×C4⋊C4—142no—
396C2×C4⋊C4—142no—
397C2×C22⋊C4—74no—
398C2×C22⋊C4—74no—
399C2×C22⋊C4—142no—
400C2×C22⋊C4—142no—
401C2×C22⋊C4—142no—
402C2×C22⋊C4—142no—
403C2×C22⋊C4—144no—
404C2×C22⋊C4—144no—
405C2×C22⋊C4—144no—
406C2×C22⋊C4—144no—
407C2×C22⋊C4—282no—
408C2×C22⋊C4—282no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—74no—
412C2×C42—142no—
413C2×C42—142no—
414C2×C42—144no—
415C2×C42—144no—
416C2×C42—282no—
417C2×C42C4×D714yes—
418#95—24no—
419#95—42no—
420#95—74no—
421#95—74no—
422#95—144no—
423#95—144no—
424#95—144no—
425#95—144no—
426#95—144no—
427#95—282no—
428#95—282no—
429C22×C7C2×#11711yescharacteristic
430C22×C7C2×#11711yescharacteristic
431C22×C7C2×#11711yescharacteristic
432C22×C7C2×C4×D411yescharacteristic
433C22×C7C2×C4×D411yescharacteristic
434C22×C7#52011yescharacteristic
435C22×C7#52011yescharacteristic
436C22×C7C2×#12111yescharacteristic
437C22×C7C2×#12311yescharacteristic
438C22×C7C2×#12411yescharacteristic
439C22×C7C2×#12611yescharacteristic
440C22×C7#52911yescharacteristic
441C22×C7#52911yescharacteristic
442C22×C7#52911yescharacteristic
443C22×C7#52911yescharacteristic
444C22×C7#54011yescharacteristic
445C22×C7#54111yescharacteristic
446C22×C7#54211yescharacteristic
447C22×C7#54211yescharacteristic
448C22×C7#54611yescharacteristic
449C22×C7#54611yescharacteristic
450C22×C7#54611yescharacteristic
451C22×C7#54711yescharacteristic
452C22×C7#54811yescharacteristic
453C22×C7#54811yescharacteristic
454C22×C7#54811yescharacteristic
455C22×C7#55011yescharacteristic
456C22×C7#55211yescharacteristic
457C22×C7#55211yescharacteristic
458C22×C7#55211yescharacteristic
459C22×C7#55311yescharacteristic
460C22×C7#55311yescharacteristic
461C22×C7#55311yescharacteristic
462C22×C7#55511yescharacteristic
463C22×C7#55611yescharacteristic
464C2×D7—24no—
465C2×D7—24no—
466C2×D7—24no—
467C2×D7—42no—
468C2×D7—42no—
469C2×D7—42no—
470C2×D7—42no—
471C2×D7—42no—
472C2×D7—42no—
473C2×D7—42no—
474C2×D7—42no—
475C2×D7—42no—
476C2×D7—42no—
477C2×D7—42no—
478C2×D7—42no—
479C4×C7—24no—
480C4×C7—42no—
481C4×C7—82no—
482C4×C7—82no—
483C4×C7#38818yes—
484Dic7—42no—
485Dic7—42no—
486Dic7—44no—
487Dic7—44no—
488Dic7—42no—
489C24—72no—
490C24—72no—
491C24—72no—
492C24—141no—
493C24—141no—
494C24—141no—
495C24—141no—
496C24—141no—
497C24—141no—
498C24—141no—
499C24—141no—
500C24—141no—
501C24—141no—
502C24—141no—
503C24—141no—
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—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—72no—
530C22×C4—72no—
531C22×C4—72no—
532C22×C4—74no—
533C22×C4—74no—
534C22×C4—142no—
535C22×C4—142no—
536C22×C4—141no—
537C22×C4—141no—
538C22×C4—141no—
539C22×C4—141no—
540C22×C4—141no—
541C22×C4—141no—
542C22×C4—142no—
543C22×C4—141no—
544C22×C4—141no—
545C22×C4—141no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—141no—
549C22×C4—141no—
550C22×C4—142no—
551C22×C4—141no—
552C22×C4—142no—
553C22×C4—141no—
554C22×C4—142no—
555C22×C4—141no—
556C22×C4—141no—
557C22×C4—141no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—141no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—141no—
564C22×C4—148no—
565C22×C4—148no—
566C22×C4—148no—
567C22×C4—284no—
568C22×C4—284no—
569C22×C4—284no—
570C22×C4—284no—
571C22×C4C2×C4×D712yes—
572C22×C4C2×C4×D712yes—
573C22×C4C2×C4×D712yes—
574C22×C4#115712yes—
575C22×C4#115712yes—
576C22×C4D4×D712yes—
577C22×C4D4×D712yes—
578C22×C4#115912yes—
579C22×C4#115912yes—
580C22×C4#116112yes—
581C22×C4#116112yes—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—148no—
585C4⋊C4—148no—
586C22⋊C4—148no—
587C22⋊C4—148no—
588C22⋊C4—288no—
589C22⋊C4—288no—
590C42—28no—
591C42—148no—
592C42—288no—
593C2×C7#228311yescharacteristic
594C2×C7C2×#38811yescharacteristic
595C2×C7#231411yescharacteristic
596C2×C7#235211yescharacteristic
597C2×C7#235211yescharacteristic
598C2×C7#235211yescharacteristic
599C2×C7#235411yescharacteristic
600C2×C7#242011yescharacteristic
601C2×C7#242111yescharacteristic
602C2×C7#242611yescharacteristic
603C2×C7#242711yescharacteristic
604C2×C7#248911yescharacteristic
605C2×C7#249011yescharacteristic
606C2×C7#249411yescharacteristic
607C2×C7#249511yescharacteristic
608D7—44no—
609C23—74no—
610C23—142no—
611C23—142no—
612C23—142no—
613C23—142no—
614C23—142no—
615C23—142no—
616C23—142no—
617C23—142no—
618C23—142no—
619C23—142no—
620C23—142no—
621C23—142no—
622C23—142no—
623C23—142no—
624C23—142no—
625C23—142no—
626C23—142no—
627C23—142no—
628C23—281no—
629C23—281no—
630C23—281no—
631C23—281no—
632C23—281no—
633C23—281no—
634C23—281no—
635C23—281no—
636C23—281no—
637C23—281no—
638C23—281no—
639C23—281no—
640C23—281no—
641C23—281no—
642C23—281no—
643C23—281no—
644C23C22×C4×D711yescharacteristic
645C23C2×#115711yescharacteristic
646C23C2×#115711yescharacteristic
647C23C2×D4×D711yescharacteristic
648C23C2×D4×D711yescharacteristic
649C23C2×#115911yescharacteristic
650C23C2×#115911yescharacteristic
651C23#654811yescharacteristic
652C23C2×#116111yescharacteristic
653C23C2×#116111yescharacteristic
654C23#655111yescharacteristic
655C23D7×#4111yescharacteristic
656C23D7×#4111yescharacteristic
657C23#655311yescharacteristic
658C23#655411yescharacteristic
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—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—144no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—144no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—144no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—144no—
699C2×C4—144no—
700C2×C4—144no—
701C2×C4—281no—
702C2×C4—281no—
703C2×C4—282no—
704C2×C4—281no—
705C2×C4—281no—
706C2×C4—281no—
707C2×C4—281no—
708C2×C4—281no—
709C2×C4—282no—
710C2×C4—281no—
711C2×C4—281no—
712C2×C4—281no—
713C2×C4—281no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4—282no—
719C2×C4—282no—
720C2×C4—281no—
721C2×C4—2816no—
722C2×C4#643514yes—
723C2×C4(C22⋊D7)⋊C414yes—
724C2×C4#644714yes—
725C2×C4#644814yes—
726C2×C4#645514yes—
727C2×C4#645614yes—
728C2×C4#645714yes—
729C2×C4#646114yes—
730C7#1387511yescharacteristic, complemented, Sylow
731C22—144no—
732C22—144no—
733C22—144no—
734C22—282no—
735C22—282no—
736C22—282no—
737C22—282no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—282no—
742C22—282no—
743C22—282no—
744C22—282no—
745C22—282no—
746C22C2×#643511yescharacteristic
747C22C2×(C22⋊D7)⋊C411yescharacteristic
748C22C2×#644711yescharacteristic
749C22C2×#644811yescharacteristic
750C22C2×#645511yescharacteristic
751C22C2×#645611yescharacteristic
752C22#9019511yescharacteristic
753C22C2×#645711yescharacteristic
754C22C2×#646111yescharacteristic
755C22D7×#11711yescharacteristic
756C22#9021411yescharacteristic
757C22#9024811yescharacteristic
758C22#9024811yescharacteristic
759C22#9025211yescharacteristic
760C22#9025311yescharacteristic
761C22#9027111yescharacteristic
762C22#9027111yescharacteristic
763C22#9027311yescharacteristic
764C22#9027411yescharacteristic
765C22#9028911yescharacteristic
766C22#9030311yescharacteristic
767C22#9030511yescharacteristic
768C22#9030911yescharacteristic
769C22#9032111yescharacteristic
770C22#9032411yescharacteristic
771C22#9033011yescharacteristic
772C22#9033311yescharacteristic
773C22#9036711yescharacteristic
774C22#9036811yescharacteristic
775C22#9038511yescharacteristic
776C22#9038611yescharacteristic
777C22#9040911yescharacteristic
778C22#9041711yescharacteristic
779C22#9042311yescharacteristic
780C22#9042511yescharacteristic
781C4—24no—
782C4—42no—
783C4—82no—
784C4—82no—
785C4—284no—
786C4—282no—
787C4—282no—
788C4—284no—
789C4—282no—
790C4#8944118yes—
791C2—284no—
792C2C2×#8944111yescharacteristic
793C2#1173119711yescharacteristic
794C2#1173120511yescharacteristic
795C2#1173132811yescharacteristic
796C2#1173145711yescharacteristic
797C2#1173167411yescharacteristic
798C2#1173176911yescharacteristic
799C2#1173365811yescharacteristic
800C2#1173365911yescharacteristic
801C2#1173367811yescharacteristic
802C2#1173368011yescharacteristic
803C2#1173388811yescharacteristic
804C2#1173389411yescharacteristic
805C2#1173406911yescharacteristic
806C2#1173407511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC4⋊#95D7
hypocenterC7#13875
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#89749C2semidirect
4. C2×C4×C4⋊Dic7C2semidirect
6. C7×C4⋊#95C2semidirect
7. #11729317C2semidirect
9. #11727171C2semidirect
11. #11727155C2semidirect
38. C4×(C2×D7)⋊C4C4semidirect
112. C4⋊#95D7semidirect
730. C7#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#897592
C2×#897492
C2×C4×C4⋊Dic72
C2×C4×(C2×D7)⋊C42
C7×C4⋊#952
#117293172
#117271832
#117271712
#117271622
#117271552
#138757