Finite Group Databasebeta

← #13276166

Subgroups — #13276166

Order 1792.

2458 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×C7×#380C211yesmaximal, characteristic, complemented
3C2×#89744C212yesmaximal, complemented
4C2×#89729C212yesmaximal
5C2×#89439C211yesmaximal, characteristic, complemented
6#11729881C211yesmaximal, characteristic, complemented
7#11729324C212yesmaximal, complemented
8#11729301C212yesmaximal, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
10Dic7⋊#95C211yesmaximal, characteristic, complemented
11Dic7×#95C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C22×C7×C4⋊C4C2212yes—
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)⋊C4C2212yes—
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2212yes—
25C22×Dic7⋊C4C2212yes—
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29C7×#380—24no—
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89744—28no—
39#89729—28no—
40#89439—24no—
41#13920—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×C414yes—
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—22no—
64C22×C4×D7—22no—
65C22×C4×D7—24no—
66C22×C4×D7—42no—
67C22×C4×D7C2×C414yes—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—24no—
70C2×C7×C4⋊C4—42no—
71C2×C7×C22⋊C4—24no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—42no—
74C2×C22⋊Dic7—24no—
75C2×C22⋊Dic7—24no—
76C2×C22⋊Dic7—24no—
77C2×C22⋊Dic7—42no—
78C2×C22⋊Dic7C2×C414yes—
79C4×C22⋊D7—232no—
80C2×(C2×D7)⋊C4—24no—
81C2×(C2×D7)⋊C4—24no—
82C2×(C2×D7)⋊C4—24no—
83C2×(C2×D7)⋊C4—24no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—42no—
86C2×(C2×D7)⋊C4—42no—
87C2×(C2×D7)⋊C4C2×C414yes—
88C2×Dic7⋊C4—24no—
89C2×Dic7⋊C4—24no—
90C2×Dic7⋊C4—24no—
91C2×Dic7⋊C4—24no—
92C2×Dic7⋊C4—24no—
93C2×Dic7⋊C4—42no—
94C2×Dic7⋊C4C2×C414yes—
95C2×Dic7⋊C4D418yes—
96C2×C4×Dic7—24no—
97C2×C4×Dic7—24no—
98C2×C4×Dic7—24no—
99C2×C4×Dic7—24no—
100C2×C4×Dic7C2×C414yes—
101C7×#95—22no—
102C7×#95D414yescomplemented
103C7⋊#95—22no—
104C7⋊#95—24no—
105C7⋊#95—22no—
106C7⋊#95—24no—
107C7⋊#95—24no—
108C7⋊#95—42no—
109C22×C4×D4—71no—
110C2×#390—72no—
111C2×#389—72no—
112C2×#380—71no—
113C2×#380D711yescharacteristic, complemented
114#1439—72no—
115#1439—72no—
116C4⋊#95—71no—
117C22⋊#95—71no—
118C22⋊#95—71no—
119C4×#95—71no—
120C24×C7—22no—
121C24×C7—21no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—21no—
125C24×C7—22no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7C22×C412yes—
129C24×C7C2×D412yes—
130C24×C7C2×Q812yes—
131C24×C7C2411yescharacteristic
132C23×D7—21no—
133C23×D7—22no—
134C23×D7—22no—
135C23×D7—21no—
136C23×D7—22no—
137C23×D7—21no—
138C23×D7—22no—
139C23×D7—21no—
140C23×D7C22×C412yes—
141C23×D7C2×D412yes—
142C23×D7C2×Q812yes—
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×D414yes—
170C22×C4×C7C2×D412yes—
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—21no—
178C22×Dic7—21no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—21no—
187C22×Dic7—22no—
188C22×Dic7—21no—
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×Dic7C22×C412yes—
198C22×Dic7C22×C412yes—
199C22×Dic7C22×C412yes—
200C22×Dic7C2×D414yes—
201C22×Dic7C2×D414yes—
202C22×Dic7C2×D412yes—
203C22×Dic7C2×Q812yes—
204C22×Dic7#4114yes—
205C22×Dic7#4114yes—
206C2×C4×D7—28no—
207C2×C4×D7—28no—
208C2×C4×D7—44no—
209C2×C4×D7—48no—
210C2×C4×D7—48no—
211C7×C4⋊C4—48no—
212C7×C22⋊C4—48no—
213C22⋊Dic7—28no—
214C22⋊Dic7—48no—
215(C2×D7)⋊C4—28no—
216(C2×D7)⋊C4—48no—
217(C2×D7)⋊C4—48no—
218Dic7⋊C4—48no—
219Dic7⋊C4—48no—
220Dic7⋊C4C22⋊C4116yescomplemented
221C4×Dic7—28no—
222C4×Dic7—48no—
223C23×D4—71no—
224C24×C4—71no—
225C24×C4C2×D711yescharacteristic
226C2×C4×D4—78no—
227C2×C4×D4—148no—
228C22×C4⋊C4—71no—
229C22×C4⋊C4—72no—
230C22×C4⋊C4—72no—
231C22×C4⋊C4C2×D712yes—
232C22×C22⋊C4—71no—
233C22×C22⋊C4—71no—
234C22×C22⋊C4—72no—
235C22×C22⋊C4—72no—
236C22×C22⋊C4—72no—
237C22×C22⋊C4C2×D712yes—
238C22×C42—71no—
239C22×C42—72no—
240#390—148no—
241#389—148no—
242#380—24no—
243#380—144no—
244C2×#95—71no—
245C2×#95—72no—
246C2×#95—71no—
247C2×#95—72no—
248C2×#95—72no—
249C2×#95—72no—
250C2×#95C2×D711yescharacteristic
251C2×#95C2×D711yescharacteristic
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—24no—
259C23×C7—24no—
260C23×C7—22no—
261C23×C7—24no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—24no—
266C23×C7—42no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7C2×C4⋊C414yes—
275C23×C7C23×C411yescharacteristic
276C23×C7C22×D412yes—
277C23×C7C22×D411yescharacteristic
278C23×C7C22×D411yescharacteristic
279C23×C7C22×Q811yescharacteristic
280C23×C7C2×#4111yescharacteristic
281C23×C7C2×#4112yes—
282C23×C7C2×#4112yes—
283C23×C7H(5,𝔽2)12yes—
284C23×C7H(5,𝔽2)11yescharacteristic
285C23×C72−1+411yescharacteristic
286C22×D7—22no—
287C22×D7—22no—
288C22×D7—22no—
289C22×D7—22no—
290C22×D7—22no—
291C22×D7—22no—
292C22×D7—24no—
293C22×D7—24no—
294C22×D7—22no—
295C22×D7—24no—
296C22×D7—22no—
297C22×D7—22no—
298C22×D7—22no—
299C22×D7—24no—
300C22×D7—42no—
301C22×D7—42no—
302C22×D7—42no—
303C22×D7—42no—
304C22×D7—42no—
305C22×D7—42no—
306C22×D7—42no—
307C22×D7—42no—
308C22×D7C2×C4⋊C414yes—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—24no—
317C2×C4×C7—24no—
318C2×C4×C7—24no—
319C2×C4×C7—24no—
320C2×C4×C7—416no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
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×C7C2×C22⋊C414yes—
333C2×C4×C7C4×D414yes—
334C22⋊D7—232no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—24no—
338C2×Dic7—24no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—22no—
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×Dic7C2×C22⋊C414yes—
359C2×Dic7C2×C22⋊C414yes—
360C2×Dic7C2×C4⋊C414yes—
361C2×Dic7#11714yes—
362C2×Dic7#12118yes—
363C2×Dic7C22⋊Q818yes—
364C4×D7—416no—
365C25—71no—
366C25C22×D711yescharacteristic
367C22×D4—74no—
368C22×D4—74no—
369C22×D4—74no—
370C22×D4—144no—
371C22×D4—144no—
372C23×C4—22no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—42no—
376C23×C4—71no—
377C23×C4—71no—
378C23×C4—71no—
379C23×C4—72no—
380C23×C4—74no—
381C23×C4—72no—
382C23×C4—144no—
383C23×C4—142no—
384C23×C4—142no—
385C23×C4—282no—
386C23×C4C4×D714yes—
387C23×C4C22×D712yes—
388C23×C4C22×D712yes—
389C23×C4C22×D711yescharacteristic
390C23×C4C22×D711yescharacteristic
391C4×D4—1432no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—74no—
396C2×C4⋊C4—78no—
397C2×C4⋊C4—144no—
398C2×C4⋊C4—144no—
399C2×C4⋊C4—144no—
400C2×C4⋊C4—144no—
401C2×C4⋊C4—144no—
402C2×C4⋊C4—282no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—74no—
407C2×C22⋊C4—74no—
408C2×C22⋊C4—144no—
409C2×C22⋊C4—144no—
410C2×C22⋊C4—144no—
411C2×C22⋊C4—144no—
412C2×C22⋊C4—144no—
413C2×C22⋊C4—144no—
414C2×C22⋊C4—144no—
415C2×C22⋊C4—144no—
416C2×C22⋊C4—282no—
417C2×C22⋊C4—282no—
418C2×C22⋊C4—282no—
419C2×C42—74no—
420C2×C42—144no—
421C2×C42—144no—
422C2×C42—144no—
423C2×C42—144no—
424#95—22no—
425#95—144no—
426#95—144no—
427#95—142no—
428#95—144no—
429#95—142no—
430#95—282no—
431#95C22⋊D714yescomplemented
432C22×C7—24no—
433C22×C7—24no—
434C22×C7—24no—
435C22×C7—42no—
436C22×C7—42no—
437C22×C7—42no—
438C22×C7—44no—
439C22×C7—44no—
440C22×C7—44no—
441C22×C7—44no—
442C22×C7—42no—
443C22×C7C22×C22⋊C411yescharacteristic
444C22×C7C22×C4⋊C411yescharacteristic
445C22×C7C2×#11711yescharacteristic
446C22×C7C2×C4×D411yescharacteristic
447C22×C7C4×#4111yescharacteristic
448C22×C7#51811yescharacteristic
449C22×C7#52011yescharacteristic
450C22×C7C2×#12112yes—
451C22×C7C2×C22⋊Q812yes—
452C22×C7#52912yes—
453C22×C7#53212yes—
454C22×C7#54012yes—
455C22×C7#54212yes—
456C22×C7D4212yes—
457C22×C7D4211yescharacteristic
458C22×C7#54612yes—
459C22×C7#54612yes—
460C22×C7#54711yescharacteristic
461C22×C7#54812yes—
462C22×C7D4×Q811yescharacteristic
463C22×C7#55012yes—
464C22×C7#55411yescharacteristic
465C22×C7#55412yes—
466C2×D7—24no—
467C2×D7—24no—
468C2×D7—24no—
469C2×D7—42no—
470C2×D7—42no—
471C2×D7—42no—
472C2×D7—44no—
473C2×D7—44no—
474C2×D7—44no—
475C2×D7—44no—
476C2×D7—42no—
477C4×C7—24no—
478C4×C7—24no—
479C4×C7—44no—
480C4×C7—82no—
481Dic7—24no—
482Dic7—42no—
483Dic7—44no—
484Dic7—82no—
485Dic7#38018yescomplemented
486C24—21no—
487C24—22no—
488C24—21no—
489C24—22no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—72no—
495C24—72no—
496C24—72no—
497C24—141no—
498C24—142no—
499C24—141no—
500C24—142no—
501C24—141no—
502C24—142no—
503C24—142no—
504C24—141no—
505C24C2×C4×D712yes—
506C24D4×D712yes—
507C24Q8×D712yes—
508C24C23×D711yescharacteristic
509C2×D4—716no—
510C2×D4—148no—
511C2×D4—148no—
512C2×D4—1416no—
513C2×D4—1416no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—72no—
538C22×C4—74no—
539C22×C4—72no—
540C22×C4—72no—
541C22×C4—74no—
542C22×C4—72no—
543C22×C4—74no—
544C22×C4—72no—
545C22×C4—74no—
546C22×C4—148no—
547C22×C4—141no—
548C22×C4—142no—
549C22×C4—141no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—141no—
555C22×C4—142no—
556C22×C4—141no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—148no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—284no—
569C22×C4—288no—
570C22×C4—288no—
571C22×C4C2×C4×D712yes—
572C22×C4C2×C4×D712yes—
573C22×C4#115712yes—
574C22×C4D4×D714yes—
575C22×C4C2×C22⋊D714yes—
576C22×C4C2×C22⋊D712yes—
577C4⋊C4—48no—
578C4⋊C4—716no—
579C4⋊C4—288no—
580C4⋊C4—288no—
581C22⋊C4—48no—
582C22⋊C4—148no—
583C22⋊C4—148no—
584C22⋊C4—288no—
585C22⋊C4—288no—
586C22⋊C4—288no—
587C42—148no—
588C42—288no—
589C2×C7—44no—
590C2×C7C2×#38011yescharacteristic
591C2×C7#229311yescharacteristic
592C2×C7#231911yescharacteristic
593C2×C7D4×C22⋊C411yescharacteristic
594C2×C7#234111yescharacteristic
595C2×C7D4×C4⋊C411yescharacteristic
596C2×C7#234911yescharacteristic
597C2×C7#242712yes—
598C2×C7#242812yes—
599C2×C7#245212yes—
600C2×C7#245412yes—
601D7—44no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—74no—
625C23—142no—
626C23—142no—
627C23—142no—
628C23—142no—
629C23—142no—
630C23—142no—
631C23—142no—
632C23—142no—
633C23—142no—
634C23—142no—
635C23—144no—
636C23—144no—
637C23—144no—
638C23—144no—
639C23—282no—
640C23—282no—
641C23—282no—
642C23—282no—
643C23—282no—
644C23—282no—
645C23—282no—
646C23—282no—
647C23D7×C4⋊C414yes—
648C23C22×C4×D711yescharacteristic
649C23C2×#115711yescharacteristic
650C23C2×D4×D712yes—
651C23C2×D4×D711yescharacteristic
652C23#654812yes—
653C23#654811yescharacteristic
654C23C2×Q8×D711yescharacteristic
655C23#655111yescharacteristic
656C23D7×#4112yes—
657C23D7×#4112yes—
658C23C22×C22⋊D711yescharacteristic
659D4—1432no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—416no—
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—74no—
684C2×C4—74no—
685C2×C4—74no—
686C2×C4—78no—
687C2×C4—78no—
688C2×C4—74no—
689C2×C4—142no—
690C2×C4—144no—
691C2×C4—142no—
692C2×C4—144no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—144no—
697C2×C4—144no—
698C2×C4—144no—
699C2×C4—2816no—
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×C4D7×C22⋊C414yes—
714C2×C4C4×C22⋊D714yes—
715C7#1392011yescharacteristic, complemented, Sylow
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—44no—
721C22—42no—
722C22—42no—
723C22—44no—
724C22—44no—
725C22—42no—
726C22—44no—
727C22—144no—
728C22—144no—
729C22—144no—
730C22—282no—
731C22—284no—
732C22—282no—
733C22—282no—
734C22—284no—
735C22—284no—
736C22—282no—
737C22—284no—
738C22C2×D7×C22⋊C411yescharacteristic
739C22#9017711yescharacteristic
740C22#9018112yes—
741C22C2×D7×C4⋊C411yescharacteristic
742C22#9019511yescharacteristic
743C22#9019811yescharacteristic
744C22#9020211yescharacteristic
745C22D7×#11711yescharacteristic
746C22#9021311yescharacteristic
747C22#9021912yes—
748C22#9029012yes—
749C22D7×#12112yes—
750C22#9030112yes—
751C22#9030612yes—
752C22D7×C22⋊Q812yes—
753C22#9032412yes—
754C22#9032712yes—
755C22#9033112yes—
756C22C2×C4×C22⋊D711yescharacteristic
757C22D4×C22⋊D712yes—
758C22D4×C22⋊D711yescharacteristic
759C22Q8×C22⋊D711yescharacteristic
760C22#9052312yes—
761C4—24no—
762C4—24no—
763C4—44no—
764C4—78no—
765C4—82no—
766C4—144no—
767C4—282no—
768C4—284no—
769C4—562no—
770C2—44no—
771C2—284no—
772C2#1173131511yescharacteristic
773C2#1173132211yescharacteristic
774C2#1173134012yes—
775C2#1173134812yes—
776C2D7×#38011yescharacteristic
777C2#1173145611yescharacteristic
778C2C22⋊C4×C22⋊D711yescharacteristic
779C2C4⋊C4×C22⋊D711yescharacteristic
780C2#1173967011yescharacteristic
781C2#1174009512yes—
782C2#1174021112yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#380D7
hypocenterC7#13920
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C7×#380C2semidirect
3. C2×#89744C2semidirect
5. C2×#89439C2semidirect
6. #11729881C2semidirect
7. #11729324C2semidirect
8. #11729301C2semidirect
9. (C2×D7)⋊#95C2semidirect
10. Dic7⋊#95C2semidirect
11. Dic7×#95C2semidirect
20. C2×C4×C22⋊D7C4semidirect
102. C7×#95D4semidirect
113. C2×#380D7semidirect
176. C2×C22⋊D7C4⋊C4semidirect
220. Dic7⋊C4C22⋊C4semidirect
431. #95C22⋊D7semidirect
485. Dic7#380semidirect
715. C7#13920semidirect

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×C7×#3802
C2×#897442
C2×#897292
C2×#894392
#117298812
#117293242
#117293012
(C2×D7)⋊#952
Dic7⋊#952
Dic7×#952
#139207