Finite Group Databasebeta

← #13277652

Subgroups — #13277652

Order 1792.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#387C211yesmaximal, characteristic
2C2×#89750C211yesmaximal, characteristic
3C2×C4⋊C4×Dic7C211yesmaximal, characteristic
4#11729319C211yesmaximal, characteristic
5#11729318C211yesmaximal, characteristic
6#11729288C211yesmaximal, characteristic
7C4×C7⋊#95C211yesmaximal, characteristic
8#11727175C211yesmaximal, characteristic
9#11727174C211yesmaximal, characteristic
10#11727167C211yesmaximal, characteristic
11#11727160C211yesmaximal, characteristic
12#11727160C211yesmaximal, characteristic
13Dic7⋊#95C211yesmaximal, characteristic
14#11727156C211yesmaximal, characteristic
15#11727156C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C7×#387—24no—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
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
52#89750C418yescomplemented
53C4⋊C4×Dic7—24no—
54#14056—71nomaximal, Sylow
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×Dic7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4C2×C414yes—
75C2×C7×C4⋊C4D414yes—
76C2×C42×C7—22no—
77C2×C42×C7—22no—
78C2×C42×C7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×Dic7⋊C4—22no—
83C2×Dic7⋊C4—22no—
84C2×Dic7⋊C4—22no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4—41no—
88C2×Dic7⋊C4—41no—
89C2×Dic7⋊C4—41no—
90C2×Dic7⋊C4C2×C414yes—
91C2×C4×Dic7—22no—
92C2×C4×Dic7—22no—
93C2×C4×Dic7—22no—
94C2×C4×Dic7—22no—
95C2×C4×Dic7—22no—
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—41no—
100C2×C4×Dic7—41no—
101C2×C4×Dic7—41no—
102C2×C4×Dic7C2×C414yes—
103C7×#95—22no—
104C7×#95—22no—
105C7×#95—22no—
106C7×#95—22no—
107C7⋊#95—22no—
108C7⋊#95—22no—
109C7⋊#95—22no—
110C7⋊#95—22no—
111C7⋊#95—22no—
112C7⋊#95—22no—
113C7⋊#95—22no—
114C7⋊#95—22no—
115C7⋊#95—22no—
116C7⋊#95—41no—
117C7⋊#95—41no—
118C7⋊#95—41no—
119C7⋊#95—41no—
120C7⋊#95—41no—
121C7⋊#95—41no—
122C7⋊#95C2×C414yes—
123C7⋊#95C2×C414yes—
124C7⋊#95C2×C414yes—
125C7⋊#95C2×C414yes—
126C7⋊#95Q814yes—
127C2×#387—71no—
128C2×#387D711yescharacteristic
129C2×C4×C4⋊C4—71no—
130#1445—71no—
131#1444—71no—
132#1442—71no—
133#1441—71no—
134#1436—71no—
135#1436—71no—
136#1436—71no—
137C4⋊#95—71no—
138#1434—71no—
139#1434—71no—
140#1434—71no—
141C4×#95—71no—
142C24×C7C2411yescharacteristic
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
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×C7C22×C412yes—
183C22×C4×C7C22×C412yes—
184C22×C4×C7C22×C412yes—
185C22×C4×C7C2×D412yes—
186C22×C4×C7C2×D412yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7C2×Q812yes—
189C22×C4×C7#4112yes—
190C22×C4×C7#4112yes—
191C22×C4×C7#4112yes—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
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×Dic7C22×C412yes—
238C22×Dic7C22×C412yes—
239C22×Dic7C22×C412yes—
240C22×Dic7C22×C412yes—
241C22×Dic7C2×Q812yes—
242C22×Dic7C2×Q812yes—
243C22×Dic7#4112yes—
244C22×Dic7#4112yes—
245C22×Dic7#4112yes—
246C22×Dic7#4112yes—
247C22×Dic7#4112yes—
248C7×C4⋊C4—28no—
249C7×C4⋊C4—28no—
250C42×C7—44no—
251C4⋊Dic7—28no—
252Dic7⋊C4—28no—
253Dic7⋊C4—44no—
254Dic7⋊C4—44no—
255C4×Dic7—28no—
256C4×Dic7—44no—
257C4×Dic7—44no—
258C4×Dic7—44no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4C2×D711yescharacteristic
264C22×C4⋊C4C2×D711yescharacteristic
265C22×C42—71no—
266C22×C42—71no—
267C22×C42—71no—
268C22×C42—71no—
269C22×C42C2×D711yescharacteristic
270#387—24no—
271#387—78no—
272C4×C4⋊C4—144no—
273C2×#95—71no—
274C2×#95—71no—
275C2×#95—71no—
276C2×#95—71no—
277C2×#95—71no—
278C2×#95—71no—
279C2×#95—71no—
280C2×#95—71no—
281C2×#95—71no—
282C2×#95—71no—
283C2×#95—71no—
284C2×#95—71no—
285C2×#95—71no—
286C2×#95—71no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95C2×D711yescharacteristic
294C2×#95C2×D711yescharacteristic
295C2×#95C2×D711yescharacteristic
296C2×#95C2×D711yescharacteristic
297C23×C7C23×C411yescharacteristic
298C23×C7C22×D411yescharacteristic
299C23×C7C22×Q811yescharacteristic
300C23×C7C2×#4111yescharacteristic
301C23×C7C2×#4111yescharacteristic
302C23×C7C2×#4111yescharacteristic
303C23×C7C2×#4111yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C23×C7C2×#4111yescharacteristic
306C23×C7C2×#4111yescharacteristic
307C23×C7C2×#4111yescharacteristic
308C23×C7H(5,𝔽2)11yescharacteristic
309C23×C7H(5,𝔽2)11yescharacteristic
310C23×C72−1+411yescharacteristic
311C23×C72−1+411yescharacteristic
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
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—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
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×C7C4×D414yes—
360C2×C4×C7#12314yes—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
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—41no—
389C2×Dic7—41no—
390C2×Dic7—41no—
391C2×Dic7—41no—
392C2×Dic7—41no—
393C2×Dic7—41no—
394C2×Dic7—41no—
395C2×Dic7—41no—
396C2×Dic7—41no—
397C2×Dic7—41no—
398C2×Dic7—41no—
399C2×Dic7—41no—
400C2×Dic7—41no—
401C2×Dic7—41no—
402C2×Dic7—41no—
403C2×Dic7—41no—
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#11714yes—
416C2×Dic7C4×Q814yes—
417C23×C4—71no—
418C23×C4—71no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C23×C4C22×D711yescharacteristic
429C23×C4C22×D711yescharacteristic
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—74no—
437C2×C4⋊C4—142no—
438C2×C4⋊C4—142no—
439C2×C4⋊C4—142no—
440C2×C4⋊C4—142no—
441C2×C4⋊C4—142no—
442C2×C4⋊C4—142no—
443C2×C4⋊C4—142no—
444C2×C4⋊C4—142no—
445C2×C4⋊C4—281no—
446C2×C4⋊C4—281no—
447C2×C4⋊C4—281no—
448C2×C4⋊C4C4×D714yes—
449C2×C4⋊C4C22⋊D714yes—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—74no—
454C2×C42—142no—
455C2×C42—142no—
456C2×C42—142no—
457C2×C42—142no—
458C2×C42—142no—
459C2×C42—142no—
460C2×C42—142no—
461C2×C42—142no—
462C2×C42—281no—
463C2×C42—281no—
464C2×C42—281no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—74no—
470#95—74no—
471#95—74no—
472#95—74no—
473#95—74no—
474#95—142no—
475#95—142no—
476#95—142no—
477#95—142no—
478#95—142no—
479#95—142no—
480#95—142no—
481#95—142no—
482#95—142no—
483#95—281no—
484#95—281no—
485#95—281no—
486#95—281no—
487#95—281no—
488#95—281no—
489C22×C7C2×#11711yescharacteristic
490C22×C7C2×C4×D411yescharacteristic
491C22×C7C2×C4×Q811yescharacteristic
492C22×C7C4×#4111yescharacteristic
493C22×C7C4×#4111yescharacteristic
494C22×C7#52011yescharacteristic
495C22×C7#52011yescharacteristic
496C22×C7C2×#12311yescharacteristic
497C22×C7#52511yescharacteristic
498C22×C7#52911yescharacteristic
499C22×C7#52911yescharacteristic
500C22×C7#52911yescharacteristic
501C22×C7#52911yescharacteristic
502C22×C7#53311yescharacteristic
503C22×C7#53311yescharacteristic
504C22×C7#53811yescharacteristic
505C22×C7#53911yescharacteristic
506C22×C7#54111yescharacteristic
507C22×C7#54211yescharacteristic
508C22×C7#54611yescharacteristic
509C22×C7#54711yescharacteristic
510C22×C7D4×Q811yescharacteristic
511C22×C7#55011yescharacteristic
512C22×C7#55111yescharacteristic
513C22×C7#55111yescharacteristic
514C22×C7#55211yescharacteristic
515C22×C7#55211yescharacteristic
516C22×C7#55211yescharacteristic
517C22×C7#55211yescharacteristic
518C22×C7#55311yescharacteristic
519C22×C7#55411yescharacteristic
520C22×C7#55411yescharacteristic
521C22×C7#55511yescharacteristic
522C22×C7#55611yescharacteristic
523C22×C7#55711yescharacteristic
524C4×C7—24no—
525C4×C7—24no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7—42no—
530C4×C7—81no—
531Dic7—24no—
532Dic7—24no—
533Dic7—42no—
534Dic7—42no—
535Dic7—42no—
536Dic7—42no—
537Dic7—42no—
538Dic7—81no—
539C24C23×D711yescharacteristic
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
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—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—141no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—141no—
615C22×C4—141no—
616C22×C4—141no—
617C22×C4—141no—
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×C4C2×C4×D712yes—
636C22×C4C2×C4×D712yes—
637C22×C4C2×C4×D712yes—
638C22×C4#115712yes—
639C22×C4#115912yes—
640C22×C4#115912yes—
641C22×C4Q8×D712yes—
642C22×C4C2×C22⋊D712yes—
643C22×C4C2×C22⋊D712yes—
644C22×C4C2×C22⋊D712yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—148no—
648C4⋊C4—148no—
649C4⋊C4—284no—
650C4⋊C4—284no—
651C42—44no—
652C42—148no—
653C42—284no—
654C42—284no—
655C42—284no—
656C2×C7#229511yescharacteristic
657C2×C7C4×#12311yescharacteristic
658C2×C7#233411yescharacteristic
659C2×C7#234311yescharacteristic
660C2×C7#235411yescharacteristic
661C2×C7#236011yescharacteristic
662C2×C7#237011yescharacteristic
663C2×C7#241911yescharacteristic
664C2×C7#242311yescharacteristic
665C2×C7#246211yescharacteristic
666C2×C7#246711yescharacteristic
667C2×C7#252411yescharacteristic
668C2×C7#252911yescharacteristic
669C2×C7#257411yescharacteristic
670C2×C7#258811yescharacteristic
671C23C22×C4×D711yescharacteristic
672C23C2×#115711yescharacteristic
673C23C2×#115911yescharacteristic
674C23C2×#115911yescharacteristic
675C23C2×Q8×D711yescharacteristic
676C23#655111yescharacteristic
677C23D7×#4111yescharacteristic
678C23D7×#4111yescharacteristic
679C23D7×#4111yescharacteristic
680C23D7×#4111yescharacteristic
681C23D7×#4111yescharacteristic
682C23#655311yescharacteristic
683C23#655311yescharacteristic
684C23#655411yescharacteristic
685C23C22×C22⋊D711yescharacteristic
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—74no—
734C2×C4—74no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—142no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—281no—
763C2×C4—281no—
764C2×C4—281no—
765C2×C4—281no—
766C2×C4—281no—
767C2×C4—281no—
768C2×C4—281no—
769C2×C4—281no—
770C2×C4—281no—
771C2×C4—281no—
772C2×C4—281no—
773C2×C4—281no—
774C2×C4—281no—
775C2×C4—281no—
776C2×C4—281no—
777C2×C4—281no—
778C2×C4—281no—
779C2×C4—281no—
780C2×C4—281no—
781C2×C4—281no—
782C2×C4—281no—
783C2×C4—281no—
784C2×C4—281no—
785C2×C4—281no—
786C2×C4—281no—
787C2×C4—281no—
788C2×C4—281no—
789C2×C4C4×C22⋊D714yes—
790C2×C4#649814yes—
791C7#1405611yescharacteristic, complemented, Sylow
792C22D7×#11711yescharacteristic
793C22#9021411yescharacteristic
794C22#9022311yescharacteristic
795C22#9022411yescharacteristic
796C22C4×#115911yescharacteristic
797C22C4×#115911yescharacteristic
798C22#9022911yescharacteristic
799C22#9022911yescharacteristic
800C22C4×Q8×D711yescharacteristic
801C22#9026511yescharacteristic
802C22#9027011yescharacteristic
803C22#9027211yescharacteristic
804C22#9031311yescharacteristic
805C22#9032611yescharacteristic
806C22#9033011yescharacteristic
807C22#9033411yescharacteristic
808C22#9034011yescharacteristic
809C22#9034111yescharacteristic
810C22#9034911yescharacteristic
811C22#9035611yescharacteristic
812C22#9037611yescharacteristic
813C22#9037911yescharacteristic
814C22#9038411yescharacteristic
815C22#9038711yescharacteristic
816C22#9039511yescharacteristic
817C22#9039611yescharacteristic
818C22#9039711yescharacteristic
819C22#9040011yescharacteristic
820C22C2×C4×C22⋊D711yescharacteristic
821C22C2×#649811yescharacteristic
822C22Q8×C22⋊D711yescharacteristic
823C22#9051511yescharacteristic
824C22#9051911yescharacteristic
825C22#9052011yescharacteristic
826C22#9052511yescharacteristic
827C4—24no—
828C4—24no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—81no—
834C4—144no—
835C4—144no—
836C4—282no—
837C4—282no—
838C4—282no—
839C4—282no—
840C4—282no—
841C4—561no—
842C2#1173238311yescharacteristic
843C2#1173239911yescharacteristic
844C2#1173241411yescharacteristic
845C2#1173249711yescharacteristic
846C2#1173251011yescharacteristic
847C2#1173252611yescharacteristic
848C2#1173255011yescharacteristic
849C2#1173274811yescharacteristic
850C2#1173968611yescharacteristic
851C2C4×#649811yescharacteristic
852C2#1173993511yescharacteristic
853C2#1174019911yescharacteristic
854C2#1174028911yescharacteristic
855C2#1174047611yescharacteristic
856C2#1174055111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#387C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#387D7
hypocenterC7#14056
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
52. #89750C4semidirect
791. C7#14056semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3872
C2×#897502
C2×C4⋊C4×Dic72
#117293192
#117293182
#117292882
C4×C7⋊#952
#117271752
#117271742
#117271672
#117271602
Dic7⋊#952
#117271562
#140567