Finite Group Databasebeta

← #13275986

Subgroups — #13275986

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×C22⋊D7C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic, complemented
3C2×#89728C212yesmaximal
4C2×#89440C212yesmaximal, complemented
5C2×D7×#95C211yesmaximal, characteristic, complemented
6C7×C22⋊#95C211yesmaximal, characteristic, complemented
7#11729301C212yesmaximal, complemented
8(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
9#11727164C212yesmaximal, complemented
10Dic7⋊#95C211yesmaximal, characteristic, complemented
11#11727155C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2212yes—
15C23×C4×D7C2211yescharacteristic
16C22×C7×C22⋊C4C2212yes—
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2211yescharacteristic
19C2×C4×C22⋊D7—28no—
20C2×C4×C22⋊D7C418yescomplemented
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×C4⋊Dic7C2212yes—
24C22×Dic7⋊C4C2212yes—
25C22×Dic7⋊C4C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2212yes—
30#89984—24no—
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2211yescharacteristic
38#89728—28no—
39#89440—28no—
40D7×#95—24no—
41#13899—71nomaximal, Sylow
42C25×C7C2311yescharacteristic
43C24×D7C2311yescharacteristic
44C23×C4×C7—24no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—42no—
48C23×C4×C7C2×C414yescomplemented
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C22×C22⋊D7—24no—
54C22×C22⋊D7—24no—
55C22×C22⋊D7C2×C414yes—
56C22×C22⋊D7D414yes—
57C22×C22⋊D7Q814yes—
58C23×Dic7C2312yes—
59C23×Dic7C2311yescharacteristic
60C23×Dic7C2312yes—
61C23×Dic7C2311yescharacteristic
62C23×Dic7C2311yescharacteristic
63C22×C4×D7—24no—
64C22×C4×D7—24no—
65C22×C4×D7—22no—
66C22×C4×D7—24no—
67C22×C4×D7—22no—
68C22×C4×D7—24no—
69C22×C4×D7—24no—
70C22×C4×D7—24no—
71C22×C4×D7—42no—
72C22×C4×D7—42no—
73C22×C4×D7—42no—
74C22×C4×D7C2×C414yes—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—42no—
78C2×C22⋊Dic7—24no—
79C2×C22⋊Dic7—24no—
80C2×C22⋊Dic7—24no—
81C2×C22⋊Dic7—42no—
82C2×C22⋊Dic7C2×C414yescomplemented
83C4×C22⋊D7—232no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—24no—
86C2×(C2×D7)⋊C4—24no—
87C2×(C2×D7)⋊C4C2×C414yes—
88C2×(C2×D7)⋊C4D418yes—
89C2×C4⋊Dic7—24no—
90C2×C4⋊Dic7—24no—
91C2×C4⋊Dic7—42no—
92C2×Dic7⋊C4—24no—
93C2×Dic7⋊C4—24no—
94C2×Dic7⋊C4—24no—
95C2×Dic7⋊C4—42no—
96C2×Dic7⋊C4C2×C414yescomplemented
97C2×C4×Dic7—24no—
98C2×C4×Dic7C2×C414yescomplemented
99C7×#95—22no—
100C7×#95—24no—
101C7×#95—22no—
102C7⋊#95—22no—
103C7⋊#95—24no—
104C7⋊#95—24no—
105C7⋊#95—24no—
106C7⋊#95—24no—
107C7⋊#95—42no—
108C7⋊#95D414yescomplemented
109C22×C4×D4—71no—
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⋊#95D711yescharacteristic, complemented
120C24×C7—21no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—22no—
127C24×C7—21no—
128C24×C7C22×C412yes—
129C24×C7C2×D412yes—
130C24×C7C2×Q812yes—
131C24×C7C2411yescharacteristic
132C23×D7—21no—
133C23×D7—21no—
134C23×D7—22no—
135C23×D7—22no—
136C23×D7—21no—
137C23×D7—21no—
138C23×D7C22×C412yes—
139C23×D7C2×D414yes—
140C23×D7C2×D412yes—
141C23×D7C2×Q812yes—
142C23×D7#4114yes—
143C22×C4×C7—22no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
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×C7—28no—
155C22×C4×C7—28no—
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—44no—
164C22×C4×C7—48no—
165C22×C4×C7—48no—
166C22×C4×C7C22×C412yes—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C2×D414yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7#4114yes—
171C22×C4×C7#4112yes—
172C2×C22⋊D7—28no—
173C2×C22⋊D7—28no—
174C2×C22⋊D7—216no—
175C2×C22⋊D7—216no—
176C2×C22⋊D7C4⋊C4116yescomplemented
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—21no—
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×Dic7C22×C412yes—
200C22×Dic7C22×C412yes—
201C22×Dic7C22×C412yes—
202C22×Dic7C2×D414yes—
203C22×Dic7C2×D414yes—
204C22×Dic7C2×D412yes—
205C22×Dic7C2×Q812yes—
206C2×C4×D7—216no—
207C2×C4×D7—28no—
208C2×C4×D7—28no—
209C2×C4×D7—44no—
210C2×C4×D7—48no—
211C2×C4×D7—48no—
212C2×C4×D7—48no—
213C2×C4×D7—48no—
214C2×C4×D7—48no—
215C2×C4×D7—48no—
216C2×C4×D7—48no—
217C2×C4×D7—48no—
218C7×C22⋊C4—48no—
219C22⋊Dic7—28no—
220C22⋊Dic7—48no—
221(C2×D7)⋊C4—48no—
222(C2×D7)⋊C4C22⋊C4116yescomplemented
223C4⋊Dic7—48no—
224Dic7⋊C4—28no—
225Dic7⋊C4—48no—
226C4×Dic7—28no—
227C23×D4—71no—
228C24×C4—71no—
229C24×C4—72no—
230C24×C4C2×D711yescharacteristic
231C2×C4×D4—78no—
232C2×C4×D4—148no—
233C22×C4⋊C4—71no—
234C22×C4⋊C4—72no—
235C22×C4⋊C4—72no—
236C22×C22⋊C4—71no—
237C22×C22⋊C4—71no—
238C22×C22⋊C4—72no—
239C22×C22⋊C4—72no—
240C22×C22⋊C4C2×D712yes—
241C22×C42—71no—
242#386—148no—
243#385—148no—
244#380—144no—
245C2×#95—71no—
246C2×#95—71no—
247C2×#95—72no—
248C2×#95—72no—
249C2×#95—72no—
250C2×#95—72no—
251C2×#95—72no—
252C2×#95—144no—
253C2×#95C2×D711yescharacteristic
254C2×#95C2×D711yescharacteristic
255C2×#95C2×D712yes—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—22no—
265C23×C7—24no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—24no—
269C23×C7—22no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7C2×C4⋊C414yes—
279C23×C7C23×C411yescharacteristic
280C23×C7C22×D412yes—
281C23×C7C22×D411yescharacteristic
282C23×C7C22×D411yescharacteristic
283C23×C7C22×Q811yescharacteristic
284C23×C7C2×#4112yes—
285C23×C7C2×#4111yescharacteristic
286C23×C7C2×#4112yes—
287C23×C7H(5,𝔽2)12yes—
288C23×C7H(5,𝔽2)11yescharacteristic
289C23×C72−1+411yescharacteristic
290C22×D7—22no—
291C22×D7—22no—
292C22×D7—22no—
293C22×D7—22no—
294C22×D7—24no—
295C22×D7—24no—
296C22×D7—24no—
297C22×D7—24no—
298C22×D7—24no—
299C22×D7—22no—
300C22×D7—24no—
301C22×D7—24no—
302C22×D7—24no—
303C22×D7—24no—
304C22×D7—22no—
305C22×D7—22no—
306C22×D7—24no—
307C22×D7—22no—
308C22×D7C2×C22⋊C414yes—
309C22×D7C2×C4⋊C414yes—
310C22×D7#11714yes—
311C22×D7#12118yes—
312C22×D7C22⋊Q818yes—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—24no—
318C2×C4×C7—24no—
319C2×C4×C7—24no—
320C2×C4×C7—24no—
321C2×C4×C7—24no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—416no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
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×C7C2×C22⋊C414yes—
337C2×C4×C7C4×D414yes—
338C22⋊D7—232no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—22no—
342C2×Dic7—22no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—24no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—24no—
351C2×Dic7—24no—
352C2×Dic7—24no—
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×Dic7C2×C22⋊C414yes—
367C2×Dic7C2×C4⋊C414yes—
368C4×D7—416no—
369C4×D7—432no—
370C25—71no—
371C25C22×D711yescharacteristic
372C22×D4—74no—
373C22×D4—74no—
374C22×D4—74no—
375C22×D4—144no—
376C22×D4—144no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—42no—
381C23×C4—71no—
382C23×C4—71no—
383C23×C4—71no—
384C23×C4—72no—
385C23×C4—74no—
386C23×C4—72no—
387C23×C4—144no—
388C23×C4—144no—
389C23×C4—144no—
390C23×C4—144no—
391C23×C4—144no—
392C23×C4—144no—
393C23×C4—142no—
394C23×C4—142no—
395C23×C4—282no—
396C23×C4—282no—
397C23×C4—282no—
398C23×C4C4×D714yescomplemented
399C23×C4C22×D712yes—
400C23×C4C22×D712yes—
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C4×D4—1432no—
404C2×C4⋊C4—74no—
405C2×C4⋊C4—144no—
406C2×C4⋊C4—144no—
407C2×C4⋊C4—144no—
408C2×C4⋊C4—144no—
409C2×C4⋊C4—144no—
410C2×C4⋊C4—282no—
411C2×C4⋊C4—282no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—74no—
416C2×C22⋊C4—78no—
417C2×C22⋊C4—74no—
418C2×C22⋊C4—144no—
419C2×C22⋊C4—144no—
420C2×C22⋊C4—144no—
421C2×C22⋊C4—144no—
422C2×C22⋊C4—144no—
423C2×C22⋊C4—144no—
424C2×C22⋊C4—282no—
425C2×C42—74no—
426C2×C42—144no—
427#95—22no—
428#95—24no—
429#95—22no—
430#95—74no—
431#95—144no—
432#95—144no—
433#95—144no—
434#95—144no—
435#95—142no—
436#95—282no—
437C22×C7—24no—
438C22×C7—24no—
439C22×C7—24no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—42no—
443C22×C7—44no—
444C22×C7—44no—
445C22×C7—44no—
446C22×C7—44no—
447C22×C7—42no—
448C22×C7C22×C22⋊C411yescharacteristic
449C22×C7C22×C4⋊C411yescharacteristic
450C22×C7C2×#11711yescharacteristic
451C22×C7C2×C4×D411yescharacteristic
452C22×C7C4×#4111yescharacteristic
453C22×C7#51811yescharacteristic
454C22×C7#52011yescharacteristic
455C22×C7C2×#12112yes—
456C22×C7C2×C22⋊Q812yes—
457C22×C7#52512yes—
458C22×C7#52912yes—
459C22×C7#53812yes—
460C22×C7#53912yes—
461C22×C7D4212yes—
462C22×C7D4211yescharacteristic
463C22×C7#54612yes—
464C22×C7#54612yes—
465C22×C7#54612yes—
466C22×C7#54712yes—
467C22×C7#54711yescharacteristic
468C22×C7D4×Q811yescharacteristic
469C22×C7#55412yes—
470C22×C7#55411yescharacteristic
471C2×D7—24no—
472C2×D7—24no—
473C2×D7—24no—
474C2×D7—24no—
475C2×D7—24no—
476C2×D7—28no—
477C2×D7—28no—
478C2×D7—28no—
479C2×D7—28no—
480C2×D7—24no—
481C2×D7#38018yescomplemented
482C4×C7—24no—
483C4×C7—24no—
484C4×C7—44no—
485C4×C7—82no—
486Dic7—24no—
487Dic7—24no—
488Dic7—42no—
489Dic7—44no—
490Dic7—82no—
491C24—22no—
492C24—21no—
493C24—22no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—72no—
500C24—74no—
501C24—72no—
502C24—72no—
503C24—74no—
504C24—142no—
505C24—141no—
506C24—141no—
507C24—142no—
508C24—141no—
509C24—141no—
510C24C2×C4×D712yes—
511C24D4×D712yes—
512C24Q8×D712yes—
513C24C23×D711yescharacteristic
514C2×D4—716no—
515C2×D4—148no—
516C2×D4—148no—
517C2×D4—1416no—
518C2×D4—1416no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—72no—
543C22×C4—72no—
544C22×C4—72no—
545C22×C4—74no—
546C22×C4—72no—
547C22×C4—72no—
548C22×C4—74no—
549C22×C4—148no—
550C22×C4—1416no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—141no—
555C22×C4—141no—
556C22×C4—142no—
557C22×C4—141no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—141no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—148no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—284no—
575C22×C4—288no—
576C22×C4—288no—
577C22×C4—288no—
578C22×C4—288no—
579C22×C4—288no—
580C22×C4—288no—
581C22×C4—288no—
582C22×C4—288no—
583C22×C4C2×C4×D712yes—
584C22×C4C2×C4×D712yes—
585C22×C4#115714yes—
586C22×C4D4×D714yes—
587C22×C4D4×D712yes—
588C22×C4#115912yes—
589C4⋊C4—148no—
590C4⋊C4—288no—
591C4⋊C4—288no—
592C22⋊C4—48no—
593C22⋊C4—716no—
594C22⋊C4—148no—
595C22⋊C4—288no—
596C22⋊C4—288no—
597C42—148no—
598C2×C7—44no—
599C2×C7C2×#38011yescharacteristic
600C2×C7#229011yescharacteristic
601C2×C7#231811yescharacteristic
602C2×C7D4×C22⋊C411yescharacteristic
603C2×C7#233911yescharacteristic
604C2×C7D4×C4⋊C411yescharacteristic
605C2×C7#234911yescharacteristic
606C2×C7#242412yes—
607C2×C7#242512yes—
608C2×C7#244912yes—
609C2×C7#245012yes—
610D7—28no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—74no—
634C23—74no—
635C23—74no—
636C23—78no—
637C23—78no—
638C23—142no—
639C23—142no—
640C23—142no—
641C23—144no—
642C23—144no—
643C23—142no—
644C23—144no—
645C23—144no—
646C23—144no—
647C23—144no—
648C23—144no—
649C23—144no—
650C23—142no—
651C23—142no—
652C23—142no—
653C23—142no—
654C23—144no—
655C23—144no—
656C23D7×C4⋊C414yes—
657C23C22×C4×D711yescharacteristic
658C23C2×#115712yes—
659C23C2×D4×D712yes—
660C23C2×D4×D711yescharacteristic
661C23C2×D4×D711yescharacteristic
662C23C2×#115911yescharacteristic
663C23#654812yes—
664C23C2×Q8×D711yescharacteristic
665C23D7×#4112yes—
666C23#655311yescharacteristic
667C23#655411yescharacteristic
668D4—1432no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—416no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—74no—
693C2×C4—74no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—144no—
699C2×C4—144no—
700C2×C4—144no—
701C2×C4—144no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—144no—
706C2×C4—144no—
707C2×C4—144no—
708C2×C4—2816no—
709C2×C4—2832no—
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—282no—
723C2×C4D7×C22⋊C414yes—
724C2×C4(C22⋊D7)⋊C414yes—
725C7#1389911yescharacteristic, complemented, Sylow
726C22—24no—
727C22—24no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—44no—
733C22—42no—
734C22—42no—
735C22—44no—
736C22—44no—
737C22—78no—
738C22—144no—
739C22—144no—
740C22—148no—
741C22—148no—
742C22—144no—
743C22—144no—
744C22—148no—
745C22—148no—
746C22—144no—
747C22—144no—
748C22C4×#115711yescharacteristic
749C22C2×D7×C22⋊C411yescharacteristic
750C22C2×(C22⋊D7)⋊C411yescharacteristic
751C22#9017711yescharacteristic
752C22#9018112yes—
753C22C2×D7×C4⋊C411yescharacteristic
754C22#9020212yes—
755C22D7×#11711yescharacteristic
756C22#9021411yescharacteristic
757C22#9023812yes—
758C22#9024112yes—
759C22#9024212yes—
760C22#9024812yes—
761C22#9028112yes—
762C22#9028212yes—
763C22D7×#12112yes—
764C22#9030011yescharacteristic
765C22#9030211yescharacteristic
766C22D7×C22⋊Q812yes—
767C22#9032311yescharacteristic
768C22#9032611yescharacteristic
769C22#9034812yes—
770C22#9035112yes—
771C4—24no—
772C4—24no—
773C4—44no—
774C4—82no—
775C4—144no—
776C4—144no—
777C4—282no—
778C4—284no—
779C4—562no—
780C2—44no—
781C2—148no—
782C2#1173081411yescharacteristic
783C2#1173100711yescharacteristic
784C2#1173101811yescharacteristic
785C2#1173129511yescharacteristic
786C2D7×#38011yescharacteristic
787C2#1173145511yescharacteristic
788C2#1173156511yescharacteristic
789C2#1173205412yes—
790C2#1173205512yes—
791C2#1173233912yes—
792C2#1173234012yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22⋊#95D7
hypocenterC7#13899
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#89984C2semidirect
4. C2×#89440C2semidirect
5. C2×D7×#95C2semidirect
6. C7×C22⋊#95C2semidirect
7. #11729301C2semidirect
8. (C2×D7)⋊#95C2semidirect
9. #11727164C2semidirect
10. Dic7⋊#95C2semidirect
11. #11727155C2semidirect
20. C2×C4×C22⋊D7C4semidirect
48. C23×C4×C7C2×C4semidirect
82. C2×C22⋊Dic7C2×C4semidirect
96. C2×Dic7⋊C4C2×C4semidirect
98. C2×C4×Dic7C2×C4semidirect
108. C7⋊#95D4semidirect
119. C22⋊#95D7semidirect
176. C2×C22⋊D7C4⋊C4semidirect
222. (C2×D7)⋊C4C22⋊C4semidirect
398. C23×C4C4×D7semidirect
481. C2×D7#380semidirect
725. C7#13899semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C2×#899842
C2×#897282
C2×#894402
C2×D7×#952
C7×C22⋊#952
#117293012
(C2×D7)⋊#952
#117271642
Dic7⋊#952
#117271552
#138997