Finite Group Databasebeta

← C2×#11743770 #14261684

Subgroups — C2×#11743770 #14261684

Order 1792.

12378 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6553C212yesmaximal, complemented
2C2×C7×#547C211yesmaximal, characteristic, complemented
3C2×#90520C212yesmaximal, complemented
4#11743770C2132yesmaximal, direct product factor
5C2×#90417C211yesmaximal, characteristic, complemented
6C2×#90416C211yesmaximal, characteristic, complemented
7C2×#90345C214yesmaximal, complemented
8C2×#90344C214yesmaximal, complemented
9C2×#90321C212yesmaximal, complemented
10C2×#90320C212yesmaximal, complemented
11C2×#90300C212yesmaximal, complemented
12C2×D7×#121C212yesmaximal, complemented
13C2×D4×D28C211yesmaximal, characteristic, complemented
14C2×D4×D28C211yesmaximal, characteristic, complemented
15C2×#90239C211yesmaximal, characteristic, complemented
16C2×C4×D4×D7C211yesmaximal, characteristic, complemented
17C2×#90198C212yesmaximal, complemented
18C22×#6458C212yesmaximal, complemented
19C22×C7×#41C2212yescomplemented
20C2×#6553—232no—
21C2×#6553C22132yescomplemented
22C22×#1161C2212yescomplemented
23C22×#1161C2212yescomplemented
24C22×D4×D7C2211yescharacteristic
25C22×D4×D7C2214yescomplemented
26C22×D4×D7C2214yescomplemented
27C22×D4×D7C2212yescomplemented
28C22×D4×D7C2212yescomplemented
29C22×#1157C2214yescomplemented
30C22×#1157C2212yescomplemented
31C23×D28C2214yescomplemented
32C23×D28C2212yescomplemented
33C23×D28C2212yescomplemented
34C23×C4×D7C2212yescomplemented
35C7×#547C22116yescomplemented
36C2×C7×C4⋊Q8C2211yescharacteristic, complemented
37C2×C7×#123C2214yescomplemented
38C2×C7×C22⋊Q8C2212yescomplemented
39C2×C7×#121C2212yescomplemented
40C2×C4×C7×D4C2211yescharacteristic, complemented
41C2×C4×C7×D4C2211yescharacteristic, complemented
42C22×C7×C4⋊C4C2212yescomplemented
43#90520C22132yescomplemented
44C2×#6510C2212yescomplemented
45C2×#6509C2212yescomplemented
46C2×#6503C2211yescharacteristic, complemented
47C2×#6502C2214yescomplemented
48C2×#6501C2211yescharacteristic, complemented
49C2×#6500C2214yescomplemented
50C2×D4×Dic7C2211yescharacteristic, complemented
51C2×#6493C2212yescomplemented
52C2×#6493C2212yescomplemented
53C2×#6492C2214yescomplemented
54C2×C4×C22⋊D7C2212yescomplemented
55C2×C4×C22⋊D7C2212yescomplemented
56C22×(C2×D7)⋊C4C2214yescomplemented
57#90417C22116yescomplemented
58#90416C22116yescomplemented
59#90345C22164yescomplemented
60#90344C22164yescomplemented
61#90321C22132yescomplemented
62#90320C22132yescomplemented
63#90300C22132yescomplemented
64D7×#121C22132yescomplemented
65D4×D28C22116yescomplemented
66D4×D28C22116yescomplemented
67#90239C22116yescomplemented
68C4×D4×D7C22116yescomplemented
69C2×#6459C2214yescomplemented
70#90198C22132yescomplemented
71C2×#6458C2212yescomplemented
72C2×#6458C2212yescomplemented
73C2×#6458C2212yescomplemented
74C2×#6458C2211yescharacteristic, complemented
75C2×#6458C2212yescomplemented
76C2×#6458C2214yescomplemented
77C2×#6458C2214yescomplemented
78C2×#6458C2212yescomplemented
79C2×#6458C22132yescomplemented
80C2×#6457C2214yescomplemented
81C2×#6457C2214yescomplemented
82C2×#6456C2212yescomplemented
83C2×#6456C2212yescomplemented
84C2×#6456C2211yescharacteristic, complemented
85C2×D7×C4⋊C4C2212yescomplemented
86C2×D7×C4⋊C4C2211yescharacteristic, complemented
87C2×#6451C2211yescharacteristic, complemented
88C2×#6448C2212yescomplemented
89C2×#6447C2214yescomplemented
90C2×#6447C2214yescomplemented
91C2×#6447C2212yescomplemented
92C2×#6445C2214yescomplemented
93C2×#6445C2214yescomplemented
94C2×#6445C2214yescomplemented
95C2×(C22⋊D7)⋊C4C2212yescomplemented
96C2×D7×C22⋊C4C2214yescomplemented
97C2×D7×C22⋊C4C2212yescomplemented
98C2×#6437C2211yescharacteristic, complemented
99C2×C4×D28C2211yescharacteristic, complemented
100C2×C4×D28C2211yescharacteristic, complemented
101C2×C42×D7C2211yescharacteristic, complemented
102C2×#3496—71nomaximal, Sylow
103C24×D7C2314yes—
104C24×D7C2314yes—
105C24×D7C2312yes—
106C2×C7×#41—216no—
107C2×C7×#41C23116yescomplemented
108C22×C7×Q8C2312yes—
109C22×C7×D4C2314yes—
110C22×C7×D4C2311yescharacteristic
111C22×C7×D4C2311yescharacteristic
112C23×C4×C7C2314yes—
113C23×C4×C7C2312yes—
114C23×C4×C7C2312yes—
115C22×C22⋊D7C2314yes—
116C22×C22⋊D7C2312yes—
117C22×C22⋊D7C2312yes—
118C22×C22⋊D7C2312yes—
119C22×C22⋊D7C2314yes—
120C22×C22⋊D7C2312yes—
121C23×Dic7C2312yes—
122#6553—2256no—
123C2×#1161—216no—
124C2×#1161—216no—
125C2×#1161C23116yescomplemented
126C2×#1161C23116yescomplemented
127C2×D4×D7—232no—
128C2×D4×D7—216no—
129C2×D4×D7—232no—
130C2×D4×D7—48no—
131C2×D4×D7D4116yescomplemented
132C2×D4×D7C2318yes—
133C2×D4×D7C23116yescomplemented
134C2×D4×D7C23132yescomplemented
135C2×D4×D7C23132yescomplemented
136C2×D4×D7C23116yescomplemented
137C2×#1157—232no—
138C2×#1157—216no—
139C2×#1157C23132yescomplemented
140C2×#1157C23116yescomplemented
141C22×D28—232no—
142C22×D28—216no—
143C22×D28—48no—
144C22×D28C2311yescharacteristic
145C22×D28C2312yes—
146C22×D28C2312yes—
147C22×D28C2314yes—
148C22×D28C2314yes—
149C22×D28C2312yes—
150C22×D28C2314yes—
151C22×D28C2312yes—
152C22×D28C2314yes—
153C22×D28C2311yescharacteristic
154C22×D28C23132yescomplemented
155C22×D28C23116yescomplemented
156C22×D28C23116yescomplemented
157C22×C4×D7—48no—
158C22×C4×D7C2311yescharacteristic
159C22×C4×D7C2312yes—
160C22×C4×D7C2312yes—
161C22×C4×D7C2314yes—
162C22×C4×D7C2314yes—
163C22×C4×D7C2311yescharacteristic
164C22×C4×D7C2312yes—
165C22×C4×D7C2312yes—
166C22×C4×D7C2311yescharacteristic
167C22×C4×D7C23116yescomplemented
168C22×Dic14C2312yes—
169C7×C4⋊Q8C2318yescomplemented
170C7×#123C23132yescomplemented
171C7×C22⋊Q8C23116yescomplemented
172C7×#121C23116yescomplemented
173C4×C7×D4C2318yescomplemented
174C4×C7×D4C2318yescomplemented
175C2×C7×C4⋊C4C2311yescharacteristic
176C2×C7×C4⋊C4C2312yes—
177C2×C7×C4⋊C4C2311yescharacteristic
178C2×C7×C4⋊C4C2312yes—
179C2×C7×C4⋊C4C2314yes—
180C2×C7×C4⋊C4C23116yescomplemented
181C2×C7×C22⋊C4C2312yes—
182C2×C7×C22⋊C4C2314yes—
183C2×C7×C22⋊C4C2312yes—
184C2×C42×C7C2311yescharacteristic
185C2×C22⋊Dic7C2312yes—
186C2×C22⋊Dic7C2312yes—
187#6510C23116yescomplemented
188#6509C23116yescomplemented
189#6503C2318yescomplemented
190#6502C23132yescomplemented
191#6501C2318yescomplemented
192#6500C23132yescomplemented
193D4×Dic7C2318yescomplemented
194#6493C23116yescomplemented
195#6493C23116yescomplemented
196#6492C23132yescomplemented
197C4×C22⋊D7C23116yescomplemented
198C4×C22⋊D7C23116yescomplemented
199C2×(C2×D7)⋊C4C2312yes—
200C2×(C2×D7)⋊C4C2312yes—
201C2×(C2×D7)⋊C4C2312yes—
202C2×(C2×D7)⋊C4C2314yes—
203C2×(C2×D7)⋊C4C2314yes—
204C2×(C2×D7)⋊C4C2314yes—
205C2×(C2×D7)⋊C4C2314yes—
206C2×(C2×D7)⋊C4C2314yes—
207C2×(C2×D7)⋊C4C2312yes—
208C2×(C2×D7)⋊C4C23132yescomplemented
209C2×C4⋊Dic7C2311yescharacteristic
210C2×C4⋊Dic7C2311yescharacteristic
211C2×Dic7⋊C4C2312yes—
212C2×Dic7⋊C4C2312yes—
213C2×Dic7⋊C4C2314yes—
214C2×C4×Dic7C2311yescharacteristic
215C2×C4×Dic7C2311yescharacteristic
216C2×C4×Dic7C2311yescharacteristic
217#6459C23132yescomplemented
218#6458C23116yescomplemented
219#6458C23116yescomplemented
220#6458C23116yescomplemented
221#6458C2318yescomplemented
222#6458C23116yescomplemented
223#6458C23132yescomplemented
224#6458C23132yescomplemented
225#6458C23116yescomplemented
226#6457C23132yescomplemented
227#6457C23132yescomplemented
228#6456C23116yescomplemented
229#6456C23116yescomplemented
230#6456C2318yescomplemented
231D7×C4⋊C4C23116yescomplemented
232D7×C4⋊C4C2318yescomplemented
233#6451C2318yescomplemented
234#6448C23116yescomplemented
235#6447C23116yescomplemented
236#6447C23132yescomplemented
237#6447C23132yescomplemented
238#6445C23132yescomplemented
239#6445C23132yescomplemented
240#6445C23132yescomplemented
241(C22⋊D7)⋊C4C23116yescomplemented
242D7×C22⋊C4C23116yescomplemented
243D7×C22⋊C4C23132yescomplemented
244#6437C2318yescomplemented
245C4×D28C2318yescomplemented
246C4×D28C2318yescomplemented
247C42×D7C2318yescomplemented
248C22×H(5,𝔽2)—72no—
249#3496—732no—
250C2×#547—71no—
251C2×#547—72no—
252C2×#547D711yescharacteristic, complemented
253C2×#546—72no—
254C2×#546—74no—
255C2×#546—72no—
256C2×D42—72no—
257C2×D42—71no—
258C2×D42—71no—
259C2×#537—72no—
260C2×#534—74no—
261C2×#532—71no—
262C2×#532—71no—
263C22×#121—72no—
264C22×#121—72no—
265C22×C4×D4—71no—
266C24×C7C2412yes—
267C24×C7C2412yes—
268C23×D7—216no—
269C23×D7—216no—
270C23×D7—44no—
271C23×D7—44no—
272C23×D7—48no—
273C23×D7—48no—
274C23×D7—48no—
275C23×D7—48no—
276C23×D7C2×D4116yescomplemented
277C23×D7C2412yes—
278C23×D7C2414yes—
279C23×D7C2412yes—
280C23×D7C2411yescharacteristic
281C23×D7C24116yes—
282C23×D7C24116yes—
283C23×D7C2418yes—
284C7×#41—264no—
285C2×C7×Q8—28no—
286C2×C7×Q8C2418yes—
287C2×C7×D4—216no—
288C2×C7×D4—24no—
289C2×C7×D4C2×D418yescomplemented
290C2×C7×D4C24116yes—
291C2×C7×D4C2414yes—
292C2×C7×D4C2414yes—
293C22×C4×C7—216no—
294C22×C4×C7—28no—
295C22×C4×C7—28no—
296C22×C4×C7C2411yescharacteristic
297C22×C4×C7C2412yes—
298C22×C4×C7C2412yes—
299C22×C4×C7C2414yes—
300C22×C4×C7C24116yes—
301C22×C4×C7C2418yes—
302C22×C4×C7C2418yes—
303C22×C4×C7C2411yescharacteristic
304C22×C4×C7C2411yescharacteristic
305C2×C22⋊D7—216no—
306C2×C22⋊D7—28no—
307C2×C22⋊D7—28no—
308C2×C22⋊D7—48no—
309C2×C22⋊D7—44no—
310C2×C22⋊D7C2×D4116yescomplemented
311C2×C22⋊D7C24116yes—
312C2×C22⋊D7C2418yes—
313C2×C22⋊D7C2418yes—
314C2×C22⋊D7C2418yes—
315C2×C22⋊D7C24116yes—
316C2×C22⋊D7C2418yes—
317C22×Dic7—44no—
318C22×Dic7C2411yescharacteristic
319C22×Dic7C2411yescharacteristic
320C22×Dic7C2412yes—
321C22×Dic7C2412yes—
322C22×Dic7C2418yes—
323C22×Dic7C2411yescharacteristic
324#1161—264no—
325#1161—264no—
326D4×D7—2128no—
327D4×D7—264no—
328D4×D7—2128no—
329D4×D7—432no—
330D4×D7C2×D4164yescomplemented
331#1157—2128no—
332#1157—264no—
333C2×D28—216no—
334C2×D28—28no—
335C2×D28—216no—
336C2×D28—216no—
337C2×D28—2128no—
338C2×D28—28no—
339C2×D28—24no—
340C2×D28—28no—
341C2×D28—264no—
342C2×D28—432no—
343C2×D28—48no—
344C2×D28—44no—
345C2×D28C2×D418yescomplemented
346C2×D28C2414yes—
347C2×D28C2418yes—
348C2×D28C2418yes—
349C2×D28C24116yes—
350C2×D28C24116yes—
351C2×D28C2418yes—
352C2×D28C24116yes—
353C2×D28C2418yes—
354C2×D28C24116yes—
355C2×D28C2414yes—
356C2×C4×D7—216no—
357C2×C4×D7—28no—
358C2×C4×D7—24no—
359C2×C4×D7—28no—
360C2×C4×D7—216no—
361C2×C4×D7—432no—
362C2×C4×D7—44no—
363C2×C4×D7—44no—
364C2×C4×D7—42no—
365C2×C4×D7C2×D418yescomplemented
366C2×C4×D7C2414yes—
367C2×C4×D7C2418yes—
368C2×C4×D7C2418yes—
369C2×C4×D7C24116yes—
370C2×C4×D7C24116yes—
371C2×C4×D7C2414yes—
372C2×C4×D7C2418yes—
373C2×C4×D7C2418yes—
374C2×C4×D7C2414yes—
375C2×Dic14—28no—
376C2×Dic14C2418yes—
377C7×C4⋊C4C2414yes—
378C7×C4⋊C4C2418yes—
379C7×C4⋊C4C2414yes—
380C7×C4⋊C4C2418yes—
381C7×C4⋊C4C24116yes—
382C7×C22⋊C4C2418yes—
383C7×C22⋊C4C24116yes—
384C7×C22⋊C4C2418yes—
385C42×C7C2414yes—
386C22⋊Dic7C2418yes—
387C22⋊Dic7C2418yes—
388(C2×D7)⋊C4C2418yes—
389(C2×D7)⋊C4C2418yes—
390(C2×D7)⋊C4C2418yes—
391(C2×D7)⋊C4C24116yes—
392(C2×D7)⋊C4C24116yes—
393(C2×D7)⋊C4C24116yes—
394(C2×D7)⋊C4C24116yes—
395(C2×D7)⋊C4C24116yes—
396(C2×D7)⋊C4C2418yes—
397C4⋊Dic7C2414yes—
398C4⋊Dic7C2414yes—
399Dic7⋊C4C2418yes—
400Dic7⋊C4C2418yes—
401Dic7⋊C4C24116yes—
402C4×Dic7C2414yes—
403C4×Dic7C2414yes—
404C4×Dic7C2414yes—
405C2×H(5,𝔽2)—732no—
406C2×H(5,𝔽2)—1432no—
407C22×#41—72no—
408C22×#41—72no—
409C22×#41—72no—
410C22×#41—74no—
411C22×#41C2×D712yescomplemented
412C23×D4—71no—
413C23×D4—74no—
414C23×D4—74no—
415C23×D4—72no—
416C23×D4—72no—
417C23×D4—74no—
418C23×D4—72no—
419C23×D4—72no—
420C24×C4—72no—
421#547—716no—
422#547—732no—
423#547C2×D7116yescomplemented
424#546—732no—
425#546—764no—
426#546—732no—
427D42—732no—
428D42—716no—
429D42—716no—
430#537—732no—
431#534—764no—
432#532—716no—
433#532—716no—
434C2×C4⋊Q8—71no—
435C2×C4⋊Q8C2×D711yescharacteristic, complemented
436C2×#127—71no—
437C2×#127—71no—
438C2×#124—72no—
439C2×#124—72no—
440C2×#123—74no—
441C2×#123—74no—
442C2×#123—74no—
443C2×#123C2×D714yescomplemented
444C2×C22⋊Q8—72no—
445C2×C22⋊Q8—74no—
446C2×C22⋊Q8C2×D712yescomplemented
447C2×#121—71no—
448C2×#121—74no—
449C2×#121—72no—
450C2×#121—72no—
451C2×#121—732no—
452C2×#121—72no—
453C2×#121—71no—
454C2×#121—74no—
455C2×#121—72no—
456C2×#121—72no—
457C2×#121—74no—
458C2×#121—72no—
459C2×#121—72no—
460C2×#121—732no—
461C2×#121—74no—
462C2×#121—72no—
463C2×#121—74no—
464C2×#121C2×D712yescomplemented
465C2×#120—74no—
466C2×#120—74no—
467C2×#120—74no—
468C2×#120—74no—
469C2×C4×D4—71no—
470C2×C4×D4—72no—
471C2×C4×D4—72no—
472C2×C4×D4—716no—
473C2×C4×D4—71no—
474C2×C4×D4—72no—
475C2×C4×D4—72no—
476C2×C4×D4—72no—
477C2×C4×D4—71no—
478C2×C4×D4—71no—
479C2×C4×D4C2×D711yescharacteristic, complemented
480C2×C4×D4C2×D711yescharacteristic, complemented
481C22×C4⋊C4—71no—
482C22×C4⋊C4—72no—
483C22×C4⋊C4C2×D712yescomplemented
484C22×C22⋊C4—74no—
485C22×C22⋊C4—72no—
486C22×C22⋊C4—74no—
487C22×C42—71no—
488C23×C7—24no—
489C23×C7—24no—
490C23×C7—24no—
491C23×C7—24no—
492C23×C7—24no—
493C23×C7C22×D418yes—
494C23×C7C2514yes—
495C23×C7C2514yes—
496C23×C7C2511yescharacteristic
497C22×D7—22no—
498C22×D7—24no—
499C22×D7—22no—
500C22×D7—24no—
501C22×D7—24no—
502C22×D7—28no—
503C22×D7—24no—
504C22×D7—28no—
505C22×D7—28no—
506C22×D7—24no—
507C22×D7—232no—
508C22×D7—232no—
509C22×D7—48no—
510C22×D7—432no—
511C22×D7—48no—
512C22×D7—416no—
513C22×D7—416no—
514C22×D7—416no—
515C22×D7—416no—
516C22×D7—832no—
517C22×D7—832no—
518C22×D7C22×D418yes—
519C22×D7C22×D414yes—
520C22×D7C22×D4132yescomplemented
521C22×D7C2514yes—
522C22×D7C2518yes—
523C22×D7C2514yes—
524C22×D7C2512yes—
525C7×Q8—216no—
526C7×D4—232no—
527C7×D4—28no—
528C7×D4C22×D4116yescomplemented
529C2×C4×C7—24no—
530C2×C4×C7—28no—
531C2×C4×C7—232no—
532C2×C4×C7—24no—
533C2×C4×C7—22no—
534C2×C4×C7—216no—
535C2×C4×C7—216no—
536C2×C4×C7C22×D414yes—
537C2×C4×C7H(5,𝔽2)14yescomplemented
538C2×C4×C7C2512yes—
539C2×C4×C7C2514yes—
540C2×C4×C7C2514yes—
541C2×C4×C7C2518yes—
542C2×C4×C7C2512yes—
543C2×C4×C7C2512yes—
544C22⋊D7—232no—
545C22⋊D7—216no—
546C22⋊D7—216no—
547C22⋊D7—416no—
548C22⋊D7—48no—
549C22⋊D7C22×D4132yescomplemented
550C2×Dic7—24no—
551C2×Dic7—22no—
552C2×Dic7—24no—
553C2×Dic7—22no—
554C2×Dic7—48no—
555C2×Dic7C22×D414yes—
556C2×Dic7C2512yes—
557C2×Dic7C2512yes—
558C2×Dic7C2514yes—
559C2×Dic7C2514yes—
560C2×Dic7C2512yes—
561D28—232no—
562D28—216no—
563D28—232no—
564D28—232no—
565D28—216no—
566D28—28no—
567D28—216no—
568D28—416no—
569D28—48no—
570D28C22×D4116yescomplemented
571C4×D7—232no—
572C4×D7—216no—
573C4×D7—28no—
574C4×D7—216no—
575C4×D7—232no—
576C4×D7—48no—
577C4×D7—48no—
578C4×D7—44no—
579C4×D7C22×D4116yescomplemented
580Dic14—216no—
581C25—72no—
582C25—74no—
583C25—74no—
584H(5,𝔽2)—14256no—
585C2×#41—216no—
586C2×#41—716no—
587C2×#41—716no—
588C2×#41—716no—
589C2×#41—732no—
590C2×#41—1416no—
591C2×#41—1432no—
592C2×#41—1416no—
593C2×#41—1416no—
594C2×#41C22×D7116yescomplemented
595C22×Q8—72no—
596C22×Q8C22×D712yes—
597C22×D4—72no—
598C22×D4—716no—
599C22×D4—78no—
600C22×D4—74no—
601C22×D4—72no—
602C22×D4—72no—
603C22×D4—72no—
604C22×D4—74no—
605C22×D4—732no—
606C22×D4—732no—
607C22×D4—716no—
608C22×D4—716no—
609C22×D4—71no—
610C22×D4—72no—
611C22×D4—71no—
612C22×D4—74no—
613C22×D4—74no—
614C22×D4—74no—
615C22×D4—72no—
616C22×D4—72no—
617C22×D4—732no—
618C22×D4—716no—
619C22×D4—72no—
620C22×D4—74no—
621C22×D4—716no—
622C22×D4—1416no—
623C22×D4—1432no—
624C22×D4—1432no—
625C22×D4—1432no—
626C22×D4—1416no—
627C22×D4—288no—
628C22×D4—288no—
629C22×D4C22×D711yescharacteristic
630C22×D4C22×D714yes—
631C22×D4C22×D711yescharacteristic
632C23×C4—71no—
633C23×C4—72no—
634C23×C4—74no—
635C23×C4—72no—
636C23×C4—74no—
637C23×C4—72no—
638C23×C4—71no—
639C23×C4—72no—
640C23×C4—71no—
641C23×C4—72no—
642C23×C4—716no—
643C23×C4—288no—
644C23×C4C22×D714yes—
645C23×C4C22×D712yes—
646C23×C4C22×D712yes—
647C4⋊Q8—78no—
648C4⋊Q8C22×D718yescomplemented
649#127—78no—
650#127—78no—
651#124—716no—
652#124—716no—
653#123—732no—
654#123—732no—
655#123—732no—
656#123C22×D7132yescomplemented
657C22⋊Q8—716no—
658C22⋊Q8—732no—
659C22⋊Q8C22×D7116yescomplemented
660#121—78no—
661#121—732no—
662#121—716no—
663#121—716no—
664#121—716no—
665#121—78no—
666#121—732no—
667#121—716no—
668#121—716no—
669#121—732no—
670#121—716no—
671#121—716no—
672#121—732no—
673#121—716no—
674#121—732no—
675#121C22×D7116yescomplemented
676#120—732no—
677#120—732no—
678#120—732no—
679#120—732no—
680C4×D4—78no—
681C4×D4—716no—
682C4×D4—716no—
683C4×D4—78no—
684C4×D4—716no—
685C4×D4—716no—
686C4×D4—716no—
687C4×D4—78no—
688C4×D4—78no—
689C4×D4C22×D718yescomplemented
690C4×D4C22×D718yescomplemented
691C2×C4⋊C4—71no—
692C2×C4⋊C4—72no—
693C2×C4⋊C4—71no—
694C2×C4⋊C4—74no—
695C2×C4⋊C4—72no—
696C2×C4⋊C4—78no—
697C2×C4⋊C4—716no—
698C2×C4⋊C4C22×D712yes—
699C2×C4⋊C4C22×D711yescharacteristic
700C2×C4⋊C4C22×D711yescharacteristic
701C2×C4⋊C4C22×D714yes—
702C2×C4⋊C4C22×D712yes—
703C2×C4⋊C4C22×D7116yescomplemented
704C2×C22⋊C4—72no—
705C2×C22⋊C4—72no—
706C2×C22⋊C4—74no—
707C2×C22⋊C4—72no—
708C2×C22⋊C4—72no—
709C2×C22⋊C4—72no—
710C2×C22⋊C4—74no—
711C2×C22⋊C4—74no—
712C2×C22⋊C4—74no—
713C2×C22⋊C4—732no—
714C2×C22⋊C4—74no—
715C2×C22⋊C4—72no—
716C2×C22⋊C4—716no—
717C2×C22⋊C4—732no—
718C2×C22⋊C4C22×D712yes—
719C2×C22⋊C4C22×D714yes—
720C2×C22⋊C4C22×D712yes—
721C2×C42—71no—
722C2×C42—71no—
723C2×C42—71no—
724C2×C42—78no—
725C2×C42C22×D711yescharacteristic
726C22×C7—24no—
727C22×C7—24no—
728C22×C7—216no—
729C22×C7—24no—
730C22×C7—24no—
731C22×C7—24no—
732C22×C7—48no—
733C22×C7C23×D418yes—
734C22×C7C23×D412yes—
735C22×C7C2×H(5,𝔽2)12yes—
736C22×C7#58512yes—
737C22×C7C2611yescharacteristic
738C2×D7—22no—
739C2×D7—24no—
740C2×D7—22no—
741C2×D7—24no—
742C2×D7—28no—
743C2×D7—216no—
744C2×D7—24no—
745C2×D7—28no—
746C2×D7—24no—
747C2×D7—28no—
748C2×D7—28no—
749C2×D7—24no—
750C2×D7—432no—
751C2×D7—48no—
752C2×D7—416no—
753C2×D7—832no—
754C2×D7—832no—
755C2×D7C23×D418yes—
756C2×D7C23×D414yes—
757C4×C7—24no—
758C4×C7—28no—
759C4×C7—24no—
760C4×C7—22no—
761C4×C7C23×D414yes—
762C4×C7C2×H(5,𝔽2)14yescomplemented
763Dic7—24no—
764Dic7—22no—
765Dic7—24no—
766Dic7—22no—
767Dic7C23×D414yes—
768C24—72no—
769C24—71no—
770C24—716no—
771C24—78no—
772C24—74no—
773C24—72no—
774C24—716no—
775C24—716no—
776C24—1416no—
777C24—1416no—
778C24—284no—
779C24—284no—
780C24—288no—
781C24—288no—
782C24—288no—
783C24—288no—
784C24C23×D712yes—
785C24C23×D712yes—
786#41—264no—
787#41—1464no—
788#41—14128no—
789#41—1464no—
790#41—1464no—
791C2×Q8—28no—
792C2×Q8—78no—
793C2×Q8—148no—
794C2×Q8C23×D718yes—
795C2×D4—216no—
796C2×D4—24no—
797C2×D4—716no—
798C2×D4—78no—
799C2×D4—764no—
800C2×D4—716no—
801C2×D4—78no—
802C2×D4—78no—
803C2×D4—78no—
804C2×D4—716no—
805C2×D4—78no—
806C2×D4—74no—
807C2×D4—78no—
808C2×D4—74no—
809C2×D4—716no—
810C2×D4—716no—
811C2×D4—716no—
812C2×D4—78no—
813C2×D4—78no—
814C2×D4—78no—
815C2×D4—716no—
816C2×D4—1464no—
817C2×D4—148no—
818C2×D4—1416no—
819C2×D4—1416no—
820C2×D4—1416no—
821C2×D4—14128no—
822C2×D4—148no—
823C2×D4—14128no—
824C2×D4—14128no—
825C2×D4—148no—
826C2×D4—1416no—
827C2×D4—1464no—
828C2×D4—148no—
829C2×D4—144no—
830C2×D4—148no—
831C2×D4—2832no—
832C2×D4—284no—
833C2×D4—288no—
834C2×D4—2832no—
835C2×D4—288no—
836C2×D4—284no—
837C2×D4D4×D718yescomplemented
838C2×D4C23×D714yes—
839C2×D4C23×D7116yes—
840C2×D4C23×D714yes—
841C22×C4—216no—
842C22×C4—28no—
843C22×C4—28no—
844C22×C4—71no—
845C22×C4—78no—
846C22×C4—74no—
847C22×C4—71no—
848C22×C4—71no—
849C22×C4—72no—
850C22×C4—72no—
851C22×C4—78no—
852C22×C4—74no—
853C22×C4—716no—
854C22×C4—78no—
855C22×C4—716no—
856C22×C4—78no—
857C22×C4—74no—
858C22×C4—78no—
859C22×C4—78no—
860C22×C4—1416no—
861C22×C4—1416no—
862C22×C4—148no—
863C22×C4—144no—
864C22×C4—148no—
865C22×C4—2832no—
866C22×C4—282no—
867C22×C4—284no—
868C22×C4—284no—
869C22×C4—284no—
870C22×C4C23×D7116yes—
871C22×C4C23×D718yes—
872C22×C4C23×D718yes—
873C22×C4C23×D711yescharacteristic
874C22×C4C23×D712yes—
875C22×C4C23×D714yes—
876C22×C4C23×D712yes—
877C22×C4C23×D711yescharacteristic
878C22×C4C23×D711yescharacteristic
879C4⋊C4—78no—
880C4⋊C4—716no—
881C4⋊C4—78no—
882C4⋊C4—74no—
883C4⋊C4—74no—
884C4⋊C4C23×D718yes—
885C4⋊C4C23×D714yes—
886C4⋊C4C23×D714yes—
887C4⋊C4C23×D7116yes—
888C4⋊C4C23×D718yes—
889C22⋊C4—78no—
890C22⋊C4—78no—
891C22⋊C4—716no—
892C22⋊C4—78no—
893C22⋊C4—78no—
894C22⋊C4—78no—
895C22⋊C4—716no—
896C22⋊C4—716no—
897C22⋊C4—716no—
898C22⋊C4—716no—
899C22⋊C4—78no—
900C22⋊C4C23×D718yes—
901C22⋊C4C23×D7116yes—
902C22⋊C4C23×D718yes—
903C42—74no—
904C42—74no—
905C42—74no—
906C42C23×D714yes—
907C2×C7—28no—
908C2×C7—44no—
909C2×C7#349614yescomplemented
910C2×C7C24×D411yescharacteristic
911C2×C7C22×H(5,𝔽2)11yescharacteristic
912C2×C7C2×#58511yescharacteristic
913D7—24no—
914D7—28no—
915D7—44no—
916D7—48no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—74no—
923C23—72no—
924C23—74no—
925C23—78no—
926C23—732no—
927C23—78no—
928C23—74no—
929C23—1432no—
930C23—142no—
931C23—144no—
932C23—142no—
933C23—144no—
934C23—148no—
935C23—144no—
936C23—144no—
937C23—148no—
938C23—148no—
939C23—144no—
940C23—1432no—
941C23—288no—
942C23—2832no—
943C23—288no—
944C23—2816no—
945C23—2816no—
946C23—2816no—
947C23—2816no—
948C23—5632no—
949C23—5632no—
950C23C2×D4×D718yes—
951C23C24×D714yes—
952C23C24×D714yes—
953C23C24×D711yescharacteristic
954Q8—216no—
955Q8—1416no—
956D4—232no—
957D4—28no—
958D4—732no—
959D4—716no—
960D4—1416no—
961D4—1432no—
962D4—1432no—
963D4—1432no—
964D4—1416no—
965D4—1416no—
966D4—1432no—
967D4—1416no—
968D4—148no—
969D4—1416no—
970D4—288no—
971D4—2816no—
972D4—288no—
973D4—2816no—
974D4C2×D4×D7116yescomplemented
975C2×C4—24no—
976C2×C4—28no—
977C2×C4—232no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—216no—
981C2×C4—216no—
982C2×C4—72no—
983C2×C4—74no—
984C2×C4—716no—
985C2×C4—72no—
986C2×C4—72no—
987C2×C4—74no—
988C2×C4—74no—
989C2×C4—1432no—
990C2×C4—1432no—
991C2×C4—144no—
992C2×C4—142no—
993C2×C4—144no—
994C2×C4—142no—
995C2×C4—1416no—
996C2×C4—148no—
997C2×C4—1416no—
998C2×C4—284no—
999C2×C4—288no—
1000C2×C4—288no—
1001C2×C4—288no—
1002C2×C4C2×D4×D714yes—
1003C2×C4#655314yescomplemented
1004C2×C4C24×D712yes—
1005C2×C4C24×D714yes—
1006C2×C4C24×D718yes—
1007C2×C4C24×D714yes—
1008C2×C4C24×D712yes—
1009C2×C4C24×D712yes—
1010C7C2×#349611yescharacteristic, complemented, Sylow
1011C22—216no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—48no—
1018C22—74no—
1019C22—78no—
1020C22—148no—
1021C22—1416no—
1022C22—142no—
1023C22—144no—
1024C22—142no—
1025C22—144no—
1026C22—148no—
1027C22—144no—
1028C22—144no—
1029C22—148no—
1030C22—148no—
1031C22—144no—
1032C22—2832no—
1033C22—288no—
1034C22—2816no—
1035C22—5632no—
1036C22—5632no—
1037C22C22×D4×D718yes—
1038C22C22×D4×D712yes—
1039C22C2×#655312yes—
1040C22#9062012yes—
1041C22C25×D711yescharacteristic
1042C4—24no—
1043C4—28no—
1044C4—24no—
1045C4—22no—
1046C4—74no—
1047C4—144no—
1048C4—142no—
1049C4—144no—
1050C4—142no—
1051C4C22×D4×D714yes—
1052C4C2×#655314yescomplemented
1053C2—28no—
1054C2—44no—
1055C2—144no—
1056C2—148no—
1057C2—284no—
1058C2—288no—
1059C2#1174377014yesdirect product factor
1060C2C23×D4×D711yescharacteristic
1061C2C22×#655311yescharacteristic
1062C2C2×#9062011yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#547C2
socleC23×C7C25
hypercenterC2×#547D7
hypocenterC7C2×#3496
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#6553C2semidirect
2. C2×C7×#547C2semidirect
3. C2×#90520C2semidirect
4. #11743770C2direct (N × H)
5. C2×#90417C2semidirect
6. C2×#90416C2semidirect
7. C2×#90345C2semidirect
8. C2×#90344C2semidirect
9. C2×#90321C2semidirect
10. C2×#90320C2semidirect
11. C2×#90300C2semidirect
12. C2×D7×#121C2semidirect
13. C2×D4×D28C2semidirect
14. C2×D4×D28C2semidirect
15. C2×#90239C2semidirect
16. C2×C4×D4×D7C2semidirect
17. C2×#90198C2semidirect
18. C22×#6458C2semidirect
19. C22×C7×#41C22semidirect
21. C2×#6553C22semidirect
22. C22×#1161C22semidirect
23. C22×#1161C22semidirect
25. C22×D4×D7C22semidirect
26. C22×D4×D7C22semidirect
27. C22×D4×D7C22semidirect
28. C22×D4×D7C22semidirect
29. C22×#1157C22semidirect
30. C22×#1157C22semidirect
31. C23×D28C22semidirect
32. C23×D28C22semidirect
33. C23×D28C22semidirect
34. C23×C4×D7C22semidirect
35. C7×#547C22semidirect
36. C2×C7×C4⋊Q8C22semidirect
37. C2×C7×#123C22semidirect
38. C2×C7×C22⋊Q8C22semidirect
39. C2×C7×#121C22semidirect
40. C2×C4×C7×D4C22semidirect
41. C2×C4×C7×D4C22semidirect
42. C22×C7×C4⋊C4C22semidirect
43. #90520C22semidirect
44. C2×#6510C22semidirect
45. C2×#6509C22semidirect
46. C2×#6503C22semidirect
47. C2×#6502C22semidirect
48. C2×#6501C22semidirect
49. C2×#6500C22semidirect
50. C2×D4×Dic7C22semidirect
51. C2×#6493C22semidirect
52. C2×#6493C22semidirect
53. C2×#6492C22semidirect
54. C2×C4×C22⋊D7C22semidirect
55. C2×C4×C22⋊D7C22semidirect
56. C22×(C2×D7)⋊C4C22semidirect
57. #90417C22semidirect
58. #90416C22semidirect
59. #90345C22semidirect
60. #90344C22semidirect
61. #90321C22semidirect
62. #90320C22semidirect
63. #90300C22semidirect
64. D7×#121C22semidirect
65. D4×D28C22semidirect
66. D4×D28C22semidirect
67. #90239C22semidirect
68. C4×D4×D7C22semidirect
69. C2×#6459C22semidirect
70. #90198C22semidirect
71. C2×#6458C22semidirect
72. C2×#6458C22semidirect
73. C2×#6458C22semidirect
74. C2×#6458C22semidirect
75. C2×#6458C22semidirect
76. C2×#6458C22semidirect
77. C2×#6458C22semidirect
78. C2×#6458C22semidirect
79. C2×#6458C22semidirect
80. C2×#6457C22semidirect
81. C2×#6457C22semidirect
82. C2×#6456C22semidirect
83. C2×#6456C22semidirect
84. C2×#6456C22semidirect
85. C2×D7×C4⋊C4C22semidirect
86. C2×D7×C4⋊C4C22semidirect
87. C2×#6451C22semidirect
88. C2×#6448C22semidirect
89. C2×#6447C22semidirect
90. C2×#6447C22semidirect
91. C2×#6447C22semidirect
92. C2×#6445C22semidirect
93. C2×#6445C22semidirect
94. C2×#6445C22semidirect
95. C2×(C22⋊D7)⋊C4C22semidirect
96. C2×D7×C22⋊C4C22semidirect
97. C2×D7×C22⋊C4C22semidirect
98. C2×#6437C22semidirect
99. C2×C4×D28C22semidirect
100. C2×C4×D28C22semidirect
101. C2×C42×D7C22semidirect
107. C2×C7×#41C23semidirect
125. C2×#1161C23semidirect
126. C2×#1161C23semidirect
131. C2×D4×D7D4semidirect
133. C2×D4×D7C23semidirect
134. C2×D4×D7C23semidirect
135. C2×D4×D7C23semidirect
136. C2×D4×D7C23semidirect
139. C2×#1157C23semidirect
140. C2×#1157C23semidirect
154. C22×D28C23semidirect
155. C22×D28C23semidirect
156. C22×D28C23semidirect
167. C22×C4×D7C23semidirect
169. C7×C4⋊Q8C23semidirect
170. C7×#123C23semidirect
171. C7×C22⋊Q8C23semidirect
172. C7×#121C23semidirect
173. C4×C7×D4C23semidirect
174. C4×C7×D4C23semidirect
180. C2×C7×C4⋊C4C23semidirect
187. #6510C23semidirect
188. #6509C23semidirect
189. #6503C23semidirect
190. #6502C23semidirect
191. #6501C23semidirect
192. #6500C23semidirect
193. D4×Dic7C23semidirect
194. #6493C23semidirect
195. #6493C23semidirect
196. #6492C23semidirect
197. C4×C22⋊D7C23semidirect
198. C4×C22⋊D7C23semidirect
208. C2×(C2×D7)⋊C4C23semidirect
217. #6459C23semidirect
218. #6458C23semidirect
219. #6458C23semidirect
220. #6458C23semidirect
221. #6458C23semidirect
222. #6458C23semidirect
223. #6458C23semidirect
224. #6458C23semidirect
225. #6458C23semidirect
226. #6457C23semidirect
227. #6457C23semidirect
228. #6456C23semidirect
229. #6456C23semidirect
230. #6456C23semidirect
231. D7×C4⋊C4C23semidirect
232. D7×C4⋊C4C23semidirect
233. #6451C23semidirect
234. #6448C23semidirect
235. #6447C23semidirect
236. #6447C23semidirect
237. #6447C23semidirect
238. #6445C23semidirect
239. #6445C23semidirect
240. #6445C23semidirect
241. (C22⋊D7)⋊C4C23semidirect
242. D7×C22⋊C4C23semidirect
243. D7×C22⋊C4C23semidirect
244. #6437C23semidirect
245. C4×D28C23semidirect
246. C4×D28C23semidirect
247. C42×D7C23semidirect
252. C2×#547D7semidirect
276. C23×D7C2×D4semidirect
289. C2×C7×D4C2×D4semidirect
310. C2×C22⋊D7C2×D4semidirect
330. D4×D7C2×D4semidirect
345. C2×D28C2×D4semidirect
365. C2×C4×D7C2×D4semidirect
411. C22×#41C2×D7semidirect
423. #547C2×D7semidirect
435. C2×C4⋊Q8C2×D7semidirect
443. C2×#123C2×D7semidirect
446. C2×C22⋊Q8C2×D7semidirect
464. C2×#121C2×D7semidirect
479. C2×C4×D4C2×D7semidirect
480. C2×C4×D4C2×D7semidirect
483. C22×C4⋊C4C2×D7semidirect
520. C22×D7C22×D4semidirect
528. C7×D4C22×D4semidirect
537. C2×C4×C7H(5,𝔽2)semidirect
549. C22⋊D7C22×D4semidirect
570. D28C22×D4semidirect
579. C4×D7C22×D4semidirect
594. C2×#41C22×D7semidirect
648. C4⋊Q8C22×D7semidirect
656. #123C22×D7semidirect
659. C22⋊Q8C22×D7semidirect
675. #121C22×D7semidirect
689. C4×D4C22×D7semidirect
690. C4×D4C22×D7semidirect
703. C2×C4⋊C4C22×D7semidirect
762. C4×C7C2×H(5,𝔽2)semidirect
837. C2×D4D4×D7semidirect
909. C2×C7#3496semidirect
974. D4C2×D4×D7semidirect
1003. C2×C4#6553semidirect
1010. C7C2×#3496semidirect
1052. C4C2×#6553semidirect
1059. C2#11743770direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65532
C2×C7×#5472
C2×#905202
#117437702
C2×#904172
C2×#904162
C2×#903452
C2×#903442
C2×#903212
C2×#903202
C2×#903002
C2×D7×#1212
C2×D4×D282
C2×#902392
C2×C4×D4×D72
C2×#901982
C22×#64582
C2×#34967