Finite Group Databasebeta

← #13276213

Subgroups — #13276213

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic7C211yesmaximal, characteristic
2C2×#89426C211yesmaximal, characteristic
3C2×#89425C211yesmaximal, characteristic
4C7×#1446C211yesmaximal, characteristic
5#11729888C211yesmaximal, characteristic
6#11727165C211yesmaximal, characteristic
7#11727165C211yesmaximal, characteristic
8#11727161C211yesmaximal, characteristic
9#11727161C211yesmaximal, characteristic
10Dic7⋊#95C211yesmaximal, characteristic
11#11727157C211yesmaximal, characteristic
12#11727156C211yesmaximal, characteristic
13#11727156C211yesmaximal, characteristic
14#11727155C211yesmaximal, characteristic
15Dic7×#95C211yesmaximal, characteristic
16C23×C7×Q8C2211yescharacteristic
17C2×Q8×Dic7—24no—
18C2×Q8×Dic7—24no—
19C2×Q8×Dic7C418yescomplemented
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89426—24no—
55#89425—24no—
56#13927—71nomaximal, Sylow
57C22×C7×Q8—22no—
58C22×C7×Q8—22no—
59C22×C7×Q8—22no—
60C22×C7×Q8—22no—
61C22×C7×Q8—22no—
62C22×C7×Q8—22no—
63C22×C7×Q8C2×C414yes—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79Q8×Dic7—232no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7C2×C414yes—
85C2×C4⋊Dic7C2×C414yes—
86C2×C4⋊Dic7C2×C414yes—
87C2×C4⋊Dic7D414yes—
88C2×C4⋊Dic7D414yes—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—41no—
94C2×Dic7⋊C4—41no—
95C2×C4×Dic7—22no—
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—22no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—41no—
106C2×C4×Dic7—41no—
107C2×C4×Dic7C2×C414yes—
108C2×C4×Dic7C2×C414yes—
109C2×C4×Dic7C2×C414yes—
110C7×#95—22no—
111C7×#95—22no—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—22no—
115C7×#95—22no—
116C7⋊#95—22no—
117C7⋊#95—22no—
118C7⋊#95—22no—
119C7⋊#95—22no—
120C7⋊#95—22no—
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95Q814yescomplemented
134C22×C4×Q8—71no—
135C2×#387—71no—
136C2×#387—71no—
137#1446—71no—
138#1446D711yescharacteristic
139#1441—71no—
140#1441—71no—
141#1436—71no—
142#1436—71no—
143C4⋊#95—71no—
144#1434—71no—
145#1434—71no—
146#1434—71no—
147#1434—71no—
148C4×#95—71no—
149C24×C7C2411yescharacteristic
150C2×C7×Q8—28no—
151C2×C7×Q8—28no—
152C2×C7×Q8—28no—
153C2×C7×Q8—28no—
154C2×C7×Q8—28no—
155C2×C7×Q8—28no—
156C2×C7×Q8—28no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7C22×C412yes—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D412yes—
200C22×C4×C7C2×Q812yes—
201C22×C4×C7#4112yes—
202C22×C4×C7#4112yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7C22×C412yes—
251C22×Dic7C22×C412yes—
252C22×Dic7C22×C412yes—
253C22×Dic7C22×C412yes—
254C22×Dic7C2×D412yes—
255C22×Dic7C2×D412yes—
256C22×Dic7C2×D412yes—
257C22×Dic7C2×D412yes—
258C22×Dic7C2×Q812yes—
259C22×Dic7C2×Q812yes—
260C22×Dic7#4112yes—
261C22×Dic7#4112yes—
262C4⋊Dic7—28no—
263C4⋊Dic7—28no—
264C4⋊Dic7C22⋊C4116yes—
265Dic7⋊C4—44no—
266Dic7⋊C4—44no—
267C4×Dic7—28no—
268C4×Dic7—28no—
269C4×Dic7—28no—
270C4×Dic7—44no—
271C4×Dic7—44no—
272C23×Q8C2×D711yescharacteristic
273C2×C4×Q8—78no—
274C2×C4×Q8—144no—
275C2×C4×Q8—144no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C42—71no—
282C22×C42—71no—
283C22×C42—71no—
284C22×C42—71no—
285C22×C42—71no—
286#387—144no—
287#387—144no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95C2×D711yescharacteristic
307C2×#95C2×D711yescharacteristic
308C2×#95C2×D711yescharacteristic
309C2×#95C2×D711yescharacteristic
310C2×#95C2×D711yescharacteristic
311C2×#95C2×D711yescharacteristic
312C23×C7C23×C411yescharacteristic
313C23×C7C22×D411yescharacteristic
314C23×C7C22×D411yescharacteristic
315C23×C7C22×Q811yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7C2×#4111yescharacteristic
319C23×C7C2×#4111yescharacteristic
320C23×C7C2×#4111yescharacteristic
321C23×C7C2×#4111yescharacteristic
322C23×C7C2×#4111yescharacteristic
323C23×C7H(5,𝔽2)11yescharacteristic
324C23×C72−1+411yescharacteristic
325C23×C72−1+411yescharacteristic
326C23×C72−1+411yescharacteristic
327C7×Q8—232no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7C2×C22⋊C414yes—
375C2×C4×C7#11714yes—
376C2×C4×C7#11714yes—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—41no—
405C2×Dic7—41no—
406C2×Dic7—41no—
407C2×Dic7—41no—
408C2×Dic7—41no—
409C2×Dic7—41no—
410C2×Dic7—41no—
411C2×Dic7—41no—
412C2×Dic7—41no—
413C2×Dic7—41no—
414C2×Dic7—41no—
415C2×Dic7—41no—
416C2×Dic7—41no—
417C2×Dic7—41no—
418C2×Dic7—41no—
419C2×Dic7—41no—
420C2×Dic7—41no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7—41no—
424C2×Dic7—41no—
425C2×Dic7—41no—
426C2×Dic7—41no—
427C2×Dic7—41no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7C2×C22⋊C414yes—
431C2×Dic7C2×C22⋊C414yes—
432C2×Dic7C4×Q814yes—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—22no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8C4×D714yes—
440C23×C4—71no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4C22×D711yescharacteristic
449C23×C4C22×D711yescharacteristic
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C23×C4C22×D711yescharacteristic
455C4×Q8—1432no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—142no—
463C2×C4⋊C4—142no—
464C2×C4⋊C4—142no—
465C2×C4⋊C4—142no—
466C2×C4⋊C4—142no—
467C2×C4⋊C4—142no—
468C2×C4⋊C4—142no—
469C2×C4⋊C4—281no—
470C2×C4⋊C4—281no—
471C2×C42—74no—
472C2×C42—74no—
473C2×C42—74no—
474C2×C42—142no—
475C2×C42—142no—
476C2×C42—142no—
477C2×C42—142no—
478C2×C42—142no—
479C2×C42—142no—
480C2×C42—142no—
481C2×C42—142no—
482C2×C42—142no—
483C2×C42—142no—
484C2×C42—281no—
485C2×C42—281no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—74no—
493#95—142no—
494#95—142no—
495#95—142no—
496#95—142no—
497#95—142no—
498#95—142no—
499#95—142no—
500#95—142no—
501#95—142no—
502#95—142no—
503#95—142no—
504#95—142no—
505#95—142no—
506#95—142no—
507#95—142no—
508#95—281no—
509#95—281no—
510C22×C7C22×C22⋊C411yescharacteristic
511C22×C7C2×#11711yescharacteristic
512C22×C7C2×#11711yescharacteristic
513C22×C7C2×C4×Q811yescharacteristic
514C22×C7C4×#4111yescharacteristic
515C22×C7#51911yescharacteristic
516C22×C7#52011yescharacteristic
517C22×C7#52511yescharacteristic
518C22×C7#52511yescharacteristic
519C22×C7#52511yescharacteristic
520C22×C7#52511yescharacteristic
521C22×C7#52911yescharacteristic
522C22×C7#52911yescharacteristic
523C22×C7#53311yescharacteristic
524C22×C7#53311yescharacteristic
525C22×C7#54111yescharacteristic
526C22×C7#54111yescharacteristic
527C22×C7#54211yescharacteristic
528C22×C7#54211yescharacteristic
529C22×C7#54611yescharacteristic
530C22×C7#54611yescharacteristic
531C22×C7#54711yescharacteristic
532C22×C7#54711yescharacteristic
533C22×C7#54811yescharacteristic
534C22×C7#54811yescharacteristic
535C22×C7D4×Q811yescharacteristic
536C22×C7D4×Q811yescharacteristic
537C22×C7#55211yescharacteristic
538C22×C7#55211yescharacteristic
539C22×C7#55411yescharacteristic
540C22×C7#55611yescharacteristic
541C22×C7#55611yescharacteristic
542C22×C7#55611yescharacteristic
543C22×C7#55711yescharacteristic
544C22×C7#55911yescharacteristic
545C4×C7—24no—
546C4×C7—24no—
547C4×C7—24no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7—81no—
551C4×C7—81no—
552Dic7—24no—
553Dic7—24no—
554Dic7—24no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558Dic7—81no—
559Dic7—81no—
560C24C23×D711yescharacteristic
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8—28no—
566C2×Q8—28no—
567C2×Q8—28no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—72no—
607C22×C4—72no—
608C22×C4—72no—
609C22×C4—72no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—72no—
613C22×C4—72no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—141no—
625C22×C4—141no—
626C22×C4—141no—
627C22×C4—141no—
628C22×C4—141no—
629C22×C4—141no—
630C22×C4—141no—
631C22×C4—141no—
632C22×C4—141no—
633C22×C4—141no—
634C22×C4—141no—
635C22×C4—141no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—141no—
642C22×C4—141no—
643C22×C4—141no—
644C22×C4—141no—
645C22×C4—141no—
646C22×C4—141no—
647C22×C4—141no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—141no—
652C22×C4—141no—
653C22×C4—141no—
654C22×C4—141no—
655C22×C4—141no—
656C22×C4—141no—
657C22×C4—141no—
658C22×C4—141no—
659C22×C4—141no—
660C22×C4—141no—
661C22×C4—141no—
662C22×C4C2×C4×D712yes—
663C22×C4C2×C4×D712yes—
664C22×C4C2×C4×D712yes—
665C22×C4D4×D712yes—
666C22×C4D4×D712yes—
667C22×C4#115912yes—
668C22×C4#115912yes—
669C22×C4#115912yes—
670C22×C4#115912yes—
671C22×C4Q8×D712yes—
672C22×C4#116112yes—
673C4⋊C4—716no—
674C4⋊C4—148no—
675C4⋊C4—148no—
676C4⋊C4—284no—
677C4⋊C4—284no—
678C42—148no—
679C42—148no—
680C42—148no—
681C42—284no—
682C42—284no—
683C2×C7#228011yescharacteristic
684C2×C7#229511yescharacteristic
685C2×C7#232011yescharacteristic
686C2×C7#233911yescharacteristic
687C2×C7Q8×C22⋊C411yescharacteristic
688C2×C7#235511yescharacteristic
689C2×C7#235611yescharacteristic
690C2×C7#245811yescharacteristic
691C2×C7#245811yescharacteristic
692C2×C7#246211yescharacteristic
693C2×C7#246211yescharacteristic
694C2×C7#246511yescharacteristic
695C2×C7#246511yescharacteristic
696C2×C7#246911yescharacteristic
697C2×C7#246911yescharacteristic
698C23C22×C4×D711yescharacteristic
699C23C2×D4×D711yescharacteristic
700C23C2×D4×D711yescharacteristic
701C23C2×#115911yescharacteristic
702C23C2×#115911yescharacteristic
703C23C2×#115911yescharacteristic
704C23C2×#115911yescharacteristic
705C23C2×Q8×D711yescharacteristic
706C23C2×#116111yescharacteristic
707C23#655111yescharacteristic
708C23#655111yescharacteristic
709C23D7×#4111yescharacteristic
710C23D7×#4111yescharacteristic
711C23#655311yescharacteristic
712C23#655411yescharacteristic
713Q8—232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—74no—
761C2×C4—74no—
762C2×C4—74no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—142no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—281no—
791C2×C4—281no—
792C2×C4—281no—
793C2×C4—281no—
794C2×C4—281no—
795C2×C4—281no—
796C2×C4—281no—
797C2×C4—281no—
798C2×C4—281no—
799C2×C4—281no—
800C2×C4—281no—
801C2×C4—281no—
802C2×C4—281no—
803C2×C4—281no—
804C2×C4—281no—
805C2×C4—281no—
806C2×C4—281no—
807C2×C4—281no—
808C2×C4—281no—
809C2×C4—281no—
810C2×C4—281no—
811C2×C4—281no—
812C2×C4—281no—
813C2×C4—281no—
814C2×C4—281no—
815C2×C4—281no—
816C2×C4#644014yes—
817C2×C4#644014yes—
818C2×C4D7×C22⋊C414yes—
819C7#1392711yescharacteristic, complemented, Sylow
820C22C2×#644011yescharacteristic
821C22C2×#644011yescharacteristic
822C22C2×D7×C22⋊C411yescharacteristic
823C22C4×Q8×D711yescharacteristic
824C22#9026311yescharacteristic
825C22C4×#116111yescharacteristic
826C22#9026511yescharacteristic
827C22#9027711yescharacteristic
828C22#9027711yescharacteristic
829C22#9027711yescharacteristic
830C22#9027711yescharacteristic
831C22#9031311yescharacteristic
832C22#9031511yescharacteristic
833C22#9031611yescharacteristic
834C22#9032111yescharacteristic
835C22#9032211yescharacteristic
836C22#9032311yescharacteristic
837C22#9032411yescharacteristic
838C22#9032611yescharacteristic
839C22#9033011yescharacteristic
840C22#9033211yescharacteristic
841C22#9033311yescharacteristic
842C22#9033411yescharacteristic
843C22#9036211yescharacteristic
844C22#9036711yescharacteristic
845C22#9036811yescharacteristic
846C22#9037111yescharacteristic
847C22#9037211yescharacteristic
848C22#9037311yescharacteristic
849C22#9041211yescharacteristic
850C22#9041711yescharacteristic
851C22#9041811yescharacteristic
852C22#9041911yescharacteristic
853C22#9042211yescharacteristic
854C22#9042311yescharacteristic
855C4—24no—
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—144no—
863C4—144no—
864C4—144no—
865C4—282no—
866C4—282no—
867C4—282no—
868C4—561no—
869C4—561no—
870C2#1173126211yescharacteristic
871C2#1173392211yescharacteristic
872C2#1173392811yescharacteristic
873C2#1173393411yescharacteristic
874C2#1173393511yescharacteristic
875C2#1173405811yescharacteristic
876C2#1173405911yescharacteristic
877C2#1173422911yescharacteristic
878C2#1173423011yescharacteristic
879C2#1173423311yescharacteristic
880C2#1173423411yescharacteristic
881C2#1173462211yescharacteristic
882C2#1173462311yescharacteristic
883C2#1173462411yescharacteristic
884C2#1173462611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1446C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1446D7
hypocenterC7#13927
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
19. C2×Q8×Dic7C4semidirect
133. C7⋊#95Q8semidirect
819. C7#13927semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic72
C2×#894262
C2×#894252
C7×#14462
#117298882
#117271652
#117271612
Dic7⋊#952
#117271572
#117271562
#117271552
Dic7×#952
#139277