Finite Group Databasebeta

← #13277017

Subgroups — #13277017

Order 1792.

1614 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×#89744C211yesmaximal, characteristic
3C2×#89744C211yesmaximal, characteristic
4C2×#89744C211yesmaximal, characteristic
5C2×#89748C211yesmaximal, characteristic
6C2×C4×Dic7⋊C4C211yesmaximal, characteristic
7C2×#89419C211yesmaximal, characteristic
8#11729322C211yesmaximal, characteristic
9#11729322C211yesmaximal, characteristic
10#11729320C211yesmaximal, characteristic
11#11729319C211yesmaximal, characteristic
12#11729290C211yesmaximal, characteristic
13#11727160C211yesmaximal, characteristic
14Dic7⋊#95C211yesmaximal, characteristic
15Dic7×#95C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C7×#389—24no—
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#89748—24no—
53#89744—24no—
54#89744—24no—
55#89744C418yescomplemented
56C4×Dic7⋊C4—24no—
57#89419—24no—
58#14005—71nomaximal, Sylow
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—41no—
83C2×C7×C4⋊C4—41no—
84C2×C7×C4⋊C4—41no—
85C2×C7×C4⋊C4C2×C414yes—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—41no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—41no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—22no—
99C2×Dic7⋊C4—22no—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—41no—
110C2×Dic7⋊C4—41no—
111C2×Dic7⋊C4—41no—
112C2×Dic7⋊C4—41no—
113C2×Dic7⋊C4C2×C414yes—
114C2×Dic7⋊C4C2×C414yes—
115C2×Dic7⋊C4C2×C414yes—
116C2×Dic7⋊C4D414yes—
117C2×Dic7⋊C4D414yes—
118C2×Dic7⋊C4Q814yes—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—22no—
128C2×C4×Dic7—41no—
129C2×C4×Dic7C2×C414yes—
130C2×C4×Dic7Q814yes—
131C7×#95—22no—
132C7×#95D414yes—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95C2×C414yes—
145C7⋊#95C2×C414yes—
146C7⋊#95Q814yes—
147C2×#389—71no—
148C2×#389—71no—
149C2×#389—71no—
150C2×#389—71no—
151C2×#389D711yescharacteristic
152C2×#384—71no—
153C2×C4×C4⋊C4—71no—
154#1444—71no—
155#1444—71no—
156#1441—71no—
157#1441—71no—
158#1436—71no—
159#1436—71no—
160C4⋊#95—71no—
161C4×#95—71no—
162C24×C7C2411yescharacteristic
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×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7C22×C412yes—
201C22×C4×C7C22×C412yes—
202C22×C4×C7C22×C412yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D412yes—
206C22×C4×C7C2×D412yes—
207C22×C4×C7C2×D412yes—
208C22×C4×C7C2×Q812yes—
209C22×C4×C7C2×Q812yes—
210C22×C4×C7C2×Q812yes—
211C22×C4×C7#4112yes—
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×Dic7C22×C412yes—
252C22×Dic7C22×C412yes—
253C22×Dic7C22×C412yes—
254C22×Dic7C22×C412yes—
255C22×Dic7C2×D412yes—
256C22×Dic7C2×D412yes—
257C22×Dic7C2×D412yes—
258C22×Dic7C2×D412yes—
259C22×Dic7C2×Q812yes—
260C22×Dic7C2×Q812yes—
261C22×Dic7C2×Q812yes—
262C22×Dic7C2×Q812yes—
263C22×Dic7C2×Q812yes—
264C22×Dic7C2×Q812yes—
265C22×Dic7#4112yes—
266C22×Dic7#4112yes—
267C22×Dic7#4112yes—
268C7×C4⋊C4—28no—
269C7×C4⋊C4—44no—
270C7×C4⋊C4—44no—
271C7×C4⋊C4—44no—
272C42×C7—44no—
273C4⋊Dic7—44no—
274Dic7⋊C4—28no—
275Dic7⋊C4—28no—
276Dic7⋊C4—28no—
277Dic7⋊C4—44no—
278Dic7⋊C4—44no—
279Dic7⋊C4—44no—
280Dic7⋊C4—44no—
281Dic7⋊C4—44no—
282Dic7⋊C4C4⋊C4116yescomplemented
283C4×Dic7—28no—
284C4×Dic7—28no—
285C4×Dic7—44no—
286C4×Dic7—44no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4—71no—
289C22×C4⋊C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
297C22×C4⋊C4C2×D711yescharacteristic
298C22×C4⋊C4C2×D711yescharacteristic
299C22×C4⋊C4C2×D711yescharacteristic
300C22×C4⋊C4C2×D711yescharacteristic
301C22×C42—71no—
302C22×C42—71no—
303C22×C42—71no—
304C22×C42—71no—
305C22×C42C2×D711yescharacteristic
306#389—24no—
307#389—78no—
308#389—144no—
309#389—144no—
310#389—144no—
311#384—144no—
312C4×C4⋊C4—144no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95C2×D711yescharacteristic
328C2×#95C2×D711yescharacteristic
329C23×C7C23×C411yescharacteristic
330C23×C7C22×D411yescharacteristic
331C23×C7C22×D411yescharacteristic
332C23×C7C22×D411yescharacteristic
333C23×C7C22×Q811yescharacteristic
334C23×C7C22×Q811yescharacteristic
335C23×C7C22×Q811yescharacteristic
336C23×C7C2×#4111yescharacteristic
337C23×C7C2×#4111yescharacteristic
338C23×C7C2×#4111yescharacteristic
339C23×C7C2×#4111yescharacteristic
340C23×C7H(5,𝔽2)11yescharacteristic
341C23×C7H(5,𝔽2)11yescharacteristic
342C23×C72−1+411yescharacteristic
343C23×C72−1+411yescharacteristic
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—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7C2×C4⋊C414yes—
391C2×C4×C7C4×D414yes—
392C2×C4×C7C4⋊Q814yes—
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—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
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—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—41no—
440C2×Dic7C2×C4⋊C414yes—
441C2×Dic7C2×C4⋊C414yes—
442C2×Dic7C4×D414yes—
443C2×Dic7C4×Q814yes—
444C2×Dic7C4×Q814yes—
445C2×Dic7#12114yes—
446C2×Dic7C22⋊Q814yes—
447C2×Dic7#12514yes—
448C2×Dic7C4⋊Q814yes—
449C23×C4—71no—
450C23×C4—71no—
451C23×C4—71no—
452C23×C4—71no—
453C23×C4—71no—
454C23×C4—71no—
455C23×C4—71no—
456C23×C4—71no—
457C23×C4C22×D711yescharacteristic
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C23×C4C22×D711yescharacteristic
461C23×C4C22×D711yescharacteristic
462C23×C4C22×D711yescharacteristic
463C23×C4C22×D711yescharacteristic
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—41no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—74no—
479C2×C4⋊C4—74no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—142no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—142no—
484C2×C4⋊C4—142no—
485C2×C4⋊C4—142no—
486C2×C4⋊C4—142no—
487C2×C4⋊C4—142no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—142no—
490C2×C4⋊C4—142no—
491C2×C4⋊C4—142no—
492C2×C4⋊C4—142no—
493C2×C4⋊C4—142no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4—142no—
496C2×C4⋊C4—142no—
497C2×C4⋊C4—142no—
498C2×C4⋊C4—142no—
499C2×C4⋊C4—142no—
500C2×C4⋊C4—281no—
501C2×C4⋊C4—281no—
502C2×C4⋊C4—281no—
503C2×C4⋊C4—281no—
504C2×C4⋊C4—281no—
505C2×C4⋊C4C4×D714yes—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—41no—
509C2×C42—74no—
510C2×C42—74no—
511C2×C42—142no—
512C2×C42—142no—
513C2×C42—142no—
514C2×C42—142no—
515C2×C42—142no—
516C2×C42—142no—
517C2×C42—142no—
518C2×C42—142no—
519C2×C42—142no—
520C2×C42—281no—
521#95—22no—
522#95—74no—
523#95—74no—
524#95—74no—
525#95—142no—
526#95—142no—
527#95—142no—
528#95—142no—
529#95—142no—
530#95—142no—
531#95—142no—
532#95—142no—
533#95—142no—
534#95—281no—
535#95—281no—
536#95C22⋊D714yes—
537C22×C7C22×C4⋊C411yescharacteristic
538C22×C7C2×C4×D411yescharacteristic
539C22×C7C2×C4×D411yescharacteristic
540C22×C7C2×C4×Q811yescharacteristic
541C22×C7C2×C4×Q811yescharacteristic
542C22×C7#52011yescharacteristic
543C22×C7#52011yescharacteristic
544C22×C7C2×#12111yescharacteristic
545C22×C7C2×C22⋊Q811yescharacteristic
546C22×C7C2×#12511yescharacteristic
547C22×C7C2×C4⋊Q811yescharacteristic
548C22×C7C2×C4⋊Q811yescharacteristic
549C22×C7#53211yescharacteristic
550C22×C7#53311yescharacteristic
551C22×C7#53311yescharacteristic
552C22×C7#54011yescharacteristic
553C22×C7#54111yescharacteristic
554C22×C7#54411yescharacteristic
555C22×C7#54411yescharacteristic
556C22×C7D4211yescharacteristic
557C22×C7D4211yescharacteristic
558C22×C7#54611yescharacteristic
559C22×C7#54711yescharacteristic
560C22×C7#54711yescharacteristic
561C22×C7#54811yescharacteristic
562C22×C7D4×Q811yescharacteristic
563C22×C7D4×Q811yescharacteristic
564C22×C7D4×Q811yescharacteristic
565C22×C7#55011yescharacteristic
566C22×C7#55211yescharacteristic
567C22×C7#55311yescharacteristic
568C22×C7#55411yescharacteristic
569C22×C7#55411yescharacteristic
570C22×C7#55711yescharacteristic
571C22×C7Q8211yescharacteristic
572C4×C7—24no—
573C4×C7—24no—
574C4×C7—24no—
575C4×C7—42no—
576C4×C7—42no—
577C4×C7—42no—
578C4×C7—81no—
579Dic7—24no—
580Dic7—24no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584Dic7—42no—
585Dic7—81no—
586Dic7#38918yescomplemented
587C24C23×D711yescharacteristic
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—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—72no—
630C22×C4—72no—
631C22×C4—72no—
632C22×C4—72no—
633C22×C4—72no—
634C22×C4—72no—
635C22×C4—72no—
636C22×C4—72no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—72no—
640C22×C4—72no—
641C22×C4—72no—
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×C4—141no—
663C22×C4—141no—
664C22×C4—141no—
665C22×C4—141no—
666C22×C4—141no—
667C22×C4—141no—
668C22×C4—141no—
669C22×C4—141no—
670C22×C4—141no—
671C22×C4—141no—
672C22×C4—141no—
673C22×C4—141no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
678C22×C4—141no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4C2×C4×D712yes—
682C22×C4C2×C4×D712yes—
683C22×C4C2×C4×D712yes—
684C22×C4#115712yes—
685C22×C4D4×D712yes—
686C22×C4D4×D712yes—
687C22×C4Q8×D712yes—
688C22×C4Q8×D712yes—
689C22×C4Q8×D712yes—
690C22×C4C2×C22⋊D712yes—
691C22×C4C2×C22⋊D712yes—
692C22×C4C2×C22⋊D712yes—
693C4⋊C4—28no—
694C4⋊C4—44no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—716no—
698C4⋊C4—148no—
699C4⋊C4—148no—
700C4⋊C4—148no—
701C4⋊C4—284no—
702C4⋊C4—284no—
703C4⋊C4—284no—
704C4⋊C4—284no—
705C4⋊C4—284no—
706C4⋊C4—284no—
707C42—44no—
708C42—148no—
709C42—148no—
710C42—284no—
711C42—284no—
712C2×C7C2×#38911yescharacteristic
713C2×C7C4×C4⋊Q811yescharacteristic
714C2×C7#233011yescharacteristic
715C2×C7D4×C4⋊C411yescharacteristic
716C2×C7Q8×C4⋊C411yescharacteristic
717C2×C7#236011yescharacteristic
718C2×C7#236111yescharacteristic
719C2×C7#242811yescharacteristic
720C2×C7#242911yescharacteristic
721C2×C7#244011yescharacteristic
722C2×C7#244111yescharacteristic
723C2×C7#250611yescharacteristic
724C2×C7#250711yescharacteristic
725C2×C7#255011yescharacteristic
726C2×C7#255111yescharacteristic
727C23C22×C4×D711yescharacteristic
728C23C2×#115711yescharacteristic
729C23C2×D4×D711yescharacteristic
730C23C2×D4×D711yescharacteristic
731C23#654811yescharacteristic
732C23#654811yescharacteristic
733C23C2×Q8×D711yescharacteristic
734C23C2×Q8×D711yescharacteristic
735C23C2×Q8×D711yescharacteristic
736C23#655111yescharacteristic
737C23D7×#4111yescharacteristic
738C23D7×#4111yescharacteristic
739C23D7×#4111yescharacteristic
740C23#655411yescharacteristic
741C23C22×C22⋊D711yescharacteristic
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—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—74no—
789C2×C4—74no—
790C2×C4—74no—
791C2×C4—74no—
792C2×C4—74no—
793C2×C4—74no—
794C2×C4—74no—
795C2×C4—74no—
796C2×C4—74no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—142no—
808C2×C4—142no—
809C2×C4—142no—
810C2×C4—142no—
811C2×C4—142no—
812C2×C4—142no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—281no—
822C2×C4—281no—
823C2×C4—281no—
824C2×C4—281no—
825C2×C4—281no—
826C2×C4—281no—
827C2×C4—281no—
828C2×C4—281no—
829C2×C4—281no—
830C2×C4—281no—
831C2×C4—281no—
832C2×C4—281no—
833C2×C4—281no—
834C2×C4—281no—
835C2×C4—281no—
836C2×C4—281no—
837C2×C4—281no—
838C2×C4—281no—
839C2×C4—281no—
840C2×C4—281no—
841C2×C4—281no—
842C2×C4—281no—
843C2×C4—281no—
844C2×C4D7×C4⋊C414yes—
845C2×C4C4×C22⋊D714yes—
846C2×C4#650714yes—
847C7#1400511yescharacteristic, complemented, Sylow
848C22C2×D7×C4⋊C411yescharacteristic
849C22#9019511yescharacteristic
850C22#9019811yescharacteristic
851C22#9020211yescharacteristic
852C22#9023111yescharacteristic
853C22C4×D4×D711yescharacteristic
854C22#9023711yescharacteristic
855C22#9024311yescharacteristic
856C22C4×Q8×D711yescharacteristic
857C22C4×Q8×D711yescharacteristic
858C22#9026911yescharacteristic
859C22#9026911yescharacteristic
860C22#9029011yescharacteristic
861C22D7×#12111yescharacteristic
862C22#9030111yescharacteristic
863C22#9030611yescharacteristic
864C22#9031411yescharacteristic
865C22D7×C22⋊Q811yescharacteristic
866C22#9032311yescharacteristic
867C22#9032711yescharacteristic
868C22#9037611yescharacteristic
869C22D7×#12511yescharacteristic
870C22#9038411yescharacteristic
871C22#9038711yescharacteristic
872C22#9041311yescharacteristic
873C22D7×C4⋊Q811yescharacteristic
874C22#9041811yescharacteristic
875C22#9042011yescharacteristic
876C22C2×C4×C22⋊D711yescharacteristic
877C22D4×C22⋊D711yescharacteristic
878C22D4×C22⋊D711yescharacteristic
879C22C2×#650711yescharacteristic
880C22Q8×C22⋊D711yescharacteristic
881C22#9051511yescharacteristic
882C22#9052311yescharacteristic
883C4—24no—
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—78no—
890C4—81no—
891C4—144no—
892C4—144no—
893C4—282no—
894C4—282no—
895C4—282no—
896C4—282no—
897C4—561no—
898C2#1173341811yescharacteristic
899C2#1173342611yescharacteristic
900C2#1173342811yescharacteristic
901C2#1173344111yescharacteristic
902C2#1173344611yescharacteristic
903C2#1173348111yescharacteristic
904C2#1173350811yescharacteristic
905C2D7×#38911yescharacteristic
906C2C4⋊C4×C22⋊D711yescharacteristic
907C2#1173978511yescharacteristic
908C2C4×#650711yescharacteristic
909C2#1174009511yescharacteristic
910C2#1174020811yescharacteristic
911C2#1174047911yescharacteristic
912C2#1174068711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#389D7
hypocenterC7#14005
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
55. #89744C4semidirect
282. Dic7⋊C4C4⋊C4semidirect
586. Dic7#389semidirect
847. C7#14005semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#897442
C2×#897482
C2×C4×Dic7⋊C42
C2×#894192
#117293222
#117293202
#117293192
#117292902
#117271602
Dic7⋊#952
Dic7×#952
#140057