Finite Group Databasebeta

← #13276345

Subgroups — #13276345

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×#89729C212yesmaximal
3C2×#89422C211yesmaximal, characteristic, complemented
4C2×#89421C211yesmaximal, characteristic, complemented
5C7×C22⋊#95C211yesmaximal, characteristic, complemented
6#11729881C211yesmaximal, characteristic, complemented
7#11729301C212yesmaximal, complemented
8#11727182C212yesmaximal, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
11Dic7⋊#95C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C22⋊Dic7C2212yes—
17C22×C22⋊Dic7C2211yescharacteristic
18C2×C4×C22⋊D7—24no—
19C2×C4×C22⋊D7—24no—
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
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89729—28no—
39#89422—24no—
40#89421—24no—
41#13941—71nomaximal, Sylow
42C25×C7C2311yescharacteristic
43C24×D7C2311yescharacteristic
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—42no—
47C23×C4×C7—42no—
48C23×C4×C7C2×C414yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2312yes—
52C23×C4×C7C2311yescharacteristic
53C22×C22⋊D7—22no—
54C22×C22⋊D7—22no—
55C22×C22⋊D7—22no—
56C22×C22⋊D7—22no—
57C22×C22⋊D7C2×C414yes—
58C22×C22⋊D7D414yes—
59C22×C22⋊D7Q814yes—
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×C22⋊C4—24no—
71C2×C7×C22⋊C4—24no—
72C2×C7×C22⋊C4—42no—
73C2×C22⋊Dic7—22no—
74C2×C22⋊Dic7—22no—
75C2×C22⋊Dic7—24no—
76C2×C22⋊Dic7—24no—
77C2×C22⋊Dic7—42no—
78C2×C22⋊Dic7C2×C414yes—
79C4×C22⋊D7—232no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—24no—
83C2×(C2×D7)⋊C4—24no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—24no—
86C2×(C2×D7)⋊C4—42no—
87C2×(C2×D7)⋊C4—42no—
88C2×(C2×D7)⋊C4C2×C414yes—
89C2×Dic7⋊C4—24no—
90C2×Dic7⋊C4—24no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—24no—
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—
104C7×#95—22no—
105C7×#95—22no—
106C7×#95—42no—
107C7⋊#95—22no—
108C7⋊#95—22no—
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—72no—
118#1439—72no—
119C4⋊#95—72no—
120C22⋊#95—71no—
121C22⋊#95—71no—
122C22⋊#95—71no—
123C22⋊#95D711yescharacteristic, complemented
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—28no—
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×C7—22no—
167C22×C4×C7—44no—
168C22×C4×C7—44no—
169C22×C4×C7—48no—
170C22×C4×C7—48no—
171C22×C4×C7C22×C412yes—
172C22×C4×C7C22×C412yes—
173C22×C4×C7C2×D412yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7#4114yes—
176C2×C22⋊D7—28no—
177C2×C22⋊D7—28no—
178C2×C22⋊D7—28no—
179C2×C22⋊D7—28no—
180C2×C22⋊D7—28no—
181C2×C22⋊D7—28no—
182C2×C22⋊D7C4⋊C4116yescomplemented
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—21no—
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×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
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—44no—
216C2×C4×D7—44no—
217C2×C4×D7—48no—
218C2×C4×D7—48no—
219C7×C22⋊C4—48no—
220C22⋊Dic7—28no—
221C22⋊Dic7—48no—
222(C2×D7)⋊C4—28no—
223(C2×D7)⋊C4—48no—
224(C2×D7)⋊C4—48no—
225Dic7⋊C4—216no—
226Dic7⋊C4—28no—
227Dic7⋊C4—48no—
228C4×Dic7—48no—
229C4×Dic7C22⋊C4116yescomplemented
230C23×D4—71no—
231C24×C4—71no—
232C24×C4C2×D711yescharacteristic
233C2×C4×D4—78no—
234C2×C4×D4—144no—
235C2×C4×D4—144no—
236C22×C4⋊C4—71no—
237C22×C4⋊C4—72no—
238C22×C4⋊C4—72no—
239C22×C22⋊C4—71no—
240C22×C22⋊C4—71no—
241C22×C22⋊C4—72no—
242C22×C22⋊C4—72no—
243C22×C22⋊C4—72no—
244C22×C22⋊C4C2×D712yes—
245C22×C42—71no—
246C22×C42—72no—
247#390—148no—
248#382—144no—
249C4×C4⋊C4—144no—
250C2×#95—71no—
251C2×#95—71no—
252C2×#95—72no—
253C2×#95—72no—
254C2×#95—72no—
255C2×#95—72no—
256C2×#95C2×D711yescharacteristic
257C2×#95C2×D711yescharacteristic
258C2×#95C2×D712yes—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—24no—
270C23×C7—24no—
271C23×C7—24no—
272C23×C7—24no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7C2×C4⋊C414yes—
282C23×C7C23×C411yescharacteristic
283C23×C7C22×D411yescharacteristic
284C23×C7C22×D411yescharacteristic
285C23×C7C22×D411yescharacteristic
286C23×C7C22×Q811yescharacteristic
287C23×C7C2×#4112yes—
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4112yes—
291C23×C7H(5,𝔽2)12yes—
292C23×C7H(5,𝔽2)12yes—
293C22×D7—22no—
294C22×D7—22no—
295C22×D7—22no—
296C22×D7—22no—
297C22×D7—22no—
298C22×D7—22no—
299C22×D7—22no—
300C22×D7—22no—
301C22×D7—22no—
302C22×D7—22no—
303C22×D7—24no—
304C22×D7—24no—
305C22×D7—24no—
306C22×D7—24no—
307C22×D7—42no—
308C22×D7—42no—
309C22×D7—42no—
310C22×D7—42no—
311C22×D7—42no—
312C22×D7—42no—
313C22×D7—42no—
314C22×D7—42no—
315C22×D7C2×C4⋊C414yes—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—24no—
319C2×C4×C7—24no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—416no—
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×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7C2×C22⋊C414yes—
341C22⋊D7—232no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—24no—
345C2×Dic7—24no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—24no—
350C2×Dic7—24no—
351C2×Dic7—24no—
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×Dic7C2×C22⋊C414yes—
366C2×Dic7C2×C22⋊C414yes—
367C2×Dic7C2×C4⋊C414yes—
368C2×Dic7#11714yes—
369C2×Dic7#12114yes—
370C2×Dic7#12114yes—
371C2×Dic7C22⋊Q814yes—
372C2×Dic7C22⋊Q814yes—
373C4×D7—416no—
374C25—71no—
375C25C22×D711yescharacteristic
376C22×D4—74no—
377C22×D4—74no—
378C22×D4—74no—
379C22×D4—142no—
380C22×D4—142no—
381C22×D4—142no—
382C22×D4—142no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—71no—
388C23×C4—71no—
389C23×C4—72no—
390C23×C4—71no—
391C23×C4—74no—
392C23×C4—72no—
393C23×C4—142no—
394C23×C4—142no—
395C23×C4—282no—
396C23×C4—282no—
397C23×C4C4×D714yes—
398C23×C4C22×D712yes—
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D712yes—
401C23×C4C22×D711yescharacteristic
402C4×D4—1432no—
403C2×C4⋊C4—74no—
404C2×C4⋊C4—142no—
405C2×C4⋊C4—142no—
406C2×C4⋊C4—144no—
407C2×C4⋊C4—144no—
408C2×C4⋊C4—144no—
409C2×C4⋊C4—144no—
410C2×C4⋊C4—144no—
411C2×C4⋊C4—144no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—74no—
416C2×C22⋊C4—74no—
417C2×C22⋊C4—142no—
418C2×C22⋊C4—142no—
419C2×C22⋊C4—142no—
420C2×C22⋊C4—142no—
421C2×C22⋊C4—144no—
422C2×C22⋊C4—144no—
423C2×C22⋊C4—144no—
424C2×C22⋊C4—144no—
425C2×C22⋊C4—144no—
426C2×C22⋊C4—144no—
427C2×C22⋊C4—282no—
428C2×C22⋊C4—282no—
429C2×C22⋊C4—282no—
430C2×C42—74no—
431C2×C42—74no—
432C2×C42—74no—
433C2×C42—144no—
434C2×C42—144no—
435C2×C42—144no—
436#95—22no—
437#95—22no—
438#95—42no—
439#95—144no—
440#95—142no—
441#95—142no—
442#95—282no—
443#95—282no—
444#95—282no—
445C22×C7—24no—
446C22×C7—24no—
447C22×C7—24no—
448C22×C7—42no—
449C22×C7—44no—
450C22×C7—44no—
451C22×C7—42no—
452C22×C7—42no—
453C22×C7—44no—
454C22×C7—44no—
455C22×C7—42no—
456C22×C7C22×C22⋊C411yescharacteristic
457C22×C7C22×C4⋊C411yescharacteristic
458C22×C7C2×#11711yescharacteristic
459C22×C7C4×#4111yescharacteristic
460C22×C7C4×#4111yescharacteristic
461C22×C7#51811yescharacteristic
462C22×C7#51811yescharacteristic
463C22×C7C2×#12111yescharacteristic
464C22×C7C2×#12111yescharacteristic
465C22×C7C2×C22⋊Q811yescharacteristic
466C22×C7C2×C22⋊Q811yescharacteristic
467C22×C7#52512yes—
468C22×C7#53212yes—
469C22×C7#53512yes—
470C22×C7#53512yes—
471C22×C7#54612yes—
472C22×C7#54612yes—
473C22×C7#55312yes—
474C22×C7#55312yes—
475C22×C7#55412yes—
476C22×C7#55412yes—
477C22×C7#55912yes—
478C22×C7#55912yes—
479C2×D7—24no—
480C2×D7—24no—
481C2×D7—24no—
482C2×D7—42no—
483C2×D7—44no—
484C2×D7—44no—
485C2×D7—42no—
486C2×D7—42no—
487C2×D7—44no—
488C2×D7—44no—
489C2×D7—42no—
490C4×C7—24no—
491C4×C7—42no—
492C4×C7—44no—
493C4×C7—82no—
494Dic7—24no—
495Dic7—42no—
496Dic7—44no—
497Dic7—82no—
498Dic7#38018yes—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24—72no—
508C24—72no—
509C24—72no—
510C24—142no—
511C24—141no—
512C24—141no—
513C24—142no—
514C24—142no—
515C24—142no—
516C24—141no—
517C24—141no—
518C24C2×C4×D712yes—
519C24D4×D712yes—
520C24Q8×D712yes—
521C24C23×D711yescharacteristic
522C2×D4—716no—
523C2×D4—148no—
524C2×D4—148no—
525C2×D4—148no—
526C2×D4—148no—
527C2×D4—148no—
528C2×D4—148no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—74no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—148no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—284no—
586C22×C4—284no—
587C22×C4—288no—
588C22×C4—288no—
589C22×C4C2×C4×D712yes—
590C22×C4C2×C4×D712yes—
591C22×C4#115714yes—
592C22×C4D4×D712yes—
593C22×C4D4×D712yes—
594C4⋊C4—148no—
595C4⋊C4—1416no—
596C4⋊C4—288no—
597C22⋊C4—48no—
598C22⋊C4—148no—
599C22⋊C4—148no—
600C22⋊C4—288no—
601C22⋊C4—288no—
602C22⋊C4—288no—
603C42—716no—
604C42—288no—
605C2×C7—44no—
606C2×C7C2×#38011yescharacteristic
607C2×C7#229711yescharacteristic
608C2×C7#230911yescharacteristic
609C2×C7#234911yescharacteristic
610C2×C7#234911yescharacteristic
611C2×C7#235711yescharacteristic
612C2×C7#235711yescharacteristic
613C2×C7#253512yes—
614C2×C7#254412yes—
615C2×C7#256612yes—
616C2×C7#258012yes—
617D7—44no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—74no—
641C23—142no—
642C23—142no—
643C23—142no—
644C23—142no—
645C23—144no—
646C23—144no—
647C23—142no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—144no—
652C23—142no—
653C23—142no—
654C23—144no—
655C23—282no—
656C23—282no—
657C23—282no—
658C23—282no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23—282no—
663C23D7×C4⋊C414yes—
664C23C22×C4×D711yescharacteristic
665C23C2×#115712yes—
666C23C2×D4×D711yescharacteristic
667C23C2×D4×D711yescharacteristic
668C23C2×D4×D711yescharacteristic
669C23#654812yes—
670C23#654812yes—
671C23C2×Q8×D711yescharacteristic
672C23D7×#4111yescharacteristic
673C23D7×#4111yescharacteristic
674C23D7×#4112yes—
675D4—1432no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—416no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—74no—
701C2×C4—74no—
702C2×C4—74no—
703C2×C4—74no—
704C2×C4—74no—
705C2×C4—74no—
706C2×C4—74no—
707C2×C4—74no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—144no—
711C2×C4—144no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—144no—
716C2×C4—144no—
717C2×C4—144no—
718C2×C4—2816no—
719C2×C4—282no—
720C2×C4—282no—
721C2×C4—282no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4—282no—
729C2×C4—282no—
730C2×C4—282no—
731C2×C4—282no—
732C2×C4D7×C22⋊C414yes—
733C7#1394111yescharacteristic, complemented, Sylow
734C22—24no—
735C22—24no—
736C22—24no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—44no—
744C22—44no—
745C22—144no—
746C22—144no—
747C22—144no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—284no—
752C22—284no—
753C22—282no—
754C22—284no—
755C22—284no—
756C22C4×#115711yescharacteristic
757C22C2×D7×C22⋊C411yescharacteristic
758C22#9017711yescharacteristic
759C22#9017711yescharacteristic
760C22#9018112yes—
761C22C2×D7×C4⋊C411yescharacteristic
762C22#9020212yes—
763C22D7×#11711yescharacteristic
764C22#9021311yescharacteristic
765C22#9023112yes—
766C22#9023812yes—
767C22#9023912yes—
768C22#9025012yes—
769C22#9028312yes—
770C22#9028312yes—
771C22D7×#12111yescharacteristic
772C22D7×#12111yescharacteristic
773C22#9030112yes—
774C22D7×C22⋊Q811yescharacteristic
775C22D7×C22⋊Q811yescharacteristic
776C22#9032712yes—
777C22#9035212yes—
778C22#9035512yes—
779C4—24no—
780C4—42no—
781C4—44no—
782C4—78no—
783C4—82no—
784C4—144no—
785C4—282no—
786C4—284no—
787C4—562no—
788C2—44no—
789C2—284no—
790C2#1173081411yescharacteristic
791C2#1173090811yescharacteristic
792C2#1173100811yescharacteristic
793C2#1173126411yescharacteristic
794C2D7×#38011yescharacteristic
795C2#1173145611yescharacteristic
796C2#1173150611yescharacteristic
797C2#1173192212yes—
798C2#1173193212yes—
799C2#1173219612yes—
800C2#1173219812yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22⋊#95D7
hypocenterC7#13941
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#89422C2semidirect
4. C2×#89421C2semidirect
5. C7×C22⋊#95C2semidirect
6. #11729881C2semidirect
7. #11729301C2semidirect
8. #11727182C2semidirect
9. (C2×D7)⋊#95C2semidirect
10. (C2×D7)⋊#95C2semidirect
11. Dic7⋊#95C2semidirect
20. C2×C4×C22⋊D7C4semidirect
123. C22⋊#95D7semidirect
182. C2×C22⋊D7C4⋊C4semidirect
229. C4×Dic7C22⋊C4semidirect
733. C7#13941semidirect

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×#897292
C2×#894222
C2×#894212
C7×C22⋊#952
#117298812
#117293012
#117271822
(C2×D7)⋊#952
Dic7⋊#952
#139417