Finite Group Databasebeta

← C2×#11742972 #14262228

Subgroups — C2×#11742972 #14262228

Order 1792.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#520C211yesmaximal, characteristic, complemented
2C2×#90519C211yesmaximal, characteristic
3C2×#90516C211yesmaximal, characteristic, complemented
4#11742972C2132yesmaximal, direct product factor
5C2×#90274C212yesmaximal, complemented
6C2×#90269C212yesmaximal, complemented
7C2×#90247C214yesmaximal, complemented
8C2×#90252C212yesmaximal, complemented
9C2×#90248C212yesmaximal, complemented
10C2×#90232C214yesmaximal, complemented
11C2×#90224C212yesmaximal, complemented
12C2×#90220C212yesmaximal, complemented
13C2×D7×#117C211yesmaximal, characteristic, complemented
14C2×#90207C211yesmaximal, characteristic, complemented
15C22×#6460C211yesmaximal, characteristic, complemented
16C2×#90202C212yesmaximal, complemented
17C2×#90204C212yesmaximal, complemented
18C2×#90191C211yesmaximal, characteristic, complemented
19C22×C7×#41C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C7×#520C22116yescomplemented
23C2×C4×C7×Q8C2212yescomplemented
24C2×C4×C7×D4C2214yes—
25C2×C4×C7×D4C2212yescomplemented
26C2×C7×#117C2211yescharacteristic
27C2×C7×#117C2212yescomplemented
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C4⋊C4C2212yescomplemented
30#90519C22116yes—
31#90516C22116yescomplemented
32C2×#6509C2211yescharacteristic
33C2×#6509C2211yescharacteristic
34C2×#6507C2212yescomplemented
35C2×#6501C2211yescharacteristic
36C2×#6501C2211yescharacteristic
37C2×#6500C2212yes—
38C2×#6499C2212yescomplemented
39C2×#6498C2214yes—
40C2×#6498C2212yes—
41C2×#6492C2214yes—
42C2×C4×C22⋊D7C2212yes—
43C2×C4×C22⋊D7C2212yes—
44C2×C4×C22⋊D7C2214yes—
45C22×(C2×D7)⋊C4C2212yes—
46C2×#6489C2211yescharacteristic
47C2×#6489C2211yescharacteristic
48C2×#6489C2214yescomplemented
49C22×C4⋊Dic7C2212yes—
50C2×#6487C2214yes—
51C2×#6487C2212yescomplemented
52C2×#6487C2212yescomplemented
53C2×#6487C2214yescomplemented
54#90274C22132yescomplemented
55#90269C22132yescomplemented
56#90252C22132yescomplemented
57#90248C22132yescomplemented
58#90247C22164yescomplemented
59#90232C22164yescomplemented
60#90224C22132yescomplemented
61#90220C22132yescomplemented
62D7×#117C22116yescomplemented
63#90207C22116yescomplemented
64#90204C22132yescomplemented
65C2×#6461C2214yes—
66#90202C22132yescomplemented
67C2×#6460C2212yes—
68C2×#6460C2212yes—
69C2×#6460C2212yes—
70C2×#6460C2212yes—
71C2×#6460C22116yescomplemented
72C2×#6459C2214yes—
73C2×#6455C2211yescharacteristic
74C2×#6455C2211yescharacteristic
75C2×D7×C4⋊C4C2211yescharacteristic
76C2×D7×C4⋊C4C2211yescharacteristic
77#90191C22116yescomplemented
78C2×#6453C2212yescomplemented
79C2×#6453C2212yescomplemented
80C2×#6452C2214yescomplemented
81C2×#6452C2214yescomplemented
82C2×#6451C2212yescomplemented
83C2×#6451C2212yescomplemented
84C2×#6450C2212yescomplemented
85C2×#6450C2212yescomplemented
86C2×#6448C2214yes—
87C2×#6446C2214yes—
88C2×D7×C22⋊C4C2212yes—
89C2×#6442C2214yescomplemented
90C2×#6442C2214yescomplemented
91C2×#6440C2214yes—
92C2×#6440C2212yes—
93C2×#6439C2214yes—
94C2×#6435C2212yes—
95C2×#6435C2214yes—
96C2×C42×D7C2212yes—
97C2×#6433C2214yescomplemented
98C2×C4×Dic14C2212yescomplemented
99C2×C4×Dic14C2212yescomplemented
100C2×C4×Dic14C2214yescomplemented
101C2×#3495—71nomaximal, Sylow
102C24×D7C2311yescharacteristic
103C2×C7×#41—28no—
104C2×C7×#41C2318yes—
105C22×C7×Q8C2311yescharacteristic
106C22×C7×D4C2312yes—
107C22×C7×D4C2311yescharacteristic
108C23×C4×C7C2312yes—
109C23×C4×C7C2312yes—
110C23×C4×C7C2314yes—
111C23×C4×C7C2311yescharacteristic
112C22×C22⋊D7C2312yes—
113C22×C22⋊D7C2312yes—
114C23×Dic7C2311yescharacteristic
115C23×Dic7C2312yes—
116C22×C4×D7—28no—
117C22×C4×D7C2311yescharacteristic
118C22×C4×D7C2312yes—
119C22×C4×D7C2311yescharacteristic
120C22×C4×D7C2311yescharacteristic
121C22×C4×D7C2311yescharacteristic
122C22×C4×D7C2318yes—
123C22×C4×D7C2312yes—
124C22×Dic14—28no—
125C22×Dic14C2312yes—
126C22×Dic14C2312yes—
127C22×Dic14C2318yes—
128C22×Dic14C2314yes—
129C4×C7×Q8C23116yescomplemented
130C4×C7×D4C23132yes—
131C4×C7×D4C23116yescomplemented
132C7×#117C2318yes—
133C7×#117C23116yescomplemented
134C2×C7×C4⋊C4C2311yescharacteristic
135C2×C7×C4⋊C4C2311yescharacteristic
136C2×C7×C4⋊C4C2312yes—
137C2×C7×C4⋊C4C2312yes—
138C2×C7×C4⋊C4C2314yes—
139C2×C7×C4⋊C4C2318yes—
140C2×C7×C4⋊C4C23116yescomplemented
141C2×C7×C22⋊C4C2312yes—
142C2×C7×C22⋊C4C2314yes—
143C2×C42×C7C2312yes—
144C2×C42×C7C2314yes—
145C2×C22⋊Dic7C2312yes—
146C2×C22⋊Dic7C2312yes—
147C2×C22⋊Dic7C2312yes—
148C2×C22⋊Dic7C2312yes—
149C2×C22⋊Dic7C2314yes—
150C2×C22⋊Dic7C2314yes—
151#6509C2318yes—
152#6509C2318yes—
153#6507C23116yescomplemented
154#6501C2318yes—
155#6501C2318yes—
156#6500C23116yes—
157#6499C23116yescomplemented
158#6498C23116yes—
159#6498C23132yes—
160#6492C23132yes—
161C4×C22⋊D7C23116yes—
162C4×C22⋊D7C23132yes—
163C4×C22⋊D7C23116yes—
164C2×(C2×D7)⋊C4C2312yes—
165C2×(C2×D7)⋊C4C2312yes—
166C2×(C2×D7)⋊C4C2312yes—
167C2×(C2×D7)⋊C4C2314yes—
168C2×(C2×D7)⋊C4C2312yes—
169C2×(C2×D7)⋊C4C2314yes—
170C2×(C2×D7)⋊C4C23116yes—
171#6489C2318yes—
172#6489C2318yes—
173#6489C23132yescomplemented
174C2×C4⋊Dic7C2311yescharacteristic
175C2×C4⋊Dic7C2311yescharacteristic
176C2×C4⋊Dic7C2314yes—
177C2×C4⋊Dic7C2314yes—
178C2×C4⋊Dic7C2314yes—
179C2×C4⋊Dic7C2311yescharacteristic
180C2×C4⋊Dic7C2311yescharacteristic
181C2×C4⋊Dic7C23116yes—
182#6487C23132yes—
183#6487C23116yescomplemented
184#6487C23132yescomplemented
185#6487C23116yescomplemented
186C2×Dic7⋊C4C2312yes—
187C2×Dic7⋊C4C2314yes—
188C2×Dic7⋊C4C2314yes—
189C2×Dic7⋊C4C2314yes—
190C2×Dic7⋊C4C2312yes—
191C2×Dic7⋊C4C2312yes—
192C2×Dic7⋊C4C2314yes—
193C2×Dic7⋊C4C2312yes—
194C2×Dic7⋊C4C2314yes—
195C2×Dic7⋊C4C2314yes—
196C2×C4×Dic7C2312yes—
197C2×C4×Dic7C2314yes—
198C2×C4×Dic7C2314yes—
199C2×C4×Dic7C2312yes—
200C2×C4×Dic7C2312yes—
201C2×C4×Dic7C2312yes—
202#6461C23132yes—
203#6460C23116yes—
204#6460C23116yes—
205#6460C23116yes—
206#6460C23116yes—
207#6459C23132yes—
208#6455C2318yes—
209#6455C2318yes—
210D7×C4⋊C4C2318yes—
211D7×C4⋊C4C2318yes—
212#6453C23116yescomplemented
213#6453C23116yescomplemented
214#6452C23132yescomplemented
215#6452C23132yescomplemented
216#6451C23116yescomplemented
217#6451C23116yescomplemented
218#6450C23116yescomplemented
219#6450C23116yescomplemented
220#6448C23132yes—
221#6446C23132yes—
222D7×C22⋊C4C23116yes—
223#6442C23132yescomplemented
224#6442C23132yescomplemented
225#6440C23132yes—
226#6440C23116yes—
227#6439C23132yes—
228#6435C23116yes—
229#6435C23132yes—
230C42×D7C23116yes—
231#6433C23132yescomplemented
232C4×Dic14C23116yescomplemented
233C4×Dic14C23116yescomplemented
234C4×Dic14C23132yescomplemented
235#3495—732no—
236C2×#556—72no—
237C2×#554—72no—
238C2×#552—74no—
239C2×#552—72no—
240C2×#552—72no—
241C2×#551—74no—
242C2×#544—71no—
243C2×#542—72no—
244C2×#541—72no—
245C2×#536—71no—
246C2×#533—72no—
247C2×#529—72no—
248C2×#525—71no—
249C22×C22⋊Q8—71no—
250C2×#520D711yescharacteristic, complemented
251C2×#519—71no—
252C22×#117—71no—
253C24×C7C2412yes—
254C24×C7C2411yescharacteristic
255C23×D7—24no—
256C23×D7—24no—
257C23×D7—42no—
258C23×D7C2411yescharacteristic
259C23×D7C2414yes—
260C23×D7C2411yescharacteristic
261C7×#41—232no—
262C2×C7×Q8—24no—
263C2×C7×Q8C2414yes—
264C2×C7×D4—28no—
265C2×C7×D4—24no—
266C2×C7×D4C2418yes—
267C2×C7×D4C2414yes—
268C22×C4×C7—28no—
269C22×C4×C7—44no—
270C22×C4×C7—48no—
271C22×C4×C7#4118yes—
272C22×C4×C7C2412yes—
273C22×C4×C7C2412yes—
274C22×C4×C7C2412yes—
275C22×C4×C7C2414yes—
276C22×C4×C7C2418yes—
277C22×C4×C7C2418yes—
278C22×C4×C7C24116yes—
279C22×C4×C7C2411yescharacteristic
280C22×C4×C7C2411yescharacteristic
281C22×C4×C7C2414yes—
282C2×C22⋊D7—28no—
283C2×C22⋊D7—44no—
284C2×C22⋊D7C2418yes—
285C2×C22⋊D7C2418yes—
286C22×Dic7—28no—
287C22×Dic7—24no—
288C22×Dic7C2414yes—
289C22×Dic7C2418yes—
290C22×Dic7C2411yescharacteristic
291C22×Dic7C2412yes—
292C22×Dic7C2412yes—
293C22×Dic7C2412yes—
294C22×Dic7C2412yes—
295C22×Dic7C2414yes—
296C22×Dic7C2411yescharacteristic
297C2×C4×D7—28no—
298C2×C4×D7—24no—
299C2×C4×D7—24no—
300C2×C4×D7—24no—
301C2×C4×D7—24no—
302C2×C4×D7—232no—
303C2×C4×D7—44no—
304C2×C4×D7C2414yes—
305C2×C4×D7C2418yes—
306C2×C4×D7C2414yes—
307C2×C4×D7C2414yes—
308C2×C4×D7C2414yes—
309C2×C4×D7C2418yes—
310C2×Dic14—28no—
311C2×Dic14—28no—
312C2×Dic14—232no—
313C2×Dic14—48no—
314C2×Dic14C2418yes—
315C2×Dic14C2418yes—
316C2×Dic14C24116yes—
317C7×C4⋊C4C2414yes—
318C7×C4⋊C4C2414yes—
319C7×C4⋊C4C2418yes—
320C7×C4⋊C4C2418yes—
321C7×C4⋊C4C24116yes—
322C7×C22⋊C4C2418yes—
323C7×C22⋊C4C24116yes—
324C42×C7C2418yes—
325C42×C7C24116yes—
326C22⋊Dic7C2418yes—
327C22⋊Dic7C2418yes—
328C22⋊Dic7C2418yes—
329C22⋊Dic7C2418yes—
330C22⋊Dic7C24116yes—
331C22⋊Dic7C24116yes—
332(C2×D7)⋊C4C2418yes—
333(C2×D7)⋊C4C2418yes—
334(C2×D7)⋊C4C2418yes—
335(C2×D7)⋊C4C24116yes—
336(C2×D7)⋊C4C2418yes—
337(C2×D7)⋊C4C24116yes—
338C4⋊Dic7C2414yes—
339C4⋊Dic7C2414yes—
340C4⋊Dic7C24116yes—
341C4⋊Dic7C24116yes—
342C4⋊Dic7C24116yes—
343C4⋊Dic7C2414yes—
344C4⋊Dic7C2414yes—
345Dic7⋊C4C2418yes—
346Dic7⋊C4C24116yes—
347Dic7⋊C4C24116yes—
348Dic7⋊C4C24116yes—
349Dic7⋊C4C2418yes—
350Dic7⋊C4C2418yes—
351Dic7⋊C4C24116yes—
352Dic7⋊C4C2418yes—
353Dic7⋊C4C24116yes—
354Dic7⋊C4C24116yes—
355C4×Dic7C2418yes—
356C4×Dic7C24116yes—
357C4×Dic7C24116yes—
358C4×Dic7C2418yes—
359C4×Dic7C2418yes—
360C4×Dic7C2418yes—
361C22×#41C2×D711yescharacteristic
362C23×Q8—71no—
363C24×C4—71no—
364#556—732no—
365#554—732no—
366#552—764no—
367#552—732no—
368#552—732no—
369#551—764no—
370#544—716no—
371#542—732no—
372#541—732no—
373#536—716no—
374#533—732no—
375C2×C4⋊Q8—72no—
376C2×C4⋊Q8—72no—
377C2×C4⋊Q8—72no—
378#529—732no—
379C2×#126—74no—
380C2×#126—74no—
381C2×#126—74no—
382C2×#126—74no—
383C2×#125—74no—
384C2×#125—74no—
385C2×#125—72no—
386C2×#125—72no—
387C2×#125—74no—
388C2×#124—72no—
389C2×#124—74no—
390#525—716no—
391C2×#123—72no—
392C2×#123—74no—
393C2×#123—74no—
394C2×#123—74no—
395C2×C22⋊Q8—71no—
396C2×C22⋊Q8—71no—
397C2×C22⋊Q8—74no—
398C2×C22⋊Q8—72no—
399C2×C22⋊Q8—72no—
400C2×C22⋊Q8—74no—
401C2×C22⋊Q8—74no—
402C2×C22⋊Q8—72no—
403C2×C22⋊Q8—72no—
404C2×C22⋊Q8—72no—
405C2×C22⋊Q8—72no—
406C2×C22⋊Q8—716no—
407C2×#121—71no—
408C2×#121—71no—
409C2×#120—72no—
410#520C2×D7116yescomplemented
411#519—716no—
412C2×C4×Q8—72no—
413C2×C4×Q8—72no—
414C2×C4×Q8—72no—
415C2×C4×Q8—72no—
416C2×C4×Q8—74no—
417C2×C4×Q8C2×D712yescomplemented
418C2×C4×D4—72no—
419C2×C4×D4—72no—
420C2×C4×D4—74no—
421C2×C4×D4C2×D714yes—
422C2×C4×D4C2×D712yescomplemented
423C2×#117—71no—
424C2×#117—71no—
425C2×#117—74no—
426C2×#117—716no—
427C2×#117—71no—
428C2×#117—71no—
429C2×#117—72no—
430C2×#117—74no—
431C2×#117—72no—
432C2×#117—74no—
433C2×#117C2×D711yescharacteristic
434C2×#117C2×D712yescomplemented
435C22×C4⋊C4—72no—
436C22×C4⋊C4—71no—
437C22×C4⋊C4—71no—
438C22×C4⋊C4C2×D711yescharacteristic
439C22×C4⋊C4C2×D712yescomplemented
440C22×C22⋊C4—72no—
441C22×C22⋊C4—72no—
442C22×C42—72no—
443C23×C7—22no—
444C23×C7—22no—
445C23×C7—24no—
446C23×C7—24no—
447C23×C7—24no—
448C23×C7C2×#4114yes—
449C23×C7C2514yes—
450C23×C7C2512yes—
451C23×C7C2511yescharacteristic
452C22×D7—22no—
453C22×D7—22no—
454C22×D7—28no—
455C22×D7—22no—
456C22×D7—22no—
457C22×D7—22no—
458C22×D7—28no—
459C22×D7—44no—
460C22×D7—416no—
461C22×D72−1+414yes—
462C22×D7C2512yes—
463C22×D7C2512yes—
464C7×Q8—28no—
465C7×D4—216no—
466C7×D4—28no—
467C2×C4×C7—24no—
468C2×C4×C7—24no—
469C2×C4×C7—28no—
470C2×C4×C7—24no—
471C2×C4×C7—216no—
472C2×C4×C7—48no—
473C2×C4×C7—416no—
474C2×C4×C7C2×#4114yes—
475C2×C4×C7C2×#4114yes—
476C2×C4×C7C2×#41116yes—
477C2×C4×C7C2514yes—
478C2×C4×C7C2514yes—
479C2×C4×C7C2514yes—
480C2×C4×C7C2518yes—
481C2×C4×C7C2512yes—
482C2×C4×C7C2512yes—
483C22⋊D7—216no—
484C22⋊D7—48no—
485C2×Dic7—216no—
486C2×Dic7—28no—
487C2×Dic7—28no—
488C2×Dic7—22no—
489C2×Dic7—22no—
490C2×Dic7—24no—
491C2×Dic7—24no—
492C2×Dic7—24no—
493C2×Dic7—24no—
494C2×Dic7C2512yes—
495C2×Dic7C2514yes—
496C2×Dic7C2514yes—
497C2×Dic7C2514yes—
498C2×Dic7C2514yes—
499C2×Dic7C2518yes—
500C2×Dic7C2512yes—
501C4×D7—216no—
502C4×D7—28no—
503C4×D7—28no—
504C4×D7—28no—
505C4×D7—28no—
506C4×D7—48no—
507Dic14—216no—
508Dic14—216no—
509Dic14—416no—
510C25—71no—
511C2×#41—28no—
512C2×#41C22×D718yes—
513C22×Q8—72no—
514C22×Q8—72no—
515C22×Q8—78no—
516C22×Q8—74no—
517C22×Q8—148no—
518C22×Q8C22×D711yescharacteristic
519C22×D4—72no—
520C22×D4—72no—
521C22×D4C22×D712yes—
522C22×D4C22×D711yescharacteristic
523C23×C4—72no—
524C23×C4—71no—
525C23×C4—72no—
526C23×C4—71no—
527C23×C4—71no—
528C23×C4—71no—
529C23×C4—78no—
530C23×C4—71no—
531C23×C4—72no—
532C23×C4—148no—
533C23×C4C22×D712yes—
534C23×C4C22×D712yes—
535C23×C4C22×D714yes—
536C23×C4C22×D711yescharacteristic
537C4⋊Q8—716no—
538C4⋊Q8—716no—
539C4⋊Q8—716no—
540#126—732no—
541#126—732no—
542#126—732no—
543#126—732no—
544#125—716no—
545#125—732no—
546#125—732no—
547#125—716no—
548#125—732no—
549#124—716no—
550#124—732no—
551#123—716no—
552#123—732no—
553#123—732no—
554#123—732no—
555C22⋊Q8—78no—
556C22⋊Q8—78no—
557C22⋊Q8—716no—
558C22⋊Q8—716no—
559C22⋊Q8—732no—
560C22⋊Q8—732no—
561C22⋊Q8—716no—
562C22⋊Q8—716no—
563C22⋊Q8—716no—
564C22⋊Q8—716no—
565C22⋊Q8—732no—
566#121—78no—
567#121—78no—
568#120—716no—
569C4×Q8—716no—
570C4×Q8—716no—
571C4×Q8—716no—
572C4×Q8—716no—
573C4×Q8—732no—
574C4×Q8C22×D7116yescomplemented
575C4×D4—716no—
576C4×D4—716no—
577C4×D4—732no—
578C4×D4C22×D7132yes—
579C4×D4C22×D7116yescomplemented
580#117—78no—
581#117—78no—
582#117—732no—
583#117—78no—
584#117—78no—
585#117—716no—
586#117—732no—
587#117—716no—
588#117—732no—
589#117C22×D718yes—
590#117C22×D7116yescomplemented
591C2×C4⋊C4—72no—
592C2×C4⋊C4—71no—
593C2×C4⋊C4—71no—
594C2×C4⋊C4—72no—
595C2×C4⋊C4—74no—
596C2×C4⋊C4—74no—
597C2×C4⋊C4—716no—
598C2×C4⋊C4—71no—
599C2×C4⋊C4—71no—
600C2×C4⋊C4—74no—
601C2×C4⋊C4—74no—
602C2×C4⋊C4—74no—
603C2×C4⋊C4—74no—
604C2×C4⋊C4—74no—
605C2×C4⋊C4—72no—
606C2×C4⋊C4—72no—
607C2×C4⋊C4—74no—
608C2×C4⋊C4—74no—
609C2×C4⋊C4—78no—
610C2×C4⋊C4—78no—
611C2×C4⋊C4C22×D711yescharacteristic
612C2×C4⋊C4C22×D711yescharacteristic
613C2×C4⋊C4C22×D712yes—
614C2×C4⋊C4C22×D712yes—
615C2×C4⋊C4C22×D718yes—
616C2×C4⋊C4C22×D714yes—
617C2×C4⋊C4C22×D7116yescomplemented
618C2×C22⋊C4—72no—
619C2×C22⋊C4—72no—
620C2×C22⋊C4—72no—
621C2×C22⋊C4—74no—
622C2×C22⋊C4—72no—
623C2×C22⋊C4—74no—
624C2×C22⋊C4—72no—
625C2×C22⋊C4—72no—
626C2×C22⋊C4—74no—
627C2×C22⋊C4—74no—
628C2×C22⋊C4—716no—
629C2×C22⋊C4—72no—
630C2×C22⋊C4—72no—
631C2×C22⋊C4—716no—
632C2×C22⋊C4C22×D712yes—
633C2×C22⋊C4C22×D714yes—
634C2×C42—72no—
635C2×C42—74no—
636C2×C42—74no—
637C2×C42—72no—
638C2×C42—72no—
639C2×C42—72no—
640C2×C42—716no—
641C2×C42C22×D712yes—
642C2×C42C22×D714yes—
643C22×C7—22no—
644C22×C7—22no—
645C22×C7—28no—
646C22×C7—24no—
647C22×C7—24no—
648C22×C7—24no—
649C22×C7—48no—
650C22×C7C22×#4114yes—
651C22×C7C22×#4112yes—
652C22×C7C2×2−1+412yes—
653C22×C7#58512yes—
654C22×C7C2611yescharacteristic
655C2×D7—22no—
656C2×D7—22no—
657C2×D7—28no—
658C2×D7—22no—
659C2×D7—22no—
660C2×D7—22no—
661C2×D7—416no—
662C2×D7—44no—
663C2×D7C2×2−1+414yes—
664C4×C7—24no—
665C4×C7—24no—
666C4×C7—28no—
667C4×C7—24no—
668C4×C7C22×#4114yes—
669C4×C7C22×#4114yes—
670Dic7—28no—
671Dic7—22no—
672Dic7—22no—
673Dic7—24no—
674Dic7—24no—
675Dic7—24no—
676Dic7—24no—
677C24—71no—
678C24—71no—
679C24—74no—
680C24—144no—
681C24—144no—
682C24—282no—
683C24C23×D712yes—
684C24C23×D711yescharacteristic
685#41—232no—
686C2×Q8—24no—
687C2×Q8—78no—
688C2×Q8—78no—
689C2×Q8—716no—
690C2×Q8—148no—
691C2×Q8—148no—
692C2×Q8—1432no—
693C2×Q8—288no—
694C2×Q8C23×D714yes—
695C2×D4—28no—
696C2×D4—24no—
697C2×D4—78no—
698C2×D4—78no—
699C2×D4—148no—
700C2×D4—284no—
701C2×D4C23×D718yes—
702C2×D4C23×D714yes—
703C22×C4—28no—
704C22×C4—48no—
705C22×C4—44no—
706C22×C4—78no—
707C22×C4—74no—
708C22×C4—71no—
709C22×C4—72no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—74no—
713C22×C4—72no—
714C22×C4—71no—
715C22×C4—74no—
716C22×C4—78no—
717C22×C4—74no—
718C22×C4—74no—
719C22×C4—74no—
720C22×C4—78no—
721C22×C4—148no—
722C22×C4—144no—
723C22×C4—148no—
724C22×C4—144no—
725C22×C4—144no—
726C22×C4—144no—
727C22×C4—144no—
728C22×C4—1432no—
729C22×C4—284no—
730C22×C4#115718yes—
731C22×C4C23×D718yes—
732C22×C4C23×D712yes—
733C22×C4C23×D712yes—
734C22×C4C23×D712yes—
735C22×C4C23×D714yes—
736C22×C4C23×D718yes—
737C22×C4C23×D7116yes—
738C22×C4C23×D714yes—
739C22×C4C23×D711yescharacteristic
740C22×C4C23×D711yescharacteristic
741C4⋊C4—78no—
742C4⋊C4—78no—
743C4⋊C4—716no—
744C4⋊C4—716no—
745C4⋊C4—716no—
746C4⋊C4—716no—
747C4⋊C4—78no—
748C4⋊C4—78no—
749C4⋊C4—716no—
750C4⋊C4—716no—
751C4⋊C4—74no—
752C4⋊C4—74no—
753C4⋊C4—716no—
754C4⋊C4—716no—
755C4⋊C4—74no—
756C4⋊C4—74no—
757C4⋊C4—716no—
758C4⋊C4C23×D714yes—
759C4⋊C4C23×D714yes—
760C4⋊C4C23×D718yes—
761C4⋊C4C23×D718yes—
762C4⋊C4C23×D7116yes—
763C22⋊C4—78no—
764C22⋊C4—78no—
765C22⋊C4—78no—
766C22⋊C4—716no—
767C22⋊C4—78no—
768C22⋊C4—716no—
769C22⋊C4—78no—
770C22⋊C4—78no—
771C22⋊C4—716no—
772C22⋊C4—716no—
773C22⋊C4—78no—
774C22⋊C4—78no—
775C22⋊C4C23×D718yes—
776C22⋊C4C23×D7116yes—
777C42—78no—
778C42—78no—
779C42—78no—
780C42—716no—
781C42—716no—
782C42—78no—
783C42C23×D718yes—
784C42C23×D7116yes—
785C2×C7—24no—
786C2×C7—44no—
787C2×C7#349514yescomplemented
788C2×C7C23×#4111yescharacteristic
789C2×C7C22×2−1+411yescharacteristic
790C2×C7C2×#58511yescharacteristic
791D7—24no—
792D7—42no—
793C23—22no—
794C23—22no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—72no—
799C23—74no—
800C23—72no—
801C23—148no—
802C23—142no—
803C23—142no—
804C23—148no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—284no—
809C23—2816no—
810C23C2×#115714yes—
811C23C24×D714yes—
812C23C24×D712yes—
813C23C24×D711yescharacteristic
814Q8—28no—
815Q8—1416no—
816Q8—1416no—
817Q8—2816no—
818D4—216no—
819D4—28no—
820D4—1416no—
821D4—288no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—216no—
827C2×C4—416no—
828C2×C4—48no—
829C2×C4—72no—
830C2×C4—74no—
831C2×C4—74no—
832C2×C4—74no—
833C2×C4—78no—
834C2×C4—74no—
835C2×C4—72no—
836C2×C4—1416no—
837C2×C4—148no—
838C2×C4—142no—
839C2×C4—142no—
840C2×C4—1416no—
841C2×C4—148no—
842C2×C4—144no—
843C2×C4—144no—
844C2×C4—144no—
845C2×C4—144no—
846C2×C4—148no—
847C2×C4—148no—
848C2×C4—148no—
849C2×C4—148no—
850C2×C4—288no—
851C2×C4C2×#115714yes—
852C2×C4C2×#115714yes—
853C2×C4C2×#1157116yes—
854C2×C4C24×D714yes—
855C2×C4C24×D714yes—
856C2×C4C24×D714yes—
857C2×C4C24×D718yes—
858C2×C4C24×D712yes—
859C2×C4C24×D712yes—
860C7C2×#349511yescharacteristic, complemented, Sylow
861C22—22no—
862C22—22no—
863C22—28no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—74no—
869C22—142no—
870C22—142no—
871C22—148no—
872C22—142no—
873C22—142no—
874C22—142no—
875C22—2816no—
876C22—284no—
877C22C22×#115714yes—
878C22C22×#115712yes—
879C22#9061812yes—
880C22D7×2−1+412yes—
881C22C25×D711yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—142no—
887C4—142no—
888C4—148no—
889C4—144no—
890C4—144no—
891C4—144no—
892C4—144no—
893C4C22×#115714yes—
894C4C22×#115714yes—
895C2—24no—
896C2—44no—
897C2—144no—
898C2—282no—
899C2#1174297214yesdirect product factor
900C2C23×#115711yescharacteristic
901C2C2×#9061811yescharacteristic
902C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#520C2
socleC23×C7C25
prime radicalC2×#90519C2
hypercenterC2×#520D7
hypocenterC7C2×#3495
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×C7×#520C2semidirect
3. C2×#90516C2semidirect
4. #11742972C2direct (N × H)
5. C2×#90274C2semidirect
6. C2×#90269C2semidirect
7. C2×#90247C2semidirect
8. C2×#90252C2semidirect
9. C2×#90248C2semidirect
10. C2×#90232C2semidirect
11. C2×#90224C2semidirect
12. C2×#90220C2semidirect
13. C2×D7×#117C2semidirect
14. C2×#90207C2semidirect
15. C22×#6460C2semidirect
16. C2×#90202C2semidirect
17. C2×#90204C2semidirect
18. C2×#90191C2semidirect
22. C7×#520C22semidirect
23. C2×C4×C7×Q8C22semidirect
25. C2×C4×C7×D4C22semidirect
27. C2×C7×#117C22semidirect
29. C22×C7×C4⋊C4C22semidirect
31. #90516C22semidirect
34. C2×#6507C22semidirect
38. C2×#6499C22semidirect
48. C2×#6489C22semidirect
51. C2×#6487C22semidirect
52. C2×#6487C22semidirect
53. C2×#6487C22semidirect
54. #90274C22semidirect
55. #90269C22semidirect
56. #90252C22semidirect
57. #90248C22semidirect
58. #90247C22semidirect
59. #90232C22semidirect
60. #90224C22semidirect
61. #90220C22semidirect
62. D7×#117C22semidirect
63. #90207C22semidirect
64. #90204C22semidirect
66. #90202C22semidirect
71. C2×#6460C22semidirect
77. #90191C22semidirect
78. C2×#6453C22semidirect
79. C2×#6453C22semidirect
80. C2×#6452C22semidirect
81. C2×#6452C22semidirect
82. C2×#6451C22semidirect
83. C2×#6451C22semidirect
84. C2×#6450C22semidirect
85. C2×#6450C22semidirect
89. C2×#6442C22semidirect
90. C2×#6442C22semidirect
97. C2×#6433C22semidirect
98. C2×C4×Dic14C22semidirect
99. C2×C4×Dic14C22semidirect
100. C2×C4×Dic14C22semidirect
129. C4×C7×Q8C23semidirect
131. C4×C7×D4C23semidirect
133. C7×#117C23semidirect
140. C2×C7×C4⋊C4C23semidirect
153. #6507C23semidirect
157. #6499C23semidirect
173. #6489C23semidirect
183. #6487C23semidirect
184. #6487C23semidirect
185. #6487C23semidirect
212. #6453C23semidirect
213. #6453C23semidirect
214. #6452C23semidirect
215. #6452C23semidirect
216. #6451C23semidirect
217. #6451C23semidirect
218. #6450C23semidirect
219. #6450C23semidirect
223. #6442C23semidirect
224. #6442C23semidirect
231. #6433C23semidirect
232. C4×Dic14C23semidirect
233. C4×Dic14C23semidirect
234. C4×Dic14C23semidirect
250. C2×#520D7semidirect
410. #520C2×D7semidirect
417. C2×C4×Q8C2×D7semidirect
422. C2×C4×D4C2×D7semidirect
434. C2×#117C2×D7semidirect
439. C22×C4⋊C4C2×D7semidirect
574. C4×Q8C22×D7semidirect
579. C4×D4C22×D7semidirect
590. #117C22×D7semidirect
617. C2×C4⋊C4C22×D7semidirect
787. C2×C7#3495semidirect
860. C7C2×#3495semidirect
899. C2#11742972direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5202
C2×#905192
C2×#905162
#117429722
C2×#902742
C2×#902692
C2×#902472
C2×#902522
C2×#902482
C2×#902322
C2×#902242
C2×#902202
C2×D7×#1172
C2×#902072
C22×#64602
C2×#902022
C2×#902042
C2×#901912
C2×#34957