Finite Group Databasebeta

← #13276929

Subgroups — #13276929

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6459C211yesmaximal, characteristic
2C2×#89744C211yesmaximal, characteristic, complemented
3C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
4C2×#89439C211yesmaximal, characteristic
5C2×#89418C211yesmaximal, characteristic, complemented
6C2×#89418C211yesmaximal, characteristic, complemented
7C2×#89438C211yesmaximal, characteristic
8C7×C4⋊#95C211yesmaximal, characteristic, complemented
9#11729324C211yesmaximal, characteristic
10#11729323C211yesmaximal, characteristic, complemented
11#11729291C211yesmaximal, characteristic
12#11727182C211yesmaximal, characteristic
13#11727175C211yesmaximal, characteristic, complemented
14#11727162C211yesmaximal, characteristic
15Dic7⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×Dic14C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C2×#6459—24no—
36C2×#6459—24no—
37C2×#6459C418yescomplemented
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#89744—24no—
55C4×Dic7⋊C4—24no—
56#89439—24no—
57#89438—24no—
58#89418—24no—
59#89418—24no—
60#13997—71nomaximal, Sylow
61C24×D7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C22×C4×D7—22no—
77C22×C4×D7—22no—
78C22×C4×D7—22no—
79C22×C4×D7—22no—
80C22×C4×D7—22no—
81C22×C4×D7—22no—
82C22×C4×D7C2×C414yes—
83C22×Dic14—22no—
84C22×Dic14—22no—
85C22×Dic14—22no—
86C22×Dic14—22no—
87C22×Dic14—22no—
88C22×Dic14—22no—
89C22×Dic14C2×C414yes—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—41no—
95C2×C7×C4⋊C4C2×C414yes—
96C2×C42×C7—22no—
97C2×C42×C7—22no—
98C2×C42×C7—41no—
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—22no—
105C2×(C2×D7)⋊C4—22no—
106C2×(C2×D7)⋊C4—22no—
107C2×(C2×D7)⋊C4—22no—
108C2×(C2×D7)⋊C4—22no—
109C2×(C2×D7)⋊C4—22no—
110C2×(C2×D7)⋊C4—22no—
111C2×(C2×D7)⋊C4—22no—
112C2×(C2×D7)⋊C4—41no—
113C2×(C2×D7)⋊C4—41no—
114C2×(C2×D7)⋊C4C2×C414yes—
115C2×(C2×D7)⋊C4C2×C414yes—
116C2×(C2×D7)⋊C4Q814yescomplemented
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4—22no—
122C2×Dic7⋊C4—22no—
123C2×Dic7⋊C4—22no—
124C2×Dic7⋊C4—22no—
125C2×Dic7⋊C4—22no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4C2×C414yes—
128C2×Dic7⋊C4C2×C414yes—
129C2×Dic7⋊C4D414yes—
130C2×Dic7⋊C4D414yes—
131C2×Dic7⋊C4D414yes—
132C2×C4×Dic7—22no—
133C2×C4×Dic7—22no—
134C2×C4×Dic7—22no—
135C2×C4×Dic7—22no—
136C2×C4×Dic7—22no—
137C2×C4×Dic7—22no—
138C2×C4×Dic7—22no—
139C2×C4×Dic7—41no—
140C2×C4×Dic7D414yes—
141#6459—232no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—22no—
146C7⋊#95—22no—
147C7⋊#95—22no—
148C7⋊#95—22no—
149C7⋊#95—22no—
150C7⋊#95—22no—
151C7⋊#95—22no—
152C7⋊#95—22no—
153C7⋊#95—22no—
154C7⋊#95—22no—
155C7⋊#95—22no—
156C7⋊#95—22no—
157C7⋊#95—22no—
158C22×C22⋊Q8—71no—
159C2×#391—71no—
160C2×#391—71no—
161C2×#389—71no—
162C2×#380—71no—
163C2×C4×C4⋊C4—71no—
164C2×C4×C22⋊C4—71no—
165#1445—71no—
166#1445—71no—
167#1439—71no—
168#1439—71no—
169#1437—71no—
170#1437—71no—
171C4⋊#95—71no—
172C4⋊#95D711yescharacteristic, complemented
173C24×C7C2411yescharacteristic
174C23×D7—21no—
175C23×D7—21no—
176C23×D7—21no—
177C23×D7—21no—
178C23×D7—21no—
179C23×D7—21no—
180C23×D7—21no—
181C23×D7—21no—
182C23×D7—21no—
183C23×D7—21no—
184C23×D7—21no—
185C23×D7—21no—
186C23×D7C22×C412yes—
187C23×D7C2×Q812yes—
188C23×D7#4112yes—
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×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7C22×C412yes—
229C22×C4×C7C22×C412yes—
230C22×C4×C7C22×C412yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2×D412yes—
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2×Q812yes—
236C22×C4×C7#4112yes—
237C22×C4×C7#4112yes—
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×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7C22×C412yes—
274C22×Dic7C22×C412yes—
275C22×Dic7C22×C412yes—
276C22×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7C2×D412yes—
280C22×Dic7C2×D412yes—
281C22×Dic7C2×D412yes—
282C22×Dic7C2×D412yes—
283C22×Dic7C2×D412yes—
284C22×Dic7C2×Q812yes—
285C22×Dic7#4112yes—
286C22×Dic7#4112yes—
287C2×C4×D7—28no—
288C2×C4×D7—28no—
289C2×C4×D7—28no—
290C2×C4×D7—44no—
291C2×C4×D7—44no—
292C2×C4×D7—44no—
293C2×C4×D7—44no—
294C2×Dic14—28no—
295C2×Dic14—28no—
296C2×Dic14—28no—
297C2×Dic14—44no—
298C2×Dic14—44no—
299C2×Dic14—44no—
300C2×Dic14—44no—
301C7×C4⋊C4—28no—
302C7×C4⋊C4—44no—
303C42×C7—44no—
304(C2×D7)⋊C4—28no—
305(C2×D7)⋊C4—28no—
306(C2×D7)⋊C4—28no—
307(C2×D7)⋊C4—28no—
308(C2×D7)⋊C4—44no—
309(C2×D7)⋊C4—44no—
310Dic7⋊C4—28no—
311Dic7⋊C4—28no—
312Dic7⋊C4—44no—
313Dic7⋊C4—44no—
314Dic7⋊C4C22⋊C4116yescomplemented
315C4×Dic7—28no—
316C4×Dic7—44no—
317C4×Dic7—44no—
318C23×Q8—71no—
319C24×C4—71no—
320C2×C22⋊Q8—78no—
321C2×C22⋊Q8—144no—
322C2×C22⋊Q8—144no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326C22×C4⋊C4—71no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4C2×D711yescharacteristic
329C22×C4⋊C4C2×D711yescharacteristic
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4—71no—
335C22×C22⋊C4—71no—
336C22×C42—71no—
337C22×C42—71no—
338C22×C42—71no—
339C22×C42C2×D711yescharacteristic
340#391—144no—
341#391—144no—
342#389—144no—
343#380—144no—
344C4×C4⋊C4—144no—
345C4×C22⋊C4—144no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—71no—
357C2×#95—71no—
358C2×#95C2×D711yescharacteristic
359C2×#95C2×D711yescharacteristic
360C2×#95C2×D711yescharacteristic
361C2×#95C2×D711yescharacteristic
362C23×C7C23×C411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C22×D411yescharacteristic
365C23×C7C22×D411yescharacteristic
366C23×C7C22×D411yescharacteristic
367C23×C7C22×Q811yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7H(5,𝔽2)11yescharacteristic
374C23×C72−1+411yescharacteristic
375C23×C72−1+411yescharacteristic
376C23×C72−1+411yescharacteristic
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—22no—
389C22×D7—22no—
390C22×D7—22no—
391C22×D7—22no—
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—41no—
396C22×D7—41no—
397C22×D7—41no—
398C22×D7—41no—
399C22×D7—41no—
400C22×D7—41no—
401C22×D7—41no—
402C22×D7—41no—
403C22×D7—41no—
404C22×D7—41no—
405C22×D7—41no—
406C22×D7—41no—
407C22×D7—41no—
408C22×D7—41no—
409C22×D7—41no—
410C22×D7—41no—
411C22×D7C4×Q814yes—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7C2×C22⋊C414yes—
460C2×C4×C7C22⋊Q814yescomplemented
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7—41no—
494C2×Dic7—41no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C2×Dic7—41no—
502C2×Dic7C2×C22⋊C414yes—
503C2×Dic7C2×C22⋊C414yes—
504C2×Dic7C4×D414yes—
505C2×Dic7C4×D414yes—
506C2×Dic7#12114yes—
507C2×Dic7#12114yes—
508C2×Dic7#12414yes—
509C2×Dic7#12714yes—
510C4×D7—416no—
511Dic14—416no—
512C25—71no—
513C22×Q8—74no—
514C22×Q8—142no—
515C22×Q8—142no—
516C22×Q8—142no—
517C22×Q8—142no—
518C22×Q8—142no—
519C22×Q8—142no—
520C23×C4—71no—
521C23×C4—71no—
522C23×C4—71no—
523C23×C4—71no—
524C23×C4—71no—
525C23×C4—71no—
526C23×C4—74no—
527C23×C4—71no—
528C23×C4—142no—
529C23×C4—142no—
530C23×C4—142no—
531C23×C4—142no—
532C23×C4—142no—
533C23×C4—142no—
534C23×C4C22×D711yescharacteristic
535C23×C4C22×D711yescharacteristic
536C23×C4C22×D711yescharacteristic
537C23×C4C22×D711yescharacteristic
538C23×C4C22×D711yescharacteristic
539C23×C4C22×D711yescharacteristic
540C23×C4C22×D711yescharacteristic
541C22⋊Q8—1432no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—74no—
548C2×C4⋊C4—74no—
549C2×C4⋊C4—74no—
550C2×C4⋊C4—74no—
551C2×C4⋊C4—74no—
552C2×C4⋊C4—142no—
553C2×C4⋊C4—142no—
554C2×C4⋊C4—142no—
555C2×C4⋊C4—142no—
556C2×C4⋊C4—142no—
557C2×C4⋊C4—142no—
558C2×C4⋊C4—142no—
559C2×C4⋊C4—142no—
560C2×C4⋊C4—142no—
561C2×C4⋊C4—281no—
562C2×C4⋊C4C4×D714yes—
563C2×C22⋊C4—74no—
564C2×C22⋊C4—74no—
565C2×C22⋊C4—74no—
566C2×C22⋊C4—142no—
567C2×C22⋊C4—142no—
568C2×C22⋊C4—142no—
569C2×C22⋊C4—142no—
570C2×C22⋊C4—142no—
571C2×C22⋊C4—142no—
572C2×C22⋊C4—142no—
573C2×C22⋊C4—142no—
574C2×C22⋊C4—142no—
575C2×C22⋊C4—142no—
576C2×C22⋊C4—142no—
577C2×C22⋊C4—142no—
578C2×C22⋊C4—142no—
579C2×C22⋊C4—281no—
580C2×C22⋊C4—281no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—41no—
584C2×C42—74no—
585C2×C42—142no—
586C2×C42—142no—
587C2×C42—142no—
588C2×C42—142no—
589C2×C42—142no—
590C2×C42—142no—
591C2×C42—142no—
592C2×C42—281no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—142no—
598#95—142no—
599#95—142no—
600#95—142no—
601#95—142no—
602#95—142no—
603#95—142no—
604#95—142no—
605#95—142no—
606#95—142no—
607#95—142no—
608#95—142no—
609C22×C7C22×C22⋊C411yescharacteristic
610C22×C7C2×C4×D411yescharacteristic
611C22×C7C2×C4×D411yescharacteristic
612C22×C7C2×C4×Q811yescharacteristic
613C22×C7C4×#4111yescharacteristic
614C22×C7#51911yescharacteristic
615C22×C7#52011yescharacteristic
616C22×C7C2×#12111yescharacteristic
617C22×C7C2×#12111yescharacteristic
618C22×C7C2×C22⋊Q811yescharacteristic
619C22×C7#52511yescharacteristic
620C22×C7C2×#12411yescharacteristic
621C22×C7#52911yescharacteristic
622C22×C7C2×#12711yescharacteristic
623C22×C7#53311yescharacteristic
624C22×C7#53611yescharacteristic
625C22×C7#53711yescharacteristic
626C22×C7#54111yescharacteristic
627C22×C7#54211yescharacteristic
628C22×C7#54611yescharacteristic
629C22×C7#54611yescharacteristic
630C22×C7#54611yescharacteristic
631C22×C7#54711yescharacteristic
632C22×C7#54711yescharacteristic
633C22×C7#54711yescharacteristic
634C22×C7#54811yescharacteristic
635C22×C7#54811yescharacteristic
636C22×C7#54811yescharacteristic
637C22×C7D4×Q811yescharacteristic
638C22×C7D4×Q811yescharacteristic
639C22×C7D4×Q811yescharacteristic
640C22×C7#55211yescharacteristic
641C22×C7#55211yescharacteristic
642C22×C7#55411yescharacteristic
643C22×C7#55611yescharacteristic
644C2×D7—24no—
645C2×D7—24no—
646C2×D7—24no—
647C2×D7—42no—
648C2×D7—42no—
649C2×D7—42no—
650C2×D7—42no—
651C2×D7—42no—
652C2×D7—42no—
653C2×D7—42no—
654C2×D7—42no—
655C2×D7—42no—
656C2×D7—42no—
657C2×D7—42no—
658C2×D7—42no—
659C4×C7—24no—
660C4×C7—24no—
661C4×C7—42no—
662C4×C7—42no—
663C4×C7—42no—
664C4×C7—42no—
665C4×C7—81no—
666Dic7—24no—
667Dic7—42no—
668Dic7—42no—
669Dic7—42no—
670Dic7—42no—
671Dic7—81no—
672Dic7#39018yes—
673C24—72no—
674C24—72no—
675C24—72no—
676C24—141no—
677C24—141no—
678C24—141no—
679C24—141no—
680C24—141no—
681C24—141no—
682C24—141no—
683C24—141no—
684C24—141no—
685C24—141no—
686C24—141no—
687C24—141no—
688C24C23×D711yescharacteristic
689C2×Q8—148no—
690C2×Q8—148no—
691C2×Q8—148no—
692C2×Q8—284no—
693C2×Q8—284no—
694C2×Q8—284no—
695C2×Q8—284no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—72no—
736C22×C4—72no—
737C22×C4—72no—
738C22×C4—72no—
739C22×C4—72no—
740C22×C4—72no—
741C22×C4—72no—
742C22×C4—72no—
743C22×C4—72no—
744C22×C4—72no—
745C22×C4—72no—
746C22×C4—72no—
747C22×C4—72no—
748C22×C4—72no—
749C22×C4—148no—
750C22×C4—148no—
751C22×C4—148no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—141no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—141no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—141no—
773C22×C4—141no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—141no—
779C22×C4—141no—
780C22×C4—141no—
781C22×C4—141no—
782C22×C4—141no—
783C22×C4—141no—
784C22×C4—141no—
785C22×C4—141no—
786C22×C4—141no—
787C22×C4—284no—
788C22×C4—284no—
789C22×C4—284no—
790C22×C4—284no—
791C22×C4C2×C4×D712yes—
792C22×C4C2×C4×D712yes—
793C22×C4C2×C4×D712yes—
794C22×C4#115712yes—
795C22×C4#115712yes—
796C22×C4D4×D712yes—
797C22×C4D4×D712yes—
798C22×C4D4×D712yes—
799C22×C4D4×D712yes—
800C22×C4Q8×D712yes—
801C4⋊C4—28no—
802C4⋊C4—44no—
803C4⋊C4—716no—
804C4⋊C4—148no—
805C4⋊C4—148no—
806C4⋊C4—284no—
807C4⋊C4—284no—
808C22⋊C4—148no—
809C22⋊C4—148no—
810C22⋊C4—148no—
811C22⋊C4—148no—
812C22⋊C4—284no—
813C22⋊C4—284no—
814C42—44no—
815C42—148no—
816C42—284no—
817C42—284no—
818C2×C7C2×#39011yescharacteristic
819C2×C7C4×C22⋊Q811yescharacteristic
820C2×C7#232311yescharacteristic
821C2×C7#233911yescharacteristic
822C2×C7Q8×C22⋊C411yescharacteristic
823C2×C7#236011yescharacteristic
824C2×C7#236211yescharacteristic
825C2×C7#241511yescharacteristic
826C2×C7#241711yescharacteristic
827C2×C7#242711yescharacteristic
828C2×C7#242911yescharacteristic
829C2×C7#248911yescharacteristic
830C2×C7#249211yescharacteristic
831C2×C7#254011yescharacteristic
832C2×C7#254211yescharacteristic
833D7—44no—
834C23—74no—
835C23—142no—
836C23—142no—
837C23—142no—
838C23—142no—
839C23—142no—
840C23—142no—
841C23—142no—
842C23—142no—
843C23—142no—
844C23—142no—
845C23—142no—
846C23—142no—
847C23—142no—
848C23—142no—
849C23—142no—
850C23—142no—
851C23—142no—
852C23—142no—
853C23—281no—
854C23—281no—
855C23—281no—
856C23—281no—
857C23—281no—
858C23—281no—
859C23—281no—
860C23—281no—
861C23—281no—
862C23—281no—
863C23—281no—
864C23—281no—
865C23—281no—
866C23—281no—
867C23—281no—
868C23—281no—
869C23C22×C4×D711yescharacteristic
870C23C2×#115711yescharacteristic
871C23C2×#115711yescharacteristic
872C23C2×D4×D711yescharacteristic
873C23C2×D4×D711yescharacteristic
874C23C2×D4×D711yescharacteristic
875C23C2×D4×D711yescharacteristic
876C23#654811yescharacteristic
877C23C2×Q8×D711yescharacteristic
878C23#655111yescharacteristic
879C23#655111yescharacteristic
880C23D7×#4111yescharacteristic
881C23D7×#4111yescharacteristic
882C23D7×#4111yescharacteristic
883C23#655411yescharacteristic
884Q8—2816no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—74no—
933C2×C4—74no—
934C2×C4—74no—
935C2×C4—74no—
936C2×C4—74no—
937C2×C4—74no—
938C2×C4—74no—
939C2×C4—74no—
940C2×C4—142no—
941C2×C4—142no—
942C2×C4—142no—
943C2×C4—142no—
944C2×C4—142no—
945C2×C4—142no—
946C2×C4—142no—
947C2×C4—142no—
948C2×C4—142no—
949C2×C4—142no—
950C2×C4—142no—
951C2×C4—142no—
952C2×C4—142no—
953C2×C4—142no—
954C2×C4—142no—
955C2×C4—142no—
956C2×C4—142no—
957C2×C4—142no—
958C2×C4—2816no—
959C2×C4—281no—
960C2×C4—281no—
961C2×C4—281no—
962C2×C4—281no—
963C2×C4—281no—
964C2×C4—281no—
965C2×C4—281no—
966C2×C4—281no—
967C2×C4—281no—
968C2×C4—281no—
969C2×C4—281no—
970C2×C4—281no—
971C2×C4—281no—
972C2×C4—281no—
973C2×C4—281no—
974C2×C4—281no—
975C2×C4—281no—
976C2×C4—281no—
977C2×C4—281no—
978C2×C4—281no—
979C2×C4—281no—
980C2×C4—281no—
981C2×C4—281no—
982C2×C4D7×C22⋊C414yes—
983C2×C4#645914yescomplemented
984C7#1399711yescharacteristic, complemented, Sylow
985C22—144no—
986C22—144no—
987C22—144no—
988C22—282no—
989C22—282no—
990C22—282no—
991C22—282no—
992C22—282no—
993C22—282no—
994C22—282no—
995C22—282no—
996C22—282no—
997C22—282no—
998C22—282no—
999C22—282no—
1000C22C4×#115711yescharacteristic
1001C22C2×D7×C22⋊C411yescharacteristic
1002C22#9018111yescharacteristic
1003C22#9018111yescharacteristic
1004C22#9019511yescharacteristic
1005C22#9019811yescharacteristic
1006C22#9019811yescharacteristic
1007C22#9019811yescharacteristic
1008C22C2×#645911yescharacteristic
1009C22#9021911yescharacteristic
1010C22#9022211yescharacteristic
1011C22C4×D4×D711yescharacteristic
1012C22C4×D4×D711yescharacteristic
1013C22#9023811yescharacteristic
1014C22#9024311yescharacteristic
1015C22#9025911yescharacteristic
1016C22C4×Q8×D711yescharacteristic
1017C22#9026311yescharacteristic
1018C22#9026911yescharacteristic
1019C22#9028811yescharacteristic
1020C22D7×#12111yescharacteristic
1021C22D7×#12111yescharacteristic
1022C22#9030111yescharacteristic
1023C22#9032311yescharacteristic
1024C22#9032411yescharacteristic
1025C22#9032711yescharacteristic
1026C22#9033111yescharacteristic
1027C22D7×#12411yescharacteristic
1028C22#9036811yescharacteristic
1029C22#9038411yescharacteristic
1030C22#9038711yescharacteristic
1031C22D7×#12711yescharacteristic
1032C22#9041511yescharacteristic
1033C22#9041811yescharacteristic
1034C22#9041811yescharacteristic
1035C4—24no—
1036C4—24no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—78no—
1042C4—81no—
1043C4—144no—
1044C4—282no—
1045C4—282no—
1046C4—282no—
1047C4—282no—
1048C4—561no—
1049C2—284no—
1050C2#1173081311yescharacteristic
1051C2#1173109311yescharacteristic
1052C2C4×#645911yescharacteristic
1053C2#1173133411yescharacteristic
1054C2#1173134011yescharacteristic
1055C2#1173160911yescharacteristic
1056C2#1173177911yescharacteristic
1057C2#1173341611yescharacteristic
1058C2#1173342811yescharacteristic
1059C2#1173344011yescharacteristic
1060C2#1173344111yescharacteristic
1061C2#1173379211yescharacteristic
1062C2D7×#39011yescharacteristic
1063C2#1173396211yescharacteristic
1064C2#1173405911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC4⋊#95D7
hypocenterC7#13997
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#89744C2semidirect
3. C2×C4×Dic7⋊C4C2semidirect
5. C2×#89418C2semidirect
6. C2×#89418C2semidirect
8. C7×C4⋊#95C2semidirect
10. #11729323C2semidirect
13. #11727175C2semidirect
15. Dic7⋊#95C2semidirect
37. C2×#6459C4semidirect
116. C2×(C2×D7)⋊C4Q8semidirect
172. C4⋊#95D7semidirect
314. Dic7⋊C4C22⋊C4semidirect
460. C2×C4×C7C22⋊Q8semidirect
983. C2×C4#6459semidirect
984. C7#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#64592
C2×#897442
C2×C4×Dic7⋊C42
C2×#894392
C2×#894182
C2×#894382
C7×C4⋊#952
#117293242
#117293232
#117292912
#117271822
#117271752
#117271622
Dic7⋊#952
#139977