Finite Group Databasebeta

← #13281783

Subgroups — #13281783

Order 1792.

1390 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
1C2×C7×#387C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic
3C2×#89757C211yesmaximal, characteristic
4C2×#89753C211yesmaximal, characteristic
5C2×#89707C211yesmaximal, characteristic
6#11729319C211yesmaximal, characteristic
7#11729288C211yesmaximal, characteristic
8#11727173C211yesmaximal, characteristic
9#11727173C211yesmaximal, characteristic
10#11727173C211yesmaximal, characteristic
11#11727173C211yesmaximal, characteristic
12#11727166C211yesmaximal, characteristic
13#11727161C211yesmaximal, characteristic
14#11727161C211yesmaximal, characteristic
15#11727161C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C7×#387C418yescomplemented
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#89757—24no—
53#89757—24no—
54#89753—24no—
55#89707—24no—
56#14406—71nomaximal, Sylow
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4C2×C414yes—
75C2×C7×C4⋊C4C2×C414yes—
76C2×C7×C4⋊C4D414yes—
77C2×C7×C4⋊C4Q814yes—
78C2×C42×C7—22no—
79C2×C42×C7—22no—
80C2×C42×C7C2×C414yes—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7—41no—
95C2×C4⋊Dic7—41no—
96C2×C4⋊Dic7—41no—
97C2×C4⋊Dic7—41no—
98C2×C4⋊Dic7—41no—
99C2×C4⋊Dic7—41no—
100C2×C4⋊Dic7—41no—
101C2×C4⋊Dic7—41no—
102C2×C4⋊Dic7—41no—
103C2×C4⋊Dic7—41no—
104C2×C4⋊Dic7—41no—
105C2×C4⋊Dic7—41no—
106C2×C4⋊Dic7—41no—
107C2×C4⋊Dic7—41no—
108C2×C4⋊Dic7—41no—
109C2×C4⋊Dic7—41no—
110C2×C4⋊Dic7D414yes—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—22no—
113C2×C4×Dic7—22no—
114C2×C4×Dic7—41no—
115C2×C4×Dic7—41no—
116C2×C4×Dic7—41no—
117C7×#95C2×C414yes—
118C7×#95C2×C414yes—
119C7×#95C2×C414yes—
120C7×#95C2×C414yes—
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⋊#95—41no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95Q814yes—
137C2×#389—71no—
138C2×#389—71no—
139C2×#387—71no—
140C2×#387D711yescharacteristic
141C2×#384—71no—
142#1444—71no—
143#1444—71no—
144#1444—71no—
145#1444—71no—
146#1442—71no—
147#1441—71no—
148#1436—71no—
149#1436—71no—
150#1436—71no—
151#1434—71no—
152C24×C7C2411yescharacteristic
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×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7C22×C412yes—
186C22×C4×C7C22×C412yes—
187C22×C4×C7C22×C412yes—
188C22×C4×C7C22×C412yes—
189C22×C4×C7C22×C412yes—
190C22×C4×C7C22×C412yes—
191C22×C4×C7C22×C412yes—
192C22×C4×C7C2×D412yes—
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2×D412yes—
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2×Q812yes—
197C22×C4×C7C2×Q812yes—
198C22×C4×C7C2×Q812yes—
199C22×C4×C7C2×Q812yes—
200C22×C4×C7#4112yes—
201C22×C4×C7#4112yes—
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×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×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7C2×D412yes—
255C22×Dic7C2×D412yes—
256C22×Dic7C2×Q812yes—
257C22×Dic7C2×Q812yes—
258C7×C4⋊C4—28no—
259C7×C4⋊C4C4⋊C4116yescomplemented
260C42×C7—28no—
261C4⋊Dic7—44no—
262C4⋊Dic7—44no—
263C4⋊Dic7—44no—
264C4⋊Dic7—44no—
265C4⋊Dic7—44no—
266C4⋊Dic7—44no—
267C4⋊Dic7—44no—
268C4⋊Dic7—44no—
269C4⋊Dic7—44no—
270C4⋊Dic7—44no—
271C4×Dic7—44no—
272C4×Dic7—44no—
273C22×C4⋊C4—71no—
274C22×C4⋊C4—71no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4C2×D711yescharacteristic
284C22×C4⋊C4C2×D711yescharacteristic
285C22×C42—71no—
286C22×C42—71no—
287C22×C42C2×D711yescharacteristic
288#389—144no—
289#389—144no—
290#387—144no—
291#387Dic718yescomplemented
292#384—144no—
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×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95C2×D711yescharacteristic
310C2×#95C2×D711yescharacteristic
311C2×#95C2×D711yescharacteristic
312C2×#95C2×D711yescharacteristic
313C23×C7C23×C411yescharacteristic
314C23×C7C22×D411yescharacteristic
315C23×C7C22×D411yescharacteristic
316C23×C7C22×Q811yescharacteristic
317C23×C7C22×Q811yescharacteristic
318C23×C7C2×#4111yescharacteristic
319C23×C7C2×#4111yescharacteristic
320C23×C7H(5,𝔽2)11yescharacteristic
321C23×C7H(5,𝔽2)11yescharacteristic
322C23×C7H(5,𝔽2)11yescharacteristic
323C23×C7H(5,𝔽2)11yescharacteristic
324C23×C72−1+411yescharacteristic
325C23×C72−1+411yescharacteristic
326C23×C72−1+411yescharacteristic
327C23×C72−1+411yescharacteristic
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—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
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×C7C2×C4⋊C414yes—
373C2×C4×C7C2×C4⋊C414yes—
374C2×C4×C7C2×C4⋊C414yes—
375C2×C4×C7C4×D414yes—
376C2×C4×C7C4×Q814yes—
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—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—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×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—71no—
437C23×C4—71no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—71no—
441C23×C4C22×D711yescharacteristic
442C23×C4C22×D711yescharacteristic
443C23×C4C22×D711yescharacteristic
444C23×C4C22×D711yescharacteristic
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C23×C4C22×D711yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—74no—
451C2×C4⋊C4—142no—
452C2×C4⋊C4—142no—
453C2×C4⋊C4—142no—
454C2×C4⋊C4—142no—
455C2×C4⋊C4—142no—
456C2×C4⋊C4—142no—
457C2×C4⋊C4—142no—
458C2×C4⋊C4—142no—
459C2×C4⋊C4—142no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—142no—
463C2×C4⋊C4—142no—
464C2×C4⋊C4—281no—
465C2×C4⋊C4—281no—
466C2×C4⋊C4—281no—
467C2×C4⋊C4—281no—
468C2×C4⋊C4—281no—
469C2×C4⋊C4—281no—
470C2×C4⋊C4—281no—
471C2×C4⋊C4—281no—
472C2×C4⋊C4—281no—
473C2×C4⋊C4—281no—
474C2×C4⋊C4—281no—
475C2×C4⋊C4—281no—
476C2×C4⋊C4—281no—
477C2×C4⋊C4—281no—
478C2×C4⋊C4—281no—
479C2×C4⋊C4—281no—
480C2×C4⋊C4Dic1414yes—
481C2×C4⋊C4D2814yes—
482C2×C4⋊C4C2×Dic714yes—
483C2×C4⋊C4C2×Dic714yes—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—142no—
487C2×C42—142no—
488C2×C42—142no—
489C2×C42—281no—
490C2×C42—281no—
491C2×C42—281no—
492C2×C42C2×Dic714yes—
493#95—74no—
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—281no—
505#95—281no—
506#95—281no—
507#95—281no—
508#95—281no—
509#95C2×Dic714yes—
510#95C2×Dic714yes—
511#95C2×Dic714yes—
512#95C2×Dic714yes—
513C22×C7C22×C4⋊C411yescharacteristic
514C22×C7C2×C4×D411yescharacteristic
515C22×C7C2×C4×Q811yescharacteristic
516C22×C7#52011yescharacteristic
517C22×C7#52011yescharacteristic
518C22×C7#52011yescharacteristic
519C22×C7#52011yescharacteristic
520C22×C7#53411yescharacteristic
521C22×C7#53511yescharacteristic
522C22×C7#53611yescharacteristic
523C22×C7#53611yescharacteristic
524C22×C7#53911yescharacteristic
525C22×C7#53911yescharacteristic
526C22×C7#54011yescharacteristic
527C22×C7#54111yescharacteristic
528C22×C7#54411yescharacteristic
529C22×C7#54411yescharacteristic
530C22×C7#54411yescharacteristic
531C22×C7#54411yescharacteristic
532C22×C7D4211yescharacteristic
533C22×C7#54611yescharacteristic
534C22×C7#54711yescharacteristic
535C22×C7D4×Q811yescharacteristic
536C22×C7D4×Q811yescharacteristic
537C22×C7D4×Q811yescharacteristic
538C22×C7#55011yescharacteristic
539C22×C7#55211yescharacteristic
540C22×C7#55411yescharacteristic
541C22×C7#55411yescharacteristic
542C22×C7#55711yescharacteristic
543C22×C7Q8211yescharacteristic
544C22×C7#56011yescharacteristic
545C22×C7#56311yescharacteristic
546C22×C7#56311yescharacteristic
547C22×C7#56311yescharacteristic
548C4×C7—24no—
549C4×C7—24no—
550C4×C7—24no—
551C4×C7—24no—
552C4×C7—24no—
553C4×C7—42no—
554C4×C7—42no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—81no—
560Dic7—81no—
561Dic7—81no—
562Dic7—81no—
563C24C23×D711yescharacteristic
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—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—72no—
597C22×C4—72no—
598C22×C4—72no—
599C22×C4—72no—
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×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×C4C2×Dic1412yes—
653C22×C4C2×Dic1412yes—
654C22×C4C2×Dic1412yes—
655C22×C4C2×D2812yes—
656C22×C4C2×D2812yes—
657C22×C4C2×D2812yes—
658C22×C4D4×D712yes—
659C22×C4#115912yes—
660C22×C4Q8×D712yes—
661C22×C4#116112yes—
662C22×C4C22×Dic712yes—
663C22×C4C22×Dic712yes—
664C22×C4C22×Dic712yes—
665C22×C4C22×Dic712yes—
666C22×C4C22×Dic712yes—
667C22×C4C22×Dic712yes—
668C22×C4C22×Dic712yes—
669C4⋊C4—28no—
670C4⋊C4—284no—
671C4⋊C4—284no—
672C4⋊C4—284no—
673C4⋊C4—284no—
674C4⋊C4—284no—
675C4⋊C4—284no—
676C4⋊C4—284no—
677C4⋊C4—284no—
678C4⋊C4—284no—
679C4⋊C4—284no—
680C4⋊C4C4⋊Dic7116yescomplemented
681C42—28no—
682C42—284no—
683C42—284no—
684C2×C7#231711yescharacteristic
685C2×C7#232211yescharacteristic
686C2×C7#233011yescharacteristic
687C2×C7D4×C4⋊C411yescharacteristic
688C2×C7Q8×C4⋊C411yescharacteristic
689C2×C7#236011yescharacteristic
690C2×C7#238311yescharacteristic
691C2×C7#267311yescharacteristic
692C2×C7#267711yescharacteristic
693C2×C7#271311yescharacteristic
694C2×C7#272011yescharacteristic
695C2×C7#272111yescharacteristic
696C2×C7#273411yescharacteristic
697C2×C7#279111yescharacteristic
698C2×C7#279211yescharacteristic
699C23C22×Dic1411yescharacteristic
700C23C22×D2811yescharacteristic
701C23C2×D4×D711yescharacteristic
702C23C2×#115911yescharacteristic
703C23C2×Q8×D711yescharacteristic
704C23C2×#116111yescharacteristic
705C23#655311yescharacteristic
706C23#655311yescharacteristic
707C23#655311yescharacteristic
708C23#655311yescharacteristic
709C23#655411yescharacteristic
710C23#655411yescharacteristic
711C23#655411yescharacteristic
712C23#655411yescharacteristic
713C23C23×Dic711yescharacteristic
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—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
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—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
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×C4—281no—
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×C4C2×C4⋊Dic714yes—
815C2×C4C2×C4⋊Dic714yes—
816C2×C4C2×C4⋊Dic714yes—
817C2×C4D4×Dic714yes—
818C2×C4Q8×Dic714yes—
819C7#1440611yescharacteristic, complemented, Sylow
820C22#9021011yescharacteristic
821C22#9021011yescharacteristic
822C22#9021611yescharacteristic
823C22#9021711yescharacteristic
824C22D4×Dic1411yescharacteristic
825C22#9023411yescharacteristic
826C22D4×D2811yescharacteristic
827C22#9024611yescharacteristic
828C22Q8×Dic1411yescharacteristic
829C22#9026111yescharacteristic
830C22Q8×D2811yescharacteristic
831C22#9026811yescharacteristic
832C22#9032111yescharacteristic
833C22#9032311yescharacteristic
834C22#9032611yescharacteristic
835C22#9033311yescharacteristic
836C22#9033911yescharacteristic
837C22#9034411yescharacteristic
838C22#9035611yescharacteristic
839C22#9035611yescharacteristic
840C22#9038011yescharacteristic
841C22#9038011yescharacteristic
842C22#9038811yescharacteristic
843C22#9038911yescharacteristic
844C22#9040211yescharacteristic
845C22#9040311yescharacteristic
846C22#9040311yescharacteristic
847C22#9040311yescharacteristic
848C22C22×C4⋊Dic711yescharacteristic
849C22C2×D4×Dic711yescharacteristic
850C22C2×Q8×Dic711yescharacteristic
851C22#9051811yescharacteristic
852C22#9051811yescharacteristic
853C22#9051811yescharacteristic
854C22#9051811yescharacteristic
855C4—24no—
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—42no—
861C4—42no—
862C4—282no—
863C4—282no—
864C4—282no—
865C4—282no—
866C4—561no—
867C4—561no—
868C4—561no—
869C4—561no—
870C2#1173260311yescharacteristic
871C2#1173261411yescharacteristic
872C2#1173261611yescharacteristic
873C2#1173262411yescharacteristic
874C2#1173269411yescharacteristic
875C2#1173270011yescharacteristic
876C2#1173283211yescharacteristic
877C2#1173283511yescharacteristic
878C2#1173967811yescharacteristic
879C2D4×C4⋊Dic711yescharacteristic
880C2Q8×C4⋊Dic711yescharacteristic
881C2#1174019211yescharacteristic
882C2#1174028111yescharacteristic
883C2#1174046811yescharacteristic
884C2#1174052111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#387C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#387D7
hypocenterC7#14406
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
31. C7×#387C4semidirect
259. C7×C4⋊C4C4⋊C4semidirect
291. #387Dic7semidirect
680. C4⋊C4C4⋊Dic7semidirect
819. C7#14406semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3872
C2×#897572
C2×#897532
C2×#897072
#117293192
#117292882
#117271732
#117271662
#117271612
#144067