Finite Group Databasebeta

← #13276343

Subgroups — #13276343

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
3C2×#89729C212yesmaximal
4C2×#89422C211yesmaximal, characteristic, complemented
5C7×#1439C211yesmaximal, characteristic, complemented
6#11729324C211yesmaximal, characteristic, complemented
7#11729300C211yesmaximal, characteristic, complemented
8#11729298C212yesmaximal, complemented
9#11727181C211yesmaximal, characteristic, complemented
10(C2×D7)⋊#95C212yesmaximal, complemented
11Dic7⋊#95C212yesmaximal, complemented
12C23×C22⋊D7C2211yescharacteristic
13C24×Dic7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C22⋊C4C2212yes—
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic7C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4C2212yes—
24C22×Dic7⋊C4C2211yescharacteristic
25C22×C4×Dic7C2212yes—
26C22×C4×Dic7C2211yescharacteristic
27C2×(C22⋊D7)⋊C4—24no—
28C2×(C22⋊D7)⋊C4—24no—
29C2×(C22⋊D7)⋊C4C418yescomplemented
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C4⋊C4×Dic7—24no—
39#89729—28no—
40#89422—24no—
41#13941—71nomaximal, Sylow
42C25×C7C2311yescharacteristic
43C24×D7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2312yes—
47C23×C4×C7C2311yescharacteristic
48C22×C22⋊D7—22no—
49C22×C22⋊D7—22no—
50C22×C22⋊D7—22no—
51C22×C22⋊D7—22no—
52C22×C22⋊D7C2×C414yes—
53C22×C22⋊D7D414yes—
54C22×C22⋊D7Q814yes—
55C23×Dic7—22no—
56C23×Dic7—22no—
57C23×Dic7—42no—
58C23×Dic7—42no—
59C23×Dic7C2×C414yes—
60C23×Dic7C2312yes—
61C23×Dic7C2311yescharacteristic
62C23×Dic7C2312yes—
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C22×C4×D7—22no—
66C22×C4×D7—22no—
67C22×C4×D7—42no—
68C22×C4×D7—42no—
69C22×C4×D7C2×C414yes—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—42no—
77C2×C7×C22⋊C4C2×C414yes—
78C2×C22⋊Dic7—24no—
79C2×C22⋊Dic7—24no—
80C2×C22⋊Dic7—42no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—24no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—24no—
86C2×(C2×D7)⋊C4—24no—
87C2×(C2×D7)⋊C4—42no—
88C2×(C2×D7)⋊C4—42no—
89C2×(C2×D7)⋊C4C2×C414yes—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—24no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—24no—
95C2×Dic7⋊C4—24no—
96C2×Dic7⋊C4—24no—
97C2×Dic7⋊C4C2×C414yes—
98C2×C4×Dic7—24no—
99C2×C4×Dic7—24no—
100C2×C4×Dic7—24no—
101C2×C4×Dic7C2×C414yes—
102C2×C4×Dic7D414yes—
103C2×C4×Dic7D414yes—
104(C22⋊D7)⋊C4—232no—
105C7×#95—22no—
106C7×#95—42no—
107C7⋊#95—22no—
108C7⋊#95—24no—
109C7⋊#95—24no—
110C7⋊#95—42no—
111C7⋊#95—42no—
112C7⋊#95—42no—
113C22×C4×D4—71no—
114C2×#390—72no—
115C2×#382—71no—
116C2×C4×C4⋊C4—71no—
117#1439—71no—
118#1439—71no—
119#1439—71no—
120#1439D711yescharacteristic, complemented
121C4⋊#95—72no—
122C22⋊#95—72no—
123C22⋊#95—72no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7C22×C412yes—
133C24×C7C2×D412yes—
134C24×C7C2×Q812yes—
135C24×C7C2411yescharacteristic
136C23×D7—21no—
137C23×D7—21no—
138C23×D7—22no—
139C23×D7—22no—
140C23×D7—21no—
141C23×D7—21no—
142C23×D7—22no—
143C23×D7—22no—
144C23×D7C22×C412yes—
145C23×D7C2×D412yes—
146C23×D7C2×Q812yes—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7C22×C412yes—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C2×D412yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7#4114yes—
171C2×C22⋊D7—28no—
172C2×C22⋊D7—28no—
173C2×C22⋊D7—28no—
174C2×C22⋊D7—28no—
175C2×C22⋊D7—28no—
176C2×C22⋊D7—28no—
177C2×C22⋊D7C4⋊C4116yescomplemented
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—28no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—48no—
199C22×Dic7—44no—
200C22×Dic7—48no—
201C22×Dic7—44no—
202C22×Dic7C22×C412yes—
203C22×Dic7C22×C412yes—
204C22×Dic7C22×C412yes—
205C22×Dic7C2×D412yes—
206C22×Dic7C2×D412yes—
207C22×Dic7C2×D412yes—
208C22×Dic7C2×D412yes—
209C22×Dic7C2×D412yes—
210C22×Dic7C2×Q812yes—
211C22×Dic7#4114yes—
212C22×Dic7#4112yes—
213C22×Dic7#4112yes—
214C2×C4×D7—28no—
215C2×C4×D7—48no—
216C2×C4×D7—44no—
217C2×C4×D7—48no—
218C2×C4×D7—44no—
219C7×C4⋊C4—28no—
220C7×C22⋊C4—28no—
221C7×C22⋊C4—48no—
222C22⋊Dic7—48no—
223(C2×D7)⋊C4—28no—
224(C2×D7)⋊C4—48no—
225(C2×D7)⋊C4—48no—
226C4⋊Dic7—28no—
227Dic7⋊C4—28no—
228Dic7⋊C4—48no—
229C4×Dic7—48no—
230C4×Dic7C22⋊C4116yescomplemented
231C23×D4—71no—
232C24×C4—71no—
233C24×C4—71no—
234C2×C4×D4—78no—
235C2×C4×D4—144no—
236C2×C4×D4—144no—
237C22×C4⋊C4—71no—
238C22×C4⋊C4—72no—
239C22×C4⋊C4—71no—
240C22×C4⋊C4C2×D711yescharacteristic
241C22×C22⋊C4—71no—
242C22×C22⋊C4—72no—
243C22×C22⋊C4—72no—
244C22×C22⋊C4—72no—
245C22×C22⋊C4C2×D712yes—
246C22×C22⋊C4C2×D711yescharacteristic
247C22×C42—71no—
248C22×C42—72no—
249#390—148no—
250#382—144no—
251C4×C4⋊C4—144no—
252C2×#95—72no—
253C2×#95—72no—
254C2×#95—71no—
255C2×#95—72no—
256C2×#95—72no—
257C2×#95—72no—
258C2×#95C2×D711yescharacteristic
259C2×#95C2×D712yes—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—24no—
271C23×C7—24no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—42no—
275C23×C7—41no—
276C23×C7—42no—
277C23×C7—41no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7C2×C4⋊C414yes—
283C23×C7C23×C411yescharacteristic
284C23×C7C22×D411yescharacteristic
285C23×C7C22×D411yescharacteristic
286C23×C7C22×D411yescharacteristic
287C23×C7C22×Q811yescharacteristic
288C23×C7C2×#4112yes—
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4112yes—
292C23×C7H(5,𝔽2)12yes—
293C23×C7H(5,𝔽2)12yes—
294C22×D7—22no—
295C22×D7—22no—
296C22×D7—24no—
297C22×D7—24no—
298C22×D7—22no—
299C22×D7—22no—
300C22×D7—22no—
301C22×D7—22no—
302C22×D7—24no—
303C22×D7—24no—
304C22×D7—24no—
305C22×D7—24no—
306C22×D7—41no—
307C22×D7—41no—
308C22×D7—42no—
309C22×D7—41no—
310C22×D7—42no—
311C22×D7—41no—
312C22×D7—42no—
313C22×D7—42no—
314C22×D7—42no—
315C22×D7—42no—
316C22×D7C2×C4⋊C414yes—
317C2×C4×C7—24no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—24no—
321C2×C4×C7—22no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—42no—
327C2×C4×C7—41no—
328C2×C4×C7—42no—
329C2×C4×C7—41no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7C2×C22⋊C414yes—
341C22⋊D7—232no—
342C2×Dic7—24no—
343C2×Dic7—22no—
344C2×Dic7—24no—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—24no—
348C2×Dic7—24no—
349C2×Dic7—24no—
350C2×Dic7—24no—
351C2×Dic7—416no—
352C2×Dic7—42no—
353C2×Dic7—42no—
354C2×Dic7—41no—
355C2×Dic7—42no—
356C2×Dic7—41no—
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×Dic7C2×C22⋊C414yes—
367C2×Dic7C2×C22⋊C414yes—
368C2×Dic7C2×C4⋊C414yes—
369C2×Dic7#11714yes—
370C2×Dic7#12114yes—
371C2×Dic7#12114yes—
372C2×Dic7C22⋊Q814yes—
373C2×Dic7C22⋊Q814yes—
374C4×D7—416no—
375C25—71no—
376C25C22×D711yescharacteristic
377C22×D4—74no—
378C22×D4—74no—
379C22×D4—74no—
380C22×D4—142no—
381C22×D4—142no—
382C22×D4—142no—
383C22×D4—142no—
384C23×C4—71no—
385C23×C4—71no—
386C23×C4—72no—
387C23×C4—71no—
388C23×C4—74no—
389C23×C4—74no—
390C23×C4—72no—
391C23×C4—142no—
392C23×C4—142no—
393C23×C4—142no—
394C23×C4—142no—
395C23×C4—282no—
396C23×C4—282no—
397C23×C4—282no—
398C23×C4—282no—
399C23×C4C22×D712yes—
400C23×C4C22×D711yescharacteristic
401C23×C4C22×D712yes—
402C23×C4C22×D711yescharacteristic
403C4×D4—1432no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—74no—
407C2×C4⋊C4—142no—
408C2×C4⋊C4—142no—
409C2×C4⋊C4—144no—
410C2×C4⋊C4—142no—
411C2×C4⋊C4—144no—
412C2×C4⋊C4—144no—
413C2×C4⋊C4—144no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—74no—
420C2×C22⋊C4—142no—
421C2×C22⋊C4—142no—
422C2×C22⋊C4—144no—
423C2×C22⋊C4—144no—
424C2×C22⋊C4—144no—
425C2×C22⋊C4—144no—
426C2×C22⋊C4—144no—
427C2×C22⋊C4—144no—
428C2×C22⋊C4—282no—
429C2×C22⋊C4—282no—
430C2×C22⋊C4—282no—
431C2×C22⋊C4C4×D714yes—
432C2×C42—74no—
433C2×C42—74no—
434C2×C42—74no—
435C2×C42—144no—
436C2×C42—144no—
437C2×C42—144no—
438#95—22no—
439#95—42no—
440#95—144no—
441#95—144no—
442#95—142no—
443#95—282no—
444#95—282no—
445#95—282no—
446C22×C7—28no—
447C22×C7—24no—
448C22×C7—42no—
449C22×C7—44no—
450C22×C7—42no—
451C22×C7—42no—
452C22×C7—44no—
453C22×C7—42no—
454C22×C7—42no—
455C22×C7—44no—
456C22×C7—42no—
457C22×C7C22×C22⋊C411yescharacteristic
458C22×C7C22×C4⋊C411yescharacteristic
459C22×C7C2×#11711yescharacteristic
460C22×C7C4×#4112yes—
461C22×C7#51812yes—
462C22×C7C2×#12111yescharacteristic
463C22×C7C2×#12111yescharacteristic
464C22×C7C2×C22⋊Q811yescharacteristic
465C22×C7C2×C22⋊Q811yescharacteristic
466C22×C7#52511yescharacteristic
467C22×C7#52511yescharacteristic
468C22×C7#53212yes—
469C22×C7#53511yescharacteristic
470C22×C7#53512yes—
471C22×C7#53511yescharacteristic
472C22×C7#54612yes—
473C22×C7#54612yes—
474C22×C7#55312yes—
475C22×C7#55312yes—
476C22×C7#55412yes—
477C22×C7#55412yes—
478C22×C7#55912yes—
479C22×C7#55912yes—
480C2×D7—28no—
481C2×D7—24no—
482C2×D7—42no—
483C2×D7—44no—
484C2×D7—42no—
485C2×D7—42no—
486C2×D7—44no—
487C2×D7—42no—
488C2×D7—42no—
489C2×D7—44no—
490C2×D7—42no—
491C4×C7—24no—
492C4×C7—42no—
493C4×C7—44no—
494C4×C7—82no—
495Dic7—24no—
496Dic7—42no—
497Dic7—44no—
498Dic7—82no—
499Dic7#38018yes—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—72no—
509C24—72no—
510C24—72no—
511C24—141no—
512C24—141no—
513C24—142no—
514C24—142no—
515C24—142no—
516C24—141no—
517C24—141no—
518C24—142no—
519C24C2×C4×D712yes—
520C24D4×D712yes—
521C24Q8×D712yes—
522C24C23×D711yescharacteristic
523C2×D4—716no—
524C2×D4—148no—
525C2×D4—148no—
526C2×D4—148no—
527C2×D4—148no—
528C2×D4—148no—
529C2×D4—148no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—72no—
550C22×C4—72no—
551C22×C4—72no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—74no—
561C22×C4—148no—
562C22×C4—148no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—288no—
583C22×C4—284no—
584C22×C4—288no—
585C22×C4—284no—
586C22×C4—288no—
587C22×C4—284no—
588C22×C4—288no—
589C22×C4—284no—
590C22×C4C2×C4×D712yes—
591C22×C4C2×C4×D712yes—
592C22×C4D4×D712yes—
593C22×C4D4×D712yes—
594C22×C4#115914yes—
595C4⋊C4—28no—
596C4⋊C4—148no—
597C4⋊C4—148no—
598C4⋊C4—288no—
599C22⋊C4—28no—
600C22⋊C4—48no—
601C22⋊C4—148no—
602C22⋊C4—288no—
603C22⋊C4—288no—
604C22⋊C4—288no—
605C42—716no—
606C42—288no—
607C2×C7—44no—
608C2×C7C2×#38011yescharacteristic
609C2×C7#229711yescharacteristic
610C2×C7#230911yescharacteristic
611C2×C7#234912yes—
612C2×C7#235712yes—
613C2×C7#253511yescharacteristic
614C2×C7#253511yescharacteristic
615C2×C7#254412yes—
616C2×C7#256612yes—
617C2×C7#258011yescharacteristic
618C2×C7#258011yescharacteristic
619D7—44no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—41no—
640C23—42no—
641C23—41no—
642C23—74no—
643C23—142no—
644C23—142no—
645C23—144no—
646C23—144no—
647C23—144no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—142no—
652C23—144no—
653C23—144no—
654C23—144no—
655C23—282no—
656C23—282no—
657C23—281no—
658C23—281no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23—281no—
663C23—282no—
664C23—281no—
665C23D7×C4⋊C414yes—
666C23C22×C4×D711yescharacteristic
667C23C2×D4×D711yescharacteristic
668C23C2×D4×D711yescharacteristic
669C23C2×D4×D711yescharacteristic
670C23C2×#115912yes—
671C23#654812yes—
672C23C2×Q8×D711yescharacteristic
673C23D7×#4111yescharacteristic
674C23D7×#4111yescharacteristic
675C23D7×#4112yes—
676C23#655312yes—
677D4—1432no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—74no—
702C2×C4—74no—
703C2×C4—74no—
704C2×C4—74no—
705C2×C4—74no—
706C2×C4—74no—
707C2×C4—74no—
708C2×C4—74no—
709C2×C4—142no—
710C2×C4—144no—
711C2×C4—144no—
712C2×C4—142no—
713C2×C4—144no—
714C2×C4—142no—
715C2×C4—144no—
716C2×C4—144no—
717C2×C4—144no—
718C2×C4—2816no—
719C2×C4—2816no—
720C2×C4—282no—
721C2×C4—281no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—281no—
727C2×C4—282no—
728C2×C4—282no—
729C2×C4—282no—
730C2×C4—282no—
731C2×C4—282no—
732C2×C4—282no—
733C2×C4—282no—
734C2×C4D7×C22⋊C414yes—
735C7#1394111yescharacteristic, complemented, Sylow
736C22—28no—
737C22—24no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—148no—
748C22—144no—
749C22—282no—
750C22—282no—
751C22—284no—
752C22—282no—
753C22—282no—
754C22—284no—
755C22—282no—
756C22—282no—
757C22—284no—
758C22C2×D7×C22⋊C411yescharacteristic
759C22C2×D7×C4⋊C411yescharacteristic
760C22D7×#11711yescharacteristic
761C22C4×#115912yes—
762C22#9023612yes—
763C22#9027711yescharacteristic
764C22#9028212yes—
765C22#9028712yes—
766C22#9029212yes—
767C22D7×#12111yescharacteristic
768C22D7×#12111yescharacteristic
769C22#9029812yes—
770C22D7×C22⋊Q811yescharacteristic
771C22D7×C22⋊Q811yescharacteristic
772C22#9032612yes—
773C22#9032712yes—
774C22#9034512yes—
775C22#9034711yescharacteristic
776C22#9035512yes—
777C22#9036511yescharacteristic
778C22#9037212yes—
779C22#9040012yes—
780C22#9040611yescharacteristic
781C4—24no—
782C4—42no—
783C4—44no—
784C4—78no—
785C4—82no—
786C4—144no—
787C4—282no—
788C4—284no—
789C4—562no—
790C2—44no—
791C2—284no—
792C2D7×#38011yescharacteristic
793C2#1173183912yes—
794C2#1173210311yescharacteristic
795C2#1173292112yes—
796C2#1173387311yescharacteristic
797C2#1173413111yescharacteristic
798C2#1173424711yescharacteristic
799C2#1173439012yes—
800C2#1173476512yes—
801C2#1173495811yescharacteristic
802C2#1173548611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1439C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenter#1439D7
hypocenterC7#13941
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic7C2semidirect
4. C2×#89422C2semidirect
5. C7×#1439C2semidirect
6. #11729324C2semidirect
7. #11729300C2semidirect
8. #11729298C2semidirect
9. #11727181C2semidirect
10. (C2×D7)⋊#95C2semidirect
11. Dic7⋊#95C2semidirect
29. C2×(C22⋊D7)⋊C4C4semidirect
120. #1439D7semidirect
177. C2×C22⋊D7C4⋊C4semidirect
230. C4×Dic7C22⋊C4semidirect
735. C7#13941semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D7)⋊C42
C2×C4⋊C4×Dic72
C2×#897292
C2×#894222
C7×#14392
#117293242
#117293002
#117292982
#117271812
(C2×D7)⋊#952
Dic7⋊#952
#139417