Finite Group Databasebeta

← C2×#11742960 #14261869

Subgroups — C2×#11742960 #14261869

Order 1792.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#520C211yesmaximal, characteristic, complemented
2C2×#90516C211yesmaximal, characteristic, complemented
3C2×#90523C211yesmaximal, characteristic
4#11742960C2132yesmaximal, direct product factor
5C2×#90258C212yesmaximal, complemented
6C2×#90259C212yesmaximal, complemented
7C2×#90250C212yesmaximal, complemented
8C2×#90233C212yesmaximal, complemented
9C2×#90255C214yesmaximal, complemented
10C2×#90229C214yesmaximal, complemented
11C2×#90224C212yesmaximal, complemented
12C2×#90220C212yesmaximal, complemented
13C2×#90217C211yesmaximal, characteristic, complemented
14C2×#90208C211yesmaximal, characteristic, complemented
15C2×#90195C211yesmaximal, characteristic, complemented
16C2×#90202C212yesmaximal, complemented
17C2×#90204C212yesmaximal, complemented
18C22×#6450C211yesmaximal, characteristic, complemented
19C22×C7×#41C2211yescharacteristic
20C22×#1157C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C7×#520C22116yescomplemented
23C2×C4×C7×Q8C2212yes—
24C2×C4×C7×D4C2214yes—
25C2×C4×C7×D4C2212yes—
26C2×C7×#117C2211yescharacteristic
27C2×C7×#117C2212yes—
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C4⋊C4C2212yes—
30#90523C22116yes—
31#90516C22116yescomplemented
32C2×#6510C2211yescharacteristic
33C2×#6507C2211yescharacteristic
34C2×#6507C2212yes—
35C2×#6503C2211yescharacteristic
36C2×#6502C2212yes—
37C2×#6502C2212yes—
38C2×#6499C2211yescharacteristic
39C2×#6499C2212yes—
40C2×#6498C2214yes—
41C2×#6492C2214yes—
42C2×C4×C22⋊D7C2212yes—
43C2×C4×C22⋊D7C2212yes—
44C2×C4×C22⋊D7C2214yes—
45C2×C4×C22⋊D7C2214yes—
46C2×#6489C2214yes—
47C2×#6489C2211yescharacteristic
48C2×#6487C2212yes—
49C2×#6487C2212yes—
50C2×#6487C2214yes—
51C22×Dic7⋊C4C2212yes—
52C22×C4×Dic7C2211yescharacteristic
53C22×C4×Dic7C2212yes—
54#90259C22132yescomplemented
55#90258C22132yescomplemented
56#90255C22164yescomplemented
57#90250C22132yescomplemented
58#90233C22132yescomplemented
59#90229C22164yescomplemented
60#90224C22132yescomplemented
61#90220C22132yescomplemented
62#90217C22116yescomplemented
63#90208C22116yescomplemented
64#90204C22132yescomplemented
65C2×#6461C2214yes—
66#90202C22132yescomplemented
67C2×#6460C2212yes—
68C2×#6460C2212yes—
69C2×#6459C2214yes—
70#90195C22116yescomplemented
71C2×#6456C2212yes—
72C2×#6455C2212yes—
73C2×D7×C4⋊C4C2212yes—
74C2×#6453C2211yescharacteristic
75C2×#6453C2211yescharacteristic
76C2×#6452C2214yes—
77C2×#6452C2214yes—
78C2×#6451C2211yescharacteristic
79C2×#6451C2211yescharacteristic
80C2×#6450C2212yes—
81C2×#6450C2212yes—
82C2×#6450C2212yes—
83C2×#6450C2212yes—
84C2×#6450C2212yes—
85C2×#6450C22116yescomplemented
86C2×#6449C2214yes—
87C2×#6448C2214yes—
88C2×#6446C2214yes—
89C2×#6442C2214yes—
90C2×#6442C2214yes—
91C2×#6441C2212yes—
92C2×#6441C2212yes—
93C2×#6439C2214yes—
94C2×#6438C2212yes—
95C2×#6435C2214yes—
96C2×#6433C2214yes—
97C2×#6432C2212yes—
98C2×C4×Dic14C2212yes—
99C2×C4×Dic14C2212yes—
100C2×C4×Dic14C2214yes—
101C2×#3507—71nomaximal, Sylow
102C2×C7×#41—28no—
103C2×C7×#41C2318yes—
104C22×C7×Q8C2311yescharacteristic
105C22×C7×D4C2312yes—
106C22×C7×D4C2311yescharacteristic
107C23×C4×C7C2312yes—
108C23×C4×C7C2312yes—
109C23×C4×C7C2314yes—
110C23×C4×C7C2311yescharacteristic
111C22×C22⋊D7C2312yes—
112C22×C22⋊D7C2312yes—
113C22×C22⋊D7C2312yes—
114C23×Dic7C2311yescharacteristic
115C23×Dic7C2312yes—
116C23×Dic7C2311yescharacteristic
117C2×#1157—28no—
118C2×#1157C2318yes—
119C22×D28C2311yescharacteristic
120C22×C4×D7C2312yes—
121C22×C4×D7C2314yes—
122C22×Dic14—28no—
123C22×Dic14C2312yes—
124C22×Dic14C2311yescharacteristic
125C22×Dic14C2312yes—
126C22×Dic14C2312yes—
127C22×Dic14C2318yes—
128C22×Dic14C2312yes—
129C4×C7×Q8C23116yes—
130C4×C7×D4C23132yes—
131C4×C7×D4C23116yes—
132C7×#117C2318yes—
133C7×#117C23116yes—
134C2×C7×C4⋊C4C2312yes—
135C2×C7×C4⋊C4C2312yes—
136C2×C7×C4⋊C4C2318yes—
137C2×C7×C4⋊C4C2311yescharacteristic
138C2×C7×C4⋊C4C2311yescharacteristic
139C2×C7×C4⋊C4C2314yes—
140C2×C7×C4⋊C4C23116yes—
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⋊Dic7C2314yes—
149C2×C22⋊Dic7C2314yes—
150#6510C2318yes—
151#6507C2318yes—
152#6507C23116yes—
153#6503C2318yes—
154#6502C23116yes—
155#6502C23116yes—
156#6499C2318yes—
157#6499C23116yes—
158#6498C23132yes—
159#6492C23132yes—
160C4×C22⋊D7C23132yes—
161C4×C22⋊D7C23116yes—
162C4×C22⋊D7C23132yes—
163C4×C22⋊D7C23116yes—
164C2×(C2×D7)⋊C4C2312yes—
165C2×(C2×D7)⋊C4C2314yes—
166C2×(C2×D7)⋊C4C2314yes—
167C2×(C2×D7)⋊C4C2312yes—
168C2×(C2×D7)⋊C4C2314yes—
169#6489C2318yes—
170#6489C23132yes—
171C2×C4⋊Dic7C2314yes—
172C2×C4⋊Dic7C2312yes—
173C2×C4⋊Dic7C2312yes—
174C2×C4⋊Dic7C2314yes—
175C2×C4⋊Dic7C2311yescharacteristic
176C2×C4⋊Dic7C2311yescharacteristic
177#6487C23116yes—
178#6487C23132yes—
179#6487C23116yes—
180C2×Dic7⋊C4C2312yes—
181C2×Dic7⋊C4C2312yes—
182C2×Dic7⋊C4C2312yes—
183C2×Dic7⋊C4C2314yes—
184C2×Dic7⋊C4C2312yes—
185C2×Dic7⋊C4C2312yes—
186C2×Dic7⋊C4C2312yes—
187C2×Dic7⋊C4C2314yes—
188C2×Dic7⋊C4C2314yes—
189C2×Dic7⋊C4C2314yes—
190C2×Dic7⋊C4C2314yes—
191C2×Dic7⋊C4C23116yes—
192C2×C4×Dic7C2311yescharacteristic
193C2×C4×Dic7C2311yescharacteristic
194C2×C4×Dic7C2312yes—
195C2×C4×Dic7C2314yes—
196C2×C4×Dic7C2314yes—
197C2×C4×Dic7C2314yes—
198C2×C4×Dic7C2311yescharacteristic
199C2×C4×Dic7C2311yescharacteristic
200C2×C4×Dic7C2318yes—
201C2×C4×Dic7C23116yes—
202#6461C23132yes—
203#6460C23116yes—
204#6460C23116yes—
205#6459C23132yes—
206#6456C23116yes—
207#6455C23116yes—
208D7×C4⋊C4C23116yes—
209#6453C2318yes—
210#6453C2318yes—
211#6452C23132yes—
212#6452C23132yes—
213#6451C2318yes—
214#6451C2318yes—
215#6450C23116yes—
216#6450C23116yes—
217#6450C23116yes—
218#6450C23116yes—
219#6450C23116yes—
220#6449C23132yes—
221#6448C23132yes—
222#6446C23132yes—
223#6442C23132yes—
224#6442C23132yes—
225#6441C23116yes—
226#6441C23116yes—
227#6439C23132yes—
228#6438C23116yes—
229#6435C23132yes—
230#6433C23132yes—
231#6432C23116yes—
232C4×Dic14C23116yes—
233C4×Dic14C23116yes—
234C4×Dic14C23132yes—
235#3507—732no—
236C2×#559—72no—
237C2×#557—72no—
238C2×#556—72no—
239C2×#556—72no—
240C2×#556—72no—
241C2×#554—72no—
242C2×#552—72no—
243C2×#552—72no—
244C2×#539—74no—
245C2×#536—71no—
246C2×#536—71no—
247C2×#533—71no—
248C2×#532—71no—
249C2×#529—74no—
250C2×#520—71no—
251C2×#520D711yescharacteristic, complemented
252C22×C4×Q8—71no—
253C24×C7C2412yes—
254C24×C7C2411yescharacteristic
255C23×D7C2412yes—
256C7×#41—232no—
257C2×C7×Q8—24no—
258C2×C7×Q8C2414yes—
259C2×C7×D4—28no—
260C2×C7×D4—24no—
261C2×C7×D4C2418yes—
262C2×C7×D4C2414yes—
263C22×C4×C7—28no—
264C22×C4×C7—48no—
265C22×C4×C7—44no—
266C22×C4×C7#4118yes—
267C22×C4×C7C2414yes—
268C22×C4×C7C2412yes—
269C22×C4×C7C2412yes—
270C22×C4×C7C2412yes—
271C22×C4×C7C2418yes—
272C22×C4×C7C2418yes—
273C22×C4×C7C24116yes—
274C22×C4×C7C2411yescharacteristic
275C22×C4×C7C2411yescharacteristic
276C22×C4×C7C2414yes—
277C2×C22⋊D7—28no—
278C2×C22⋊D7—28no—
279C2×C22⋊D7—44no—
280C2×C22⋊D7C2418yes—
281C2×C22⋊D7C2418yes—
282C2×C22⋊D7C2418yes—
283C22×Dic7—28no—
284C22×Dic7—24no—
285C22×Dic7—42no—
286C22×Dic7C2414yes—
287C22×Dic7C2418yes—
288C22×Dic7C2411yescharacteristic
289C22×Dic7C2412yes—
290C22×Dic7C2411yescharacteristic
291C22×Dic7C2411yescharacteristic
292C22×Dic7C2412yes—
293C22×Dic7C2414yes—
294C22×Dic7C2412yes—
295C22×Dic7C2414yes—
296C22×Dic7C2411yescharacteristic
297#1157—232no—
298C2×D28—24no—
299C2×D28C2414yes—
300C2×C4×D7—28no—
301C2×C4×D7—48no—
302C2×C4×D7C2418yes—
303C2×C4×D7C24116yes—
304C2×Dic14—28no—
305C2×Dic14—28no—
306C2×Dic14—232no—
307C2×Dic14—24no—
308C2×Dic14—28no—
309C2×Dic14—44no—
310C2×Dic14C2418yes—
311C2×Dic14C2414yes—
312C2×Dic14C2418yes—
313C2×Dic14C2418yes—
314C2×Dic14C2418yes—
315C7×C4⋊C4C2418yes—
316C7×C4⋊C4C2418yes—
317C7×C4⋊C4C2414yes—
318C7×C4⋊C4C2414yes—
319C7×C4⋊C4C24116yes—
320C7×C22⋊C4C2418yes—
321C7×C22⋊C4C24116yes—
322C42×C7C2418yes—
323C42×C7C24116yes—
324C22⋊Dic7C2418yes—
325C22⋊Dic7C2418yes—
326C22⋊Dic7C2418yes—
327C22⋊Dic7C24116yes—
328C22⋊Dic7C24116yes—
329(C2×D7)⋊C4C2418yes—
330(C2×D7)⋊C4C24116yes—
331(C2×D7)⋊C4C24116yes—
332(C2×D7)⋊C4C2418yes—
333(C2×D7)⋊C4C24116yes—
334C4⋊Dic7C24116yes—
335C4⋊Dic7C2418yes—
336C4⋊Dic7C2418yes—
337C4⋊Dic7C24116yes—
338C4⋊Dic7C2414yes—
339C4⋊Dic7C2414yes—
340Dic7⋊C4C2418yes—
341Dic7⋊C4C2418yes—
342Dic7⋊C4C2418yes—
343Dic7⋊C4C24116yes—
344Dic7⋊C4C2418yes—
345Dic7⋊C4C2418yes—
346Dic7⋊C4C2418yes—
347Dic7⋊C4C24116yes—
348Dic7⋊C4C24116yes—
349Dic7⋊C4C24116yes—
350Dic7⋊C4C24116yes—
351C4×Dic7C2414yes—
352C4×Dic7C2414yes—
353C4×Dic7C2418yes—
354C4×Dic7C24116yes—
355C4×Dic7C24116yes—
356C4×Dic7C24116yes—
357C4×Dic7C2414yes—
358C4×Dic7C2414yes—
359C22×#41—71no—
360C22×#41C2×D711yescharacteristic
361C23×Q8—71no—
362#559—732no—
363#557—732no—
364#556—732no—
365#556—732no—
366#556—732no—
367#554—732no—
368#552—732no—
369#552—732no—
370#539—764no—
371#536—716no—
372#536—716no—
373#533—716no—
374#532—716no—
375C2×C4⋊Q8—71no—
376C2×C4⋊Q8—72no—
377C2×C4⋊Q8—71no—
378C2×C4⋊Q8—71no—
379C2×C4⋊Q8—72no—
380C2×#127—71no—
381#529—764no—
382C2×#126—74no—
383C2×#126—74no—
384C2×#126—74no—
385C2×#126—74no—
386C2×#125—74no—
387C2×#125—74no—
388C2×#125—71no—
389C2×#125—71no—
390C2×#125—74no—
391C2×#124—71no—
392C2×#124—71no—
393C2×#124—72no—
394C2×#124—74no—
395C2×#124—72no—
396C2×#123—74no—
397C2×#123—74no—
398C2×#123—74no—
399C2×#123—74no—
400C2×C22⋊Q8—72no—
401C2×C22⋊Q8—72no—
402C2×C22⋊Q8—74no—
403C2×C22⋊Q8—74no—
404C2×C22⋊Q8—72no—
405C2×C22⋊Q8—72no—
406C2×C22⋊Q8—72no—
407C2×C22⋊Q8—72no—
408C2×#121—72no—
409C2×#121—72no—
410#520—716no—
411#520C2×D7116yescomplemented
412C2×C4×Q8—72no—
413C2×C4×Q8—72no—
414C2×C4×Q8—72no—
415C2×C4×Q8—72no—
416C2×C4×Q8—72no—
417C2×C4×Q8—716no—
418C2×C4×Q8—74no—
419C2×C4×Q8—72no—
420C2×C4×Q8—72no—
421C2×C4×Q8C2×D712yes—
422C2×C4×D4—74no—
423C2×C4×D4—74no—
424C2×C4×D4—72no—
425C2×C4×D4—72no—
426C2×C4×D4—72no—
427C2×C4×D4C2×D714yes—
428C2×C4×D4C2×D712yes—
429C2×#117—71no—
430C2×#117—74no—
431C2×#117—72no—
432C2×#117—74no—
433C2×#117C2×D711yescharacteristic
434C2×#117C2×D712yes—
435C22×C4⋊C4—72no—
436C22×C4⋊C4—72no—
437C22×C4⋊C4C2×D711yescharacteristic
438C22×C4⋊C4C2×D712yes—
439C22×C42—72no—
440C22×C42—71no—
441C23×C7—22no—
442C23×C7—22no—
443C23×C7—24no—
444C23×C7—24no—
445C23×C7—24no—
446C23×C7C2×#4114yes—
447C23×C7C2514yes—
448C23×C7C2512yes—
449C23×C7C2511yescharacteristic
450C22×D7—24no—
451C22×D7—24no—
452C22×D7—24no—
453C22×D7C2514yes—
454C7×Q8—28no—
455C7×D4—216no—
456C7×D4—28no—
457C2×C4×C7—24no—
458C2×C4×C7—24no—
459C2×C4×C7—24no—
460C2×C4×C7—28no—
461C2×C4×C7—216no—
462C2×C4×C7—416no—
463C2×C4×C7—48no—
464C2×C4×C7C2×#4114yes—
465C2×C4×C7C2×#4114yes—
466C2×C4×C7C2×#41116yes—
467C2×C4×C7C2518yes—
468C2×C4×C7C2514yes—
469C2×C4×C7C2514yes—
470C2×C4×C7C2514yes—
471C2×C4×C7C2512yes—
472C2×C4×C7C2512yes—
473C22⋊D7—216no—
474C22⋊D7—216no—
475C22⋊D7—48no—
476C2×Dic7—216no—
477C2×Dic7—28no—
478C2×Dic7—24no—
479C2×Dic7—24no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—24no—
483C2×Dic7—22no—
484C2×Dic7—28no—
485C2×Dic7—44no—
486C2×Dic72−1+414yes—
487C2×Dic7C2512yes—
488C2×Dic7C2514yes—
489C2×Dic7C2512yes—
490C2×Dic7C2512yes—
491C2×Dic7C2514yes—
492C2×Dic7C2518yes—
493C2×Dic7C2514yes—
494C2×Dic7C2512yes—
495D28—28no—
496C4×D7—216no—
497C4×D7—416no—
498Dic14—216no—
499Dic14—216no—
500Dic14—28no—
501Dic14—216no—
502Dic14—48no—
503C2×#41—28no—
504C2×#41—78no—
505C2×#41—148no—
506C2×#41C22×D718yes—
507C22×Q8—72no—
508C22×Q8—72no—
509C22×Q8—72no—
510C22×Q8—71no—
511C22×Q8—78no—
512C22×Q8—72no—
513C22×Q8—148no—
514C22×Q8C22×D711yescharacteristic
515C22×D4—72no—
516C22×D4—72no—
517C22×D4—72no—
518C22×D4—71no—
519C22×D4C22×D712yes—
520C22×D4C22×D711yescharacteristic
521C23×C4—72no—
522C23×C4—71no—
523C23×C4—71no—
524C23×C4—72no—
525C23×C4—74no—
526C23×C4C22×D712yes—
527C23×C4C22×D712yes—
528C23×C4C22×D714yes—
529C23×C4C22×D711yescharacteristic
530C4⋊Q8—78no—
531C4⋊Q8—716no—
532C4⋊Q8—78no—
533C4⋊Q8—78no—
534C4⋊Q8—716no—
535#127—78no—
536#126—732no—
537#126—732no—
538#126—732no—
539#126—732no—
540#125—732no—
541#125—78no—
542#125—78no—
543#125—732no—
544#125—732no—
545#124—78no—
546#124—78no—
547#124—716no—
548#124—732no—
549#124—716no—
550#123—732no—
551#123—732no—
552#123—732no—
553#123—732no—
554C22⋊Q8—716no—
555C22⋊Q8—716no—
556C22⋊Q8—732no—
557C22⋊Q8—716no—
558C22⋊Q8—716no—
559C22⋊Q8—732no—
560C22⋊Q8—716no—
561C22⋊Q8—716no—
562#121—716no—
563#121—716no—
564C4×Q8—716no—
565C4×Q8—716no—
566C4×Q8—716no—
567C4×Q8—716no—
568C4×Q8—716no—
569C4×Q8—732no—
570C4×Q8—716no—
571C4×Q8—716no—
572C4×Q8C22×D7116yes—
573C4×D4—732no—
574C4×D4—732no—
575C4×D4—716no—
576C4×D4—716no—
577C4×D4—716no—
578C4×D4C22×D7132yes—
579C4×D4C22×D7116yes—
580#117—78no—
581#117—732no—
582#117—716no—
583#117—732no—
584#117C22×D718yes—
585#117C22×D7116yes—
586C2×C4⋊C4—71no—
587C2×C4⋊C4—74no—
588C2×C4⋊C4—74no—
589C2×C4⋊C4—74no—
590C2×C4⋊C4—716no—
591C2×C4⋊C4—71no—
592C2×C4⋊C4—72no—
593C2×C4⋊C4—72no—
594C2×C4⋊C4—74no—
595C2×C4⋊C4—74no—
596C2×C4⋊C4—72no—
597C2×C4⋊C4—72no—
598C2×C4⋊C4—72no—
599C2×C4⋊C4—72no—
600C2×C4⋊C4—72no—
601C2×C4⋊C4—74no—
602C2×C4⋊C4—74no—
603C2×C4⋊C4—72no—
604C2×C4⋊C4—716no—
605C2×C4⋊C4C22×D712yes—
606C2×C4⋊C4C22×D711yescharacteristic
607C2×C4⋊C4C22×D712yes—
608C2×C4⋊C4C22×D714yes—
609C2×C4⋊C4C22×D718yes—
610C2×C4⋊C4C22×D7116yes—
611C2×C4⋊C4C22×D711yescharacteristic
612C2×C22⋊C4—72no—
613C2×C22⋊C4—72no—
614C2×C22⋊C4—74no—
615C2×C22⋊C4—72no—
616C2×C22⋊C4—74no—
617C2×C22⋊C4—72no—
618C2×C22⋊C4—74no—
619C2×C22⋊C4—74no—
620C2×C22⋊C4—72no—
621C2×C22⋊C4—74no—
622C2×C22⋊C4C22×D712yes—
623C2×C22⋊C4C22×D714yes—
624C2×C42—74no—
625C2×C42—74no—
626C2×C42—72no—
627C2×C42—71no—
628C2×C42—71no—
629C2×C42—74no—
630C2×C42—71no—
631C2×C42—71no—
632C2×C42—716no—
633C2×C42—78no—
634C2×C42C22×D714yes—
635C2×C42C22×D712yes—
636C22×C7—22no—
637C22×C7—22no—
638C22×C7—28no—
639C22×C7—24no—
640C22×C7—24no—
641C22×C7—24no—
642C22×C7—48no—
643C22×C7C22×#4114yes—
644C22×C7C22×#4112yes—
645C22×C7C2×2−1+412yes—
646C22×C7#58512yes—
647C22×C7C2611yescharacteristic
648C2×D7—24no—
649C2×D7—24no—
650C2×D7—24no—
651C2×D7—48no—
652C4×C7—24no—
653C4×C7—24no—
654C4×C7—24no—
655C4×C7—28no—
656C4×C7C22×#4114yes—
657C4×C7C22×#4114yes—
658Dic7—28no—
659Dic7—24no—
660Dic7—24no—
661Dic7—22no—
662Dic7—22no—
663Dic7—24no—
664Dic7—22no—
665Dic7C2×2−1+414yes—
666C24—72no—
667C24C23×D712yes—
668C24C23×D711yescharacteristic
669#41—232no—
670#41—1432no—
671C2×Q8—24no—
672C2×Q8—78no—
673C2×Q8—78no—
674C2×Q8—78no—
675C2×Q8—74no—
676C2×Q8—78no—
677C2×Q8—148no—
678C2×Q8—148no—
679C2×Q8—148no—
680C2×Q8—1432no—
681C2×Q8—144no—
682C2×Q8—284no—
683C2×Q8C23×D714yes—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—78no—
687C2×D4—78no—
688C2×D4—78no—
689C2×D4—74no—
690C2×D4—148no—
691C2×D4—148no—
692C2×D4—144no—
693C2×D4—284no—
694C2×D4C23×D718yes—
695C2×D4C23×D714yes—
696C22×C4—28no—
697C22×C4—44no—
698C22×C4—48no—
699C22×C4—71no—
700C22×C4—74no—
701C22×C4—78no—
702C22×C4—71no—
703C22×C4—72no—
704C22×C4—74no—
705C22×C4—71no—
706C22×C4—72no—
707C22×C4—71no—
708C22×C4—72no—
709C22×C4—74no—
710C22×C4—78no—
711C22×C4—716no—
712C22×C4—144no—
713C22×C4—148no—
714C22×C4—148no—
715C22×C4—288no—
716C22×C4—282no—
717C22×C4#115718yes—
718C22×C4C23×D718yes—
719C22×C4C23×D714yes—
720C22×C4C23×D712yes—
721C22×C4C23×D712yes—
722C22×C4C23×D712yes—
723C22×C4C23×D718yes—
724C22×C4C23×D7116yes—
725C22×C4C23×D714yes—
726C22×C4C23×D711yescharacteristic
727C22×C4C23×D711yescharacteristic
728C4⋊C4—716no—
729C4⋊C4—716no—
730C4⋊C4—716no—
731C4⋊C4—78no—
732C4⋊C4—716no—
733C4⋊C4—78no—
734C4⋊C4—78no—
735C4⋊C4—78no—
736C4⋊C4—78no—
737C4⋊C4—716no—
738C4⋊C4—78no—
739C4⋊C4—74no—
740C4⋊C4—74no—
741C4⋊C4—78no—
742C4⋊C4—716no—
743C4⋊C4—78no—
744C4⋊C4—716no—
745C4⋊C4C23×D718yes—
746C4⋊C4C23×D714yes—
747C4⋊C4C23×D718yes—
748C4⋊C4C23×D7116yes—
749C4⋊C4C23×D714yes—
750C22⋊C4—78no—
751C22⋊C4—78no—
752C22⋊C4—716no—
753C22⋊C4—78no—
754C22⋊C4—716no—
755C22⋊C4—78no—
756C22⋊C4—716no—
757C22⋊C4—716no—
758C22⋊C4—78no—
759C22⋊C4—716no—
760C22⋊C4C23×D718yes—
761C22⋊C4C23×D7116yes—
762C42—716no—
763C42—74no—
764C42—74no—
765C42—716no—
766C42—74no—
767C42—74no—
768C42—716no—
769C42—78no—
770C42C23×D7116yes—
771C42C23×D718yes—
772C2×C7—24no—
773C2×C7—44no—
774C2×C7#350714yescomplemented
775C2×C7C23×#4111yescharacteristic
776C2×C7C22×2−1+411yescharacteristic
777C2×C7C2×#58511yescharacteristic
778D7—44no—
779C23—22no—
780C23—22no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—74no—
785C23—144no—
786C23—144no—
787C23—144no—
788C23C2×#115714yes—
789C23C24×D714yes—
790C23C24×D712yes—
791C23C24×D711yescharacteristic
792Q8—28no—
793Q8—1416no—
794Q8—1416no—
795Q8—1416no—
796Q8—148no—
797Q8—288no—
798D4—216no—
799D4—28no—
800D4—1416no—
801D4—1416no—
802D4—148no—
803D4—288no—
804C2×C4—24no—
805C2×C4—28no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—216no—
809C2×C4—48no—
810C2×C4—416no—
811C2×C4—72no—
812C2×C4—74no—
813C2×C4—72no—
814C2×C4—74no—
815C2×C4—78no—
816C2×C4—72no—
817C2×C4—74no—
818C2×C4—72no—
819C2×C4—74no—
820C2×C4—148no—
821C2×C4—144no—
822C2×C4—1416no—
823C2×C4—148no—
824C2×C4—144no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—144no—
829C2×C4—1416no—
830C2×C4—2816no—
831C2×C4—284no—
832C2×C4C2×#115714yes—
833C2×C4C2×#115714yes—
834C2×C4C2×#1157116yes—
835C2×C4C24×D718yes—
836C2×C4C24×D714yes—
837C2×C4C24×D714yes—
838C2×C4C24×D714yes—
839C2×C4C24×D712yes—
840C2×C4C24×D712yes—
841C7C2×#350711yescharacteristic, complemented, Sylow
842C22—22no—
843C22—22no—
844C22—28no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—144no—
850C22—144no—
851C22—144no—
852C22—288no—
853C22C22×#115714yes—
854C22C22×#115712yes—
855C22#9061812yes—
856C22D7×2−1+412yes—
857C22C25×D711yescharacteristic
858C4—24no—
859C4—28no—
860C4—24no—
861C4—24no—
862C4—74no—
863C4—144no—
864C4—148no—
865C4—144no—
866C4—142no—
867C4—142no—
868C4—142no—
869C4—144no—
870C4C22×#115714yes—
871C4C22×#115714yes—
872C2—24no—
873C2—44no—
874C2—284no—
875C2#1174296014yesdirect product factor
876C2C23×#115711yescharacteristic
877C2C2×#9061811yescharacteristic
878C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#520C2
socleC23×C7C25
prime radicalC2×#90523C2
hypercenterC2×#520D7
hypocenterC7C2×#3507
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
2. C2×#90516C2semidirect
4. #11742960C2direct (N × H)
5. C2×#90258C2semidirect
6. C2×#90259C2semidirect
7. C2×#90250C2semidirect
8. C2×#90233C2semidirect
9. C2×#90255C2semidirect
10. C2×#90229C2semidirect
11. C2×#90224C2semidirect
12. C2×#90220C2semidirect
13. C2×#90217C2semidirect
14. C2×#90208C2semidirect
15. C2×#90195C2semidirect
16. C2×#90202C2semidirect
17. C2×#90204C2semidirect
18. C22×#6450C2semidirect
22. C7×#520C22semidirect
31. #90516C22semidirect
54. #90259C22semidirect
55. #90258C22semidirect
56. #90255C22semidirect
57. #90250C22semidirect
58. #90233C22semidirect
59. #90229C22semidirect
60. #90224C22semidirect
61. #90220C22semidirect
62. #90217C22semidirect
63. #90208C22semidirect
64. #90204C22semidirect
66. #90202C22semidirect
70. #90195C22semidirect
85. C2×#6450C22semidirect
251. C2×#520D7semidirect
411. #520C2×D7semidirect
774. C2×C7#3507semidirect
841. C7C2×#3507semidirect
875. C2#11742960direct (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×#905162
C2×#905232
#117429602
C2×#902582
C2×#902592
C2×#902502
C2×#902332
C2×#902552
C2×#902292
C2×#902242
C2×#902202
C2×#902172
C2×#902082
C2×#901952
C2×#902022
C2×#902042
C22×#64502
C2×#35077