Finite Group Databasebeta

← C2×#11744057 #14262065

Subgroups — C2×#11744057 #14262065

Order 1792.

7118 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#556C211yesmaximal, characteristic, complemented
2#11744057C2132yesmaximal, direct product factor
3C2×#90418C211yesmaximal, characteristic, complemented
4C2×#90419C211yesmaximal, characteristic, complemented
5C2×#90393C214yesmaximal, complemented
6C2×#90401C214yesmaximal, complemented
7C2×#90368C212yesmaximal, complemented
8C2×#90373C212yesmaximal, complemented
9C2×#90332C212yesmaximal, complemented
10C2×#90315C212yesmaximal, complemented
11C2×#90271C211yesmaximal, characteristic, complemented
12C2×#90263C212yesmaximal, complemented
13C2×Q8×Dic14C211yesmaximal, characteristic, complemented
14C2×#90275C212yesmaximal, complemented
15C2×#90254C211yesmaximal, characteristic, complemented
16C2×C4×#1159C211yesmaximal, characteristic, complemented
17C2×#90223C212yesmaximal, complemented
18C2×#90208C212yesmaximal, complemented
19C22×Q8×D7C2212yes—
20C22×#1159C2211yescharacteristic
21C7×#556C22116yescomplemented
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C7×#126C2214yes—
24C2×C7×#124C2212yes—
25C2×C7×C22⋊Q8C2212yes—
26C2×C4×C7×Q8C2212yes—
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117C2212yes—
30C2×#6510C2211yescharacteristic
31C2×#6509C2212yes—
32C2×#6509C2212yes—
33C2×#6509C2211yescharacteristic
34C2×Q8×Dic7C2212yes—
35C2×Q8×Dic7C2212yes—
36C2×#6501C2212yes—
37C2×D4×Dic7C2211yescharacteristic
38C2×#6493C2212yes—
39C2×C4×C22⋊D7C2212yes—
40C2×#6489C2212yes—
41C22×C4×Dic7C2212yes—
42#90419C22116yescomplemented
43#90418C22116yescomplemented
44#90401C22164yescomplemented
45#90393C22164yescomplemented
46#90373C22132yescomplemented
47#90368C22132yescomplemented
48#90332C22132yescomplemented
49#90315C22132yescomplemented
50#90275C22132yescomplemented
51#90271C22116yescomplemented
52#90263C22132yescomplemented
53Q8×Dic14C22116yescomplemented
54#90254C22116yescomplemented
55C4×#1159C22116yescomplemented
56#90223C22132yescomplemented
57#90208C22132yescomplemented
58C2×#6461C2214yes—
59C2×#6461C2214yes—
60C2×#6461C2212yes—
61C2×#6460C2212yes—
62C2×#6459C2214yes—
63C2×#6458C2211yescharacteristic
64C2×#6457C2212yes—
65C2×#6456C2212yes—
66C2×#6455C2212yes—
67C2×#6455C2214yes—
68C2×#6455C2211yescharacteristic
69C2×#6455C2212yes—
70C2×#6453C2212yes—
71C2×#6453C2211yescharacteristic
72C2×#6451C2212yes—
73C2×#6451C2212yes—
74C2×#6451C2214yes—
75C2×#6450C2212yes—
76C2×#6450C2214yes—
77C2×#6450C2211yescharacteristic
78C2×#6449C2214yes—
79C2×#6448C2214yes—
80C2×#6448C2214yes—
81C2×#6448C2214yes—
82C2×#6447C2214yes—
83C2×(C22⋊D7)⋊C4C2214yes—
84C2×(C22⋊D7)⋊C4C2212yes—
85C2×#6442C2214yes—
86C2×#6441C2214yes—
87C2×#6441C2214yes—
88C2×#6440C2212yes—
89C2×#6438C2214yes—
90C2×C4×D28C2211yescharacteristic
91C2×C4×D28C2212yes—
92C2×#6435C2214yes—
93C2×#6435C2212yes—
94C2×C42×D7C2211yescharacteristic
95C2×#6432C2211yescharacteristic
96C2×#6432C2212yes—
97C2×C4×Dic14C2211yescharacteristic
98C2×C4×Dic14C2214yes—
99C2×C4×Dic14C2214yes—
100C2×C4×Dic14C2212yes—
101C2×#3518—71nomaximal, Sylow
102C22×C7×Q8C2311yescharacteristic
103C22×C7×Q8C2312yes—
104C22×C7×D4C2311yescharacteristic
105C23×C4×C7C2312yes—
106C22×C22⋊D7C2312yes—
107C22×C22⋊D7C2314yes—
108C23×Dic7C2312yes—
109C23×Dic7C2312yes—
110C2×Q8×D7—216no—
111C2×Q8×D7C23116yes—
112C2×#1159—28no—
113C2×#1159C2318yes—
114C22×D28C2311yescharacteristic
115C22×D28C2312yes—
116C22×C4×D7C2311yescharacteristic
117C22×C4×D7C2311yescharacteristic
118C22×C4×D7C2312yes—
119C22×C4×D7C2314yes—
120C22×C4×D7C2311yescharacteristic
121C22×Dic14C2314yes—
122C22×Dic14C2314yes—
123C22×Dic14C2312yes—
124C22×Dic14C2311yescharacteristic
125C7×C4⋊Q8C2318yes—
126C7×#126C23132yes—
127C7×#124C23116yes—
128C7×C22⋊Q8C23116yes—
129C4×C7×Q8C2318yes—
130C4×C7×Q8C23116yes—
131C4×C7×D4C2318yes—
132C7×#117C23116yes—
133C2×C7×C4⋊C4C2311yescharacteristic
134C2×C7×C4⋊C4C2314yes—
135C2×C7×C4⋊C4C2312yes—
136C2×C7×C4⋊C4C2311yescharacteristic
137C2×C7×C4⋊C4C2312yes—
138C2×C7×C4⋊C4C2312yes—
139C2×C7×C22⋊C4C2312yes—
140C2×C7×C22⋊C4C2314yes—
141C2×C7×C22⋊C4C2314yes—
142C2×C42×C7C2314yes—
143C2×C42×C7C2311yescharacteristic
144C2×C42×C7C2312yes—
145C2×C22⋊Dic7C2312yes—
146C2×C22⋊Dic7C2314yes—
147#6510C2318yes—
148#6509C23116yes—
149#6509C23116yes—
150#6509C2318yes—
151Q8×Dic7C23116yes—
152Q8×Dic7C23116yes—
153#6501C23116yes—
154D4×Dic7C2318yes—
155#6493C23116yes—
156C4×C22⋊D7C23116yes—
157C2×(C2×D7)⋊C4C2312yes—
158C2×(C2×D7)⋊C4C2314yes—
159C2×(C2×D7)⋊C4C2312yes—
160C2×(C2×D7)⋊C4C2312yes—
161C2×(C2×D7)⋊C4C2312yes—
162C2×(C2×D7)⋊C4C2312yes—
163C2×(C2×D7)⋊C4C2312yes—
164C2×(C2×D7)⋊C4C2314yes—
165C2×(C2×D7)⋊C4C2314yes—
166#6489C23116yes—
167C2×C4⋊Dic7C2312yes—
168C2×C4⋊Dic7C2311yescharacteristic
169C2×C4⋊Dic7C2312yes—
170C2×C4⋊Dic7C2314yes—
171C2×C4⋊Dic7C2314yes—
172C2×C4⋊Dic7C2312yes—
173C2×C4⋊Dic7C2311yescharacteristic
174C2×Dic7⋊C4C2312yes—
175C2×Dic7⋊C4C2314yes—
176C2×Dic7⋊C4C2312yes—
177C2×Dic7⋊C4C2314yes—
178C2×Dic7⋊C4C2314yes—
179C2×Dic7⋊C4C2312yes—
180C2×Dic7⋊C4C2312yes—
181C2×C4×Dic7C2312yes—
182C2×C4×Dic7C2312yes—
183C2×C4×Dic7C2314yes—
184C2×C4×Dic7C2314yes—
185C2×C4×Dic7C2312yes—
186C2×C4×Dic7C2311yescharacteristic
187C2×C4×Dic7C2311yescharacteristic
188C2×C4×Dic7C2311yescharacteristic
189C2×C4×Dic7C2314yes—
190C2×C4×Dic7C23116yes—
191#6461C23116yes—
192#6461C23132yes—
193#6461C23132yes—
194#6460C23116yes—
195#6459C23132yes—
196#6458C2318yes—
197#6457C23116yes—
198#6456C23116yes—
199#6455C23132yes—
200#6455C23116yes—
201#6455C2318yes—
202#6455C23116yes—
203#6453C23116yes—
204#6453C2318yes—
205#6451C23132yes—
206#6451C23116yes—
207#6451C23116yes—
208#6450C23116yes—
209#6450C23132yes—
210#6450C2318yes—
211#6449C23132yes—
212#6448C23132yes—
213#6448C23132yes—
214#6448C23132yes—
215#6447C23132yes—
216(C22⋊D7)⋊C4C23132yes—
217(C22⋊D7)⋊C4C23116yes—
218#6442C23132yes—
219#6441C23132yes—
220#6441C23132yes—
221#6440C23116yes—
222#6438C23132yes—
223C4×D28C23116yes—
224C4×D28C2318yes—
225#6435C23116yes—
226#6435C23132yes—
227C42×D7C2318yes—
228#6432C23116yes—
229#6432C2318yes—
230C4×Dic14C23116yes—
231C4×Dic14C23132yes—
232C4×Dic14C23132yes—
233C4×Dic14C2318yes—
234#3518—732no—
235C2×Q82—71no—
236C2×#556—74no—
237C2×#556—72no—
238C2×#556—72no—
239C2×#556D711yescharacteristic, complemented
240C2×#555—71no—
241C2×#555—72no—
242C2×D4×Q8—71no—
243C2×#548—72no—
244C2×#542—74no—
245C2×#542—72no—
246C2×#533—71no—
247C2×#533—72no—
248C2×#529—72no—
249C2×#529—71no—
250C2×#519—72no—
251C2×C4×#41—71no—
252C24×C7C2412yes—
253C23×D7C2412yes—
254C23×D7C2411yescharacteristic
255C2×C7×Q8—28no—
256C2×C7×Q8—24no—
257C2×C7×Q8C2414yes—
258C2×C7×Q8C2418yes—
259C2×C7×D4—24no—
260C2×C7×D4C2414yes—
261C22×C4×C7—28no—
262C22×C4×C7C2412yes—
263C22×C4×C7C2412yes—
264C22×C4×C7C2418yes—
265C22×C4×C7C2414yes—
266C22×C4×C7C2411yescharacteristic
267C22×C4×C7C2412yes—
268C22×C4×C7C2411yescharacteristic
269C22×C4×C7C2411yescharacteristic
270C2×C22⋊D7—28no—
271C2×C22⋊D7—48no—
272C2×C22⋊D7C2418yes—
273C2×C22⋊D7C24116yes—
274C22×Dic7—28no—
275C22×Dic7—44no—
276C22×Dic7C2418yes—
277C22×Dic7C2411yescharacteristic
278C22×Dic7C2411yescharacteristic
279C22×Dic7C2411yescharacteristic
280C22×Dic7C2414yes—
281C22×Dic7C2412yes—
282C22×Dic7C2412yes—
283C22×Dic7C2418yes—
284C22×Dic7C2412yes—
285Q8×D7—264no—
286#1159—232no—
287C2×D28—24no—
288C2×D28—44no—
289C2×D28C2414yes—
290C2×D28C2418yes—
291C2×C4×D7—24no—
292C2×C4×D7—28no—
293C2×C4×D7—24no—
294C2×C4×D7—216no—
295C2×C4×D7—42no—
296C2×C4×D7C2414yes—
297C2×C4×D7C2414yes—
298C2×C4×D7C2418yes—
299C2×C4×D7C24116yes—
300C2×C4×D7C2414yes—
301C2×Dic14—216no—
302C2×Dic14—48no—
303C2×Dic14—44no—
304C2×Dic14#4118yes—
305C2×Dic14C24116yes—
306C2×Dic14C24116yes—
307C2×Dic14C2418yes—
308C2×Dic14C2414yes—
309C7×C4⋊C4C2414yes—
310C7×C4⋊C4C24116yes—
311C7×C4⋊C4C2418yes—
312C7×C4⋊C4C2414yes—
313C7×C4⋊C4C2418yes—
314C7×C4⋊C4C2418yes—
315C7×C22⋊C4C2418yes—
316C7×C22⋊C4C24116yes—
317C7×C22⋊C4C24116yes—
318C42×C7C24116yes—
319C42×C7C2414yes—
320C42×C7C2418yes—
321C22⋊Dic7C2418yes—
322C22⋊Dic7C24116yes—
323(C2×D7)⋊C4C2418yes—
324(C2×D7)⋊C4C24116yes—
325(C2×D7)⋊C4C2418yes—
326(C2×D7)⋊C4C2418yes—
327(C2×D7)⋊C4C2418yes—
328(C2×D7)⋊C4C2418yes—
329(C2×D7)⋊C4C2418yes—
330(C2×D7)⋊C4C24116yes—
331(C2×D7)⋊C4C24116yes—
332C4⋊Dic7C2418yes—
333C4⋊Dic7C2414yes—
334C4⋊Dic7C2418yes—
335C4⋊Dic7C24116yes—
336C4⋊Dic7C24116yes—
337C4⋊Dic7C2418yes—
338C4⋊Dic7C2414yes—
339Dic7⋊C4C2418yes—
340Dic7⋊C4C24116yes—
341Dic7⋊C4C2418yes—
342Dic7⋊C4C24116yes—
343Dic7⋊C4C24116yes—
344Dic7⋊C4C2418yes—
345Dic7⋊C4C2418yes—
346C4×Dic7C2418yes—
347C4×Dic7C2418yes—
348C4×Dic7C24116yes—
349C4×Dic7C24116yes—
350C4×Dic7C2418yes—
351C4×Dic7C2414yes—
352C4×Dic7C2414yes—
353C4×Dic7C2414yes—
354C4×Dic7C24116yes—
355C22×#41—71no—
356C23×Q8—72no—
357Q82—716no—
358#556—764no—
359#556—732no—
360#556—732no—
361#556C2×D7116yescomplemented
362#555—716no—
363#555—732no—
364D4×Q8—716no—
365#548—732no—
366#542—764no—
367#542—732no—
368#533—716no—
369#533—732no—
370C2×C4⋊Q8—72no—
371C2×C4⋊Q8—72no—
372C2×C4⋊Q8—74no—
373C2×C4⋊Q8—71no—
374C2×C4⋊Q8—72no—
375C2×C4⋊Q8C2×D711yescharacteristic
376#529—732no—
377#529—716no—
378C2×#126—72no—
379C2×#126—74no—
380C2×#126—74no—
381C2×#126—74no—
382C2×#126C2×D714yes—
383C2×#125—71no—
384C2×#125—72no—
385C2×#124—71no—
386C2×#124—74no—
387C2×#124—74no—
388C2×#124—74no—
389C2×#124—74no—
390C2×#124C2×D712yes—
391C2×#123—72no—
392C2×#123—74no—
393C2×C22⋊Q8—71no—
394C2×C22⋊Q8—72no—
395C2×C22⋊Q8—72no—
396C2×C22⋊Q8—74no—
397C2×C22⋊Q8—72no—
398C2×C22⋊Q8—74no—
399C2×C22⋊Q8—74no—
400C2×C22⋊Q8C2×D712yes—
401C2×#121—72no—
402C2×#121—72no—
403C2×#121—71no—
404C2×#121—74no—
405#519—732no—
406C4×#41—716no—
407C2×C4×Q8—72no—
408C2×C4×Q8—72no—
409C2×C4×Q8—71no—
410C2×C4×Q8—74no—
411C2×C4×Q8—72no—
412C2×C4×Q8—71no—
413C2×C4×Q8—74no—
414C2×C4×Q8—72no—
415C2×C4×Q8—74no—
416C2×C4×Q8C2×D712yes—
417C2×C4×Q8C2×D711yescharacteristic
418C2×C4×D4—71no—
419C2×C4×D4—72no—
420C2×C4×D4—72no—
421C2×C4×D4—72no—
422C2×C4×D4—74no—
423C2×C4×D4—72no—
424C2×C4×D4—71no—
425C2×C4×D4C2×D711yescharacteristic
426C2×#117—72no—
427C2×#117—71no—
428C2×#117—74no—
429C2×#117—72no—
430C2×#117—72no—
431C2×#117—72no—
432C2×#117—72no—
433C2×#117—74no—
434C2×#117C2×D712yes—
435C22×C42—72no—
436C22×C42—71no—
437C23×C7—24no—
438C23×C7—24no—
439C23×C7—24no—
440C23×C7C2514yes—
441C23×C7C2511yescharacteristic
442C22×D7—24no—
443C22×D7—22no—
444C22×D7—22no—
445C22×D7—24no—
446C22×D7—22no—
447C22×D7—24no—
448C22×D7C2514yes—
449C22×D7C2512yes—
450C7×Q8—216no—
451C7×Q8—28no—
452C7×D4—28no—
453C2×C4×C7—28no—
454C2×C4×C7—24no—
455C2×C4×C7—24no—
456C2×C4×C7—22no—
457C2×C4×C7—24no—
458C2×C4×C7—216no—
459C2×C4×C7C2×#4114yes—
460C2×C4×C72−1+414yes—
461C2×C4×C7C2514yes—
462C2×C4×C7C2514yes—
463C2×C4×C7C2518yes—
464C2×C4×C7C2512yes—
465C2×C4×C7C2514yes—
466C2×C4×C7C2512yes—
467C2×C4×C7C2512yes—
468C22⋊D7—216no—
469C22⋊D7—416no—
470C2×Dic7—24no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—24no—
474C2×Dic7—28no—
475C2×Dic7—22no—
476C2×Dic7—216no—
477C2×Dic7—48no—
478C2×Dic7C2×#4118yes—
479C2×Dic7C2512yes—
480C2×Dic7C2512yes—
481C2×Dic7C2512yes—
482C2×Dic7C2518yes—
483C2×Dic7C2514yes—
484C2×Dic7C2514yes—
485C2×Dic7C2514yes—
486D28—28no—
487D28—48no—
488C4×D7—28no—
489C4×D7—216no—
490C4×D7—28no—
491C4×D7—232no—
492C4×D7—44no—
493Dic14—232no—
494Dic14—416no—
495Dic14—48no—
496Dic14C2×#41116yes—
497C2×#41—78no—
498C2×#41—148no—
499C22×Q8—716no—
500C22×Q8—71no—
501C22×Q8—74no—
502C22×Q8—72no—
503C22×Q8—74no—
504C22×Q8—1416no—
505C22×Q8C22×D711yescharacteristic
506C22×Q8C22×D712yes—
507C22×D4—72no—
508C22×D4—74no—
509C22×D4—71no—
510C22×D4—72no—
511C22×D4C22×D711yescharacteristic
512C23×C4—72no—
513C23×C4—72no—
514C23×C4—74no—
515C23×C4—72no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4—71no—
519C23×C4C22×D712yes—
520C4⋊Q8—716no—
521C4⋊Q8—716no—
522C4⋊Q8—732no—
523C4⋊Q8—78no—
524C4⋊Q8—716no—
525C4⋊Q8C22×D718yes—
526#126—716no—
527#126—732no—
528#126—732no—
529#126—732no—
530#126C22×D7132yes—
531#125—78no—
532#125—716no—
533#124—78no—
534#124—732no—
535#124—732no—
536#124—732no—
537#124—732no—
538#124C22×D7116yes—
539#123—716no—
540#123—732no—
541C22⋊Q8—78no—
542C22⋊Q8—716no—
543C22⋊Q8—716no—
544C22⋊Q8—716no—
545C22⋊Q8—732no—
546C22⋊Q8—732no—
547C22⋊Q8—732no—
548C22⋊Q8C22×D7116yes—
549#121—716no—
550#121—716no—
551#121—78no—
552#121—732no—
553C4×Q8—716no—
554C4×Q8—716no—
555C4×Q8—78no—
556C4×Q8—732no—
557C4×Q8—716no—
558C4×Q8—78no—
559C4×Q8—732no—
560C4×Q8—716no—
561C4×Q8—732no—
562C4×Q8C22×D7116yes—
563C4×Q8C22×D718yes—
564C4×D4—78no—
565C4×D4—716no—
566C4×D4—716no—
567C4×D4—716no—
568C4×D4—732no—
569C4×D4—716no—
570C4×D4—78no—
571C4×D4C22×D718yes—
572#117—716no—
573#117—78no—
574#117—732no—
575#117—716no—
576#117—716no—
577#117—716no—
578#117—716no—
579#117—732no—
580#117C22×D7116yes—
581C2×C4⋊C4—72no—
582C2×C4⋊C4—71no—
583C2×C4⋊C4—72no—
584C2×C4⋊C4—72no—
585C2×C4⋊C4—71no—
586C2×C4⋊C4—74no—
587C2×C4⋊C4—72no—
588C2×C4⋊C4—72no—
589C2×C4⋊C4—74no—
590C2×C4⋊C4—72no—
591C2×C4⋊C4—74no—
592C2×C4⋊C4—72no—
593C2×C4⋊C4—74no—
594C2×C4⋊C4—74no—
595C2×C4⋊C4C22×D711yescharacteristic
596C2×C4⋊C4C22×D712yes—
597C2×C4⋊C4C22×D714yes—
598C2×C4⋊C4C22×D711yescharacteristic
599C2×C4⋊C4C22×D712yes—
600C2×C4⋊C4C22×D712yes—
601C2×C22⋊C4—72no—
602C2×C22⋊C4—74no—
603C2×C22⋊C4—72no—
604C2×C22⋊C4—74no—
605C2×C22⋊C4—72no—
606C2×C22⋊C4—72no—
607C2×C22⋊C4—74no—
608C2×C22⋊C4—72no—
609C2×C22⋊C4—74no—
610C2×C22⋊C4—72no—
611C2×C22⋊C4—72no—
612C2×C22⋊C4C22×D712yes—
613C2×C22⋊C4C22×D714yes—
614C2×C22⋊C4C22×D714yes—
615C2×C42—72no—
616C2×C42—71no—
617C2×C42—74no—
618C2×C42—74no—
619C2×C42—71no—
620C2×C42—72no—
621C2×C42—74no—
622C2×C42—72no—
623C2×C42—716no—
624C2×C42—71no—
625C2×C42—78no—
626C2×C42C22×D714yes—
627C2×C42C22×D712yes—
628C2×C42C22×D711yescharacteristic
629C22×C7—24no—
630C22×C7—24no—
631C22×C7—24no—
632C22×C7—48no—
633C22×C7C22×#4112yes—
634C22×C7C2×2−1+412yes—
635C22×C7#58512yes—
636C22×C7C2611yescharacteristic
637C2×D7—24no—
638C2×D7—22no—
639C2×D7—22no—
640C2×D7—24no—
641C2×D7—22no—
642C2×D7—24no—
643C2×D7—48no—
644C2×D7—44no—
645C4×C7—28no—
646C4×C7—24no—
647C4×C7—24no—
648C4×C7—22no—
649C4×C7—24no—
650C4×C7C22×#4114yes—
651C4×C7C2×2−1+414yes—
652Dic7—24no—
653Dic7—22no—
654Dic7—22no—
655Dic7—24no—
656Dic7—28no—
657Dic7—22no—
658Dic7C22×#4118yes—
659C24—72no—
660C24—71no—
661C24C23×D712yes—
662#41—1432no—
663C2×Q8—28no—
664C2×Q8—24no—
665C2×Q8—78no—
666C2×Q8—74no—
667C2×Q8—716no—
668C2×Q8—78no—
669C2×Q8—716no—
670C2×Q8—1416no—
671C2×Q8—1464no—
672C2×Q8—284no—
673C2×Q8—288no—
674C2×Q8C23×D714yes—
675C2×Q8C23×D718yes—
676C2×D4—24no—
677C2×D4—78no—
678C2×D4—716no—
679C2×D4—74no—
680C2×D4—78no—
681C2×D4—148no—
682C2×D4—144no—
683C2×D4—284no—
684C2×D4—288no—
685C2×D4C23×D714yes—
686C22×C4—28no—
687C22×C4—72no—
688C22×C4—78no—
689C22×C4—71no—
690C22×C4—71no—
691C22×C4—71no—
692C22×C4—74no—
693C22×C4—72no—
694C22×C4—72no—
695C22×C4—78no—
696C22×C4—74no—
697C22×C4—74no—
698C22×C4—716no—
699C22×C4—78no—
700C22×C4—74no—
701C22×C4—1416no—
702C22×C4—148no—
703C22×C4—148no—
704C22×C4—144no—
705C22×C4—144no—
706C22×C4—282no—
707C22×C4—284no—
708C22×C4C23×D718yes—
709C22×C4C23×D712yes—
710C22×C4C23×D712yes—
711C22×C4C23×D714yes—
712C22×C4C23×D711yescharacteristic
713C22×C4C23×D712yes—
714C22×C4C23×D711yescharacteristic
715C22×C4C23×D711yescharacteristic
716C4⋊C4—78no—
717C4⋊C4—78no—
718C4⋊C4—716no—
719C4⋊C4—78no—
720C4⋊C4—78no—
721C4⋊C4—716no—
722C4⋊C4—716no—
723C4⋊C4—74no—
724C4⋊C4—78no—
725C4⋊C4—74no—
726C4⋊C4—78no—
727C4⋊C4—716no—
728C4⋊C4—78no—
729C4⋊C4—716no—
730C4⋊C4C23×D714yes—
731C4⋊C4C23×D718yes—
732C4⋊C4C23×D7116yes—
733C4⋊C4C23×D714yes—
734C4⋊C4C23×D718yes—
735C4⋊C4C23×D718yes—
736C22⋊C4—78no—
737C22⋊C4—716no—
738C22⋊C4—78no—
739C22⋊C4—716no—
740C22⋊C4—78no—
741C22⋊C4—78no—
742C22⋊C4—716no—
743C22⋊C4—78no—
744C22⋊C4—716no—
745C22⋊C4—78no—
746C22⋊C4—78no—
747C22⋊C4C23×D718yes—
748C22⋊C4C23×D7116yes—
749C22⋊C4C23×D7116yes—
750C42—74no—
751C42—78no—
752C42—74no—
753C42—74no—
754C42—78no—
755C42—78no—
756C42—716no—
757C42—716no—
758C42—716no—
759C42C23×D714yes—
760C42C23×D7116yes—
761C42C23×D718yes—
762C2×C7—44no—
763C2×C7#351814yescomplemented
764C2×C7C23×#4111yescharacteristic
765C2×C7C22×2−1+411yescharacteristic
766C2×C7C2×#58511yescharacteristic
767D7—44no—
768D7—42no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—72no—
773C23—74no—
774C23—144no—
775C23—142no—
776C23—142no—
777C23—144no—
778C23—142no—
779C23—144no—
780C23C24×D714yes—
781C23C24×D711yescharacteristic
782Q8—216no—
783Q8—28no—
784Q8—716no—
785Q8—1432no—
786Q8—288no—
787Q8—2816no—
788D4—28no—
789D4—1416no—
790D4—148no—
791D4—288no—
792D4—2816no—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—216no—
799C2×C4—74no—
800C2×C4—78no—
801C2×C4—72no—
802C2×C4—72no—
803C2×C4—72no—
804C2×C4—78no—
805C2×C4—74no—
806C2×C4—74no—
807C2×C4—1432no—
808C2×C4—1416no—
809C2×C4—142no—
810C2×C4—144no—
811C2×C4—142no—
812C2×C4—142no—
813C2×C4—144no—
814C2×C4—148no—
815C2×C4—1416no—
816C2×C4—148no—
817C2×C4—148no—
818C2×C4—284no—
819C2×C4—288no—
820C2×C4D7×#4114yes—
821C2×C4#655414yes—
822C2×C4C24×D714yes—
823C2×C4C24×D714yes—
824C2×C4C24×D718yes—
825C2×C4C24×D712yes—
826C2×C4C24×D714yes—
827C2×C4C24×D712yes—
828C2×C4C24×D712yes—
829C7C2×#351811yescharacteristic, complemented, Sylow
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—142no—
835C22—144no—
836C22—144no—
837C22—142no—
838C22—142no—
839C22—144no—
840C22—288no—
841C22—284no—
842C22C2×D7×#4112yes—
843C22C2×#655412yes—
844C22#9062012yes—
845C22C25×D711yescharacteristic
846C4—24no—
847C4—24no—
848C4—28no—
849C4—22no—
850C4—24no—
851C4—78no—
852C4—142no—
853C4—142no—
854C4—144no—
855C4—142no—
856C4—144no—
857C4—148no—
858C4C2×D7×#4114yes—
859C4C2×#655414yes—
860C2—44no—
861C2—282no—
862C2—284no—
863C2#1174405714yesdirect product factor
864C2C22×#655411yescharacteristic
865C2C22×D7×#4111yescharacteristic
866C2C2×#9062011yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#556C2
socleC23×C7C25
hypercenterC2×#556D7
hypocenterC7C2×#3518
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×C7×#556C2semidirect
2. #11744057C2direct (N × H)
3. C2×#90418C2semidirect
4. C2×#90419C2semidirect
5. C2×#90393C2semidirect
6. C2×#90401C2semidirect
7. C2×#90368C2semidirect
8. C2×#90373C2semidirect
9. C2×#90332C2semidirect
10. C2×#90315C2semidirect
11. C2×#90271C2semidirect
12. C2×#90263C2semidirect
13. C2×Q8×Dic14C2semidirect
14. C2×#90275C2semidirect
15. C2×#90254C2semidirect
16. C2×C4×#1159C2semidirect
17. C2×#90223C2semidirect
18. C2×#90208C2semidirect
21. C7×#556C22semidirect
42. #90419C22semidirect
43. #90418C22semidirect
44. #90401C22semidirect
45. #90393C22semidirect
46. #90373C22semidirect
47. #90368C22semidirect
48. #90332C22semidirect
49. #90315C22semidirect
50. #90275C22semidirect
51. #90271C22semidirect
52. #90263C22semidirect
53. Q8×Dic14C22semidirect
54. #90254C22semidirect
55. C4×#1159C22semidirect
56. #90223C22semidirect
57. #90208C22semidirect
239. C2×#556D7semidirect
361. #556C2×D7semidirect
763. C2×C7#3518semidirect
829. C7C2×#3518semidirect
863. C2#11744057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5562
#117440572
C2×#904182
C2×#904192
C2×#903932
C2×#904012
C2×#903682
C2×#903732
C2×#903322
C2×#903152
C2×#902712
C2×#902632
C2×Q8×Dic142
C2×#902752
C2×#902542
C2×C4×#11592
C2×#902232
C2×#902082
C2×#35187