Finite Group Databasebeta

← C2×#11742795 #14262226

Subgroups — C2×#11742795 #14262226

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
1C22×C7×#117C211yesmaximal, characteristic, complemented
2C2×#90482C211yesmaximal, characteristic
3C22×#6487C211yesmaximal, characteristic, complemented
4C2×#90224C212yesmaximal, complemented
5C2×#90220C212yesmaximal, complemented
6C2×#90225C212yesmaximal, complemented
7C2×#90214C211yesmaximal, characteristic, complemented
8#11742795C2132yesmaximal, direct product factor
9C2×#90222C214yesmaximal, complemented
10C2×#90210C211yesmaximal, characteristic, complemented
11C2×#90209C212yesmaximal, complemented
12C2×#90217C211yesmaximal, characteristic, complemented
13C2×#90207C211yesmaximal, characteristic, complemented
14C2×#90202C212yesmaximal, complemented
15C2×#90204C212yesmaximal, complemented
16C2×#90186C214yesmaximal, complemented
17C2×#90170C212yesmaximal, complemented
18C2×#90161C212yesmaximal, complemented
19C24×C4×C7C2211yescharacteristic
20C22×#1157C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C2×C7×#117C2211yescharacteristic
23C2×C7×#117C2211yescharacteristic
24C2×C7×#117C2212yes—
25C2×C7×#117C2212yes—
26C2×C7×#117C2211yescharacteristic
27C2×C7×#117C2211yescharacteristic
28C2×C7×#117C22116yescomplemented
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2212yes—
32C22×C42×C7C2212yes—
33C2×#6516C2212yes—
34C22×C22⋊Dic7C2212yes—
35#90482C22116yes—
36C2×#6493C2211yescharacteristic
37C2×#6493C2211yescharacteristic
38C2×#6492C2214yes—
39C2×#6492C2212yes—
40C2×C4×C22⋊D7C2214yes—
41C2×C4×C22⋊D7C2212yes—
42C2×C4×C22⋊D7C2212yes—
43C2×#6489C2214yes—
44C2×#6489C2211yescharacteristic
45C22×C4⋊Dic7C2211yescharacteristic
46C2×#6487C2211yescharacteristic
47C2×#6487C2212yes—
48C2×#6487C2214yes—
49C2×#6487C2212yes—
50C2×#6487C2212yes—
51C2×#6487C2212yes—
52C2×#6487C2211yescharacteristic
53C2×#6487C22116yescomplemented
54C22×Dic7⋊C4C2212yes—
55#90225C22132yescomplemented
56#90224C22132yescomplemented
57#90222C22164yescomplemented
58#90220C22132yescomplemented
59#90217C22116yescomplemented
60#90214C22116yescomplemented
61#90210C22116yescomplemented
62#90209C22132yescomplemented
63#90207C22116yescomplemented
64#90204C22132yescomplemented
65C2×#6461C2214yescomplemented
66#90202C22132yescomplemented
67C2×#6460C2212yescomplemented
68C2×#6460C2212yescomplemented
69C2×#6459C2214yescomplemented
70C2×#6455C2212yescomplemented
71C2×D7×C4⋊C4C2212yescomplemented
72C2×#6453C2212yescomplemented
73C2×#6452C2214yescomplemented
74C2×#6452C2214yescomplemented
75C2×#6451C2212yescomplemented
76C2×#6450C2212yescomplemented
77C2×#6450C2212yescomplemented
78#90186C22164yescomplemented
79C2×#6449C2214yes—
80C2×#6448C2214yes—
81C2×#6446C2214yes—
82C2×(C22⋊D7)⋊C4C2214yes—
83C2×#6442C2214yes—
84C2×#6442C2214yes—
85C2×#6441C2214yes—
86C2×#6440C2214yes—
87#90170C22132yescomplemented
88C2×#6439C2214yescomplemented
89C2×#6438C2212yescomplemented
90C2×C4×D28C2212yescomplemented
91C2×#6435C2214yescomplemented
92#90161C22132yescomplemented
93C2×#6433C2214yescomplemented
94C2×#6433C2212yescomplemented
95C2×#6432C2212yescomplemented
96C2×#6432C2212yescomplemented
97C2×C4×Dic14C2212yescomplemented
98C2×C4×Dic14C2212yescomplemented
99C2×C4×Dic14C2214yescomplemented
100C2×C4×Dic14C2212yescomplemented
101C2×#3495—71nomaximal, Sylow
102C25×C7C2311yescharacteristic
103C23×C4×C7—28no—
104C23×C4×C7C2311yescharacteristic
105C23×C4×C7C2311yescharacteristic
106C23×C4×C7C2311yescharacteristic
107C23×C4×C7C2311yescharacteristic
108C23×C4×C7C2311yescharacteristic
109C23×C4×C7C2318yes—
110C23×C4×C7C2312yes—
111C23×C4×C7C2312yes—
112C23×C4×C7C2311yescharacteristic
113C22×C22⋊D7C2312yes—
114C22×C22⋊D7C2312yes—
115C22×C22⋊D7C2312yes—
116C23×Dic7C2312yes—
117C23×Dic7C2312yes—
118C2×#1157—28no—
119C2×#1157C2318yes—
120C22×D28C2311yescharacteristic
121C22×C4×D7C2312yes—
122C22×C4×D7C2314yes—
123C22×Dic14—28no—
124C22×Dic14C2311yescharacteristic
125C22×Dic14C2312yes—
126C22×Dic14C2312yes—
127C22×Dic14C2318yes—
128C22×Dic14C2314yes—
129C7×#117C2318yes—
130C7×#117C23116yes—
131C7×#117C2318yes—
132C7×#117C2318yes—
133C7×#117C23116yes—
134C7×#117C2318yes—
135C2×C7×C4⋊C4C2311yescharacteristic
136C2×C7×C4⋊C4C2311yescharacteristic
137C2×C7×C4⋊C4C2311yescharacteristic
138C2×C7×C4⋊C4C2312yes—
139C2×C7×C4⋊C4C2312yes—
140C2×C7×C4⋊C4C2311yescharacteristic
141C2×C7×C4⋊C4C2318yes—
142C2×C7×C4⋊C4C2318yes—
143C2×C7×C22⋊C4C2312yes—
144C2×C7×C22⋊C4C2312yes—
145C2×C7×C22⋊C4C2312yes—
146C2×C7×C22⋊C4C2312yes—
147C2×C7×C22⋊C4C23116yes—
148C2×C42×C7C2312yes—
149C2×C42×C7C2312yes—
150C2×C42×C7C2312yes—
151C2×C42×C7C2312yes—
152C2×C42×C7C23116yes—
153#6516C23116yes—
154C2×C22⋊Dic7C2312yes—
155C2×C22⋊Dic7C2312yes—
156C2×C22⋊Dic7C2314yes—
157C2×C22⋊Dic7C23116yes—
158C2×C22⋊Dic7C2312yes—
159C2×C22⋊Dic7C2314yes—
160#6493C2318yes—
161#6493C2318yes—
162#6492C23132yes—
163#6492C23116yes—
164C4×C22⋊D7C23132yes—
165C4×C22⋊D7C23116yes—
166C4×C22⋊D7C23116yes—
167C2×(C2×D7)⋊C4C2312yes—
168C2×(C2×D7)⋊C4C2314yes—
169C2×(C2×D7)⋊C4C2314yes—
170C2×(C2×D7)⋊C4C2314yes—
171C2×(C2×D7)⋊C4C2312yes—
172#6489C23132yes—
173#6489C2318yes—
174C2×C4⋊Dic7C2311yescharacteristic
175C2×C4⋊Dic7C2311yescharacteristic
176C2×C4⋊Dic7C2312yes—
177C2×C4⋊Dic7C2314yes—
178C2×C4⋊Dic7C2314yes—
179C2×C4⋊Dic7C2314yes—
180C2×C4⋊Dic7C2312yes—
181C2×C4⋊Dic7C2318yes—
182#6487C2318yes—
183#6487C23116yes—
184#6487C23132yes—
185#6487C23116yes—
186#6487C2318yes—
187#6487C23116yes—
188#6487C23116yes—
189C2×Dic7⋊C4C2312yes—
190C2×Dic7⋊C4C2314yes—
191C2×Dic7⋊C4C2314yes—
192C2×Dic7⋊C4C2314yes—
193C2×Dic7⋊C4C2314yes—
194C2×Dic7⋊C4C2314yes—
195C2×Dic7⋊C4C2314yes—
196C2×Dic7⋊C4C2312yes—
197C2×Dic7⋊C4C2314yes—
198C2×Dic7⋊C4C23116yes—
199C2×C4×Dic7C2314yes—
200C2×C4×Dic7C2314yes—
201C2×C4×Dic7C2314yes—
202C2×C4×Dic7C2312yes—
203#6461C23132yescomplemented
204#6460C23116yescomplemented
205#6460C23116yescomplemented
206#6459C23132yescomplemented
207#6455C23116yescomplemented
208D7×C4⋊C4C23116yescomplemented
209#6453C23116yescomplemented
210#6452C23132yescomplemented
211#6452C23132yescomplemented
212#6451C23116yescomplemented
213#6450C23116yescomplemented
214#6450C23116yescomplemented
215#6449C23132yes—
216#6448C23132yes—
217#6446C23132yes—
218(C22⋊D7)⋊C4C23132yes—
219#6442C23132yes—
220#6442C23132yes—
221#6441C23132yes—
222#6440C23132yes—
223#6439C23132yescomplemented
224#6438C23116yescomplemented
225C4×D28C23116yescomplemented
226#6435C23132yescomplemented
227#6433C23132yescomplemented
228#6433C23116yescomplemented
229#6432C23116yescomplemented
230#6432C23116yescomplemented
231C4×Dic14C23116yescomplemented
232C4×Dic14C23116yescomplemented
233C4×Dic14C23132yescomplemented
234C4×Dic14C23116yescomplemented
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×#520—71no—
251C2×#519—71no—
252C22×#117D711yescharacteristic, complemented
253C24×C7—24no—
254C24×C7—24no—
255C24×C7—42no—
256C24×C7C2411yescharacteristic
257C24×C7C2414yes—
258C24×C7C2411yescharacteristic
259C24×C7C2411yescharacteristic
260C23×D7C2412yes—
261C22×C4×C7—24no—
262C22×C4×C7—28no—
263C22×C4×C7—24no—
264C22×C4×C7—24no—
265C22×C4×C7—24no—
266C22×C4×C7—24no—
267C22×C4×C7—232no—
268C22×C4×C7—44no—
269C22×C4×C7#4118yes—
270C22×C4×C7C2412yes—
271C22×C4×C7C2412yes—
272C22×C4×C7C2411yescharacteristic
273C22×C4×C7C2411yescharacteristic
274C22×C4×C7C2414yes—
275C22×C4×C7C2412yes—
276C22×C4×C7C2412yes—
277C22×C4×C7C2414yes—
278C22×C4×C7C2414yes—
279C22×C4×C7C2414yes—
280C22×C4×C7C2414yes—
281C22×C4×C7C2418yes—
282C22×C4×C7C2418yes—
283C22×C4×C7C2411yescharacteristic
284C22×C4×C7C2411yescharacteristic
285C22×C4×C7C2414yes—
286C2×C22⋊D7—28no—
287C2×C22⋊D7—28no—
288C2×C22⋊D7—44no—
289C2×C22⋊D7C2418yes—
290C2×C22⋊D7C2418yes—
291C2×C22⋊D7C2418yes—
292C22×Dic7—28no—
293C22×Dic7—44no—
294C22×Dic7C2418yes—
295C22×Dic7C2412yes—
296C22×Dic7C2412yes—
297C22×Dic7C2412yes—
298C22×Dic7C2414yes—
299C22×Dic7C2414yes—
300C22×Dic7C2418yes—
301#1157—232no—
302C2×D28—24no—
303C2×D28C2414yes—
304C2×C4×D7—28no—
305C2×C4×D7—48no—
306C2×C4×D7C2418yes—
307C2×C4×D7C24116yes—
308C2×Dic14—28no—
309C2×Dic14—28no—
310C2×Dic14—232no—
311C2×Dic14—24no—
312C2×Dic14—48no—
313C2×Dic14C2414yes—
314C2×Dic14C2418yes—
315C2×Dic14C2418yes—
316C2×Dic14C24116yes—
317C7×C4⋊C4C2414yes—
318C7×C4⋊C4C2414yes—
319C7×C4⋊C4C2414yes—
320C7×C4⋊C4C2418yes—
321C7×C4⋊C4C2418yes—
322C7×C4⋊C4C2414yes—
323C7×C22⋊C4C2418yes—
324C7×C22⋊C4C2418yes—
325C7×C22⋊C4C2418yes—
326C7×C22⋊C4C2418yes—
327C42×C7C2418yes—
328C42×C7C2418yes—
329C42×C7C2418yes—
330C42×C7C2418yes—
331C22⋊Dic7C2418yes—
332C22⋊Dic7C2418yes—
333C22⋊Dic7C24116yes—
334C22⋊Dic7C2418yes—
335C22⋊Dic7C24116yes—
336(C2×D7)⋊C4C2418yes—
337(C2×D7)⋊C4C24116yes—
338(C2×D7)⋊C4C24116yes—
339(C2×D7)⋊C4C24116yes—
340(C2×D7)⋊C4C2418yes—
341C4⋊Dic7C2414yes—
342C4⋊Dic7C2414yes—
343C4⋊Dic7C2418yes—
344C4⋊Dic7C24116yes—
345C4⋊Dic7C24116yes—
346C4⋊Dic7C24116yes—
347C4⋊Dic7C2418yes—
348Dic7⋊C4C2418yes—
349Dic7⋊C4C24116yes—
350Dic7⋊C4C24116yes—
351Dic7⋊C4C24116yes—
352Dic7⋊C4C24116yes—
353Dic7⋊C4C24116yes—
354Dic7⋊C4C24116yes—
355Dic7⋊C4C2418yes—
356Dic7⋊C4C24116yes—
357C4×Dic7C24116yes—
358C4×Dic7C24116yes—
359C4×Dic7C24116yes—
360C4×Dic7C2418yes—
361C22×#41—71no—
362C23×Q8—71no—
363C24×C4C2×D711yescharacteristic
364#556—732no—
365#554—732no—
366#552—732no—
367#552—764no—
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—74no—
389C2×#124—72no—
390#525—716no—
391C2×#123—72no—
392C2×#123—74no—
393C2×#123—74no—
394C2×#123—74no—
395C2×C22⋊Q8—72no—
396C2×C22⋊Q8—72no—
397C2×C22⋊Q8—72no—
398C2×C22⋊Q8—72no—
399C2×C22⋊Q8—716no—
400C2×C22⋊Q8—71no—
401C2×C22⋊Q8—71no—
402C2×C22⋊Q8—74no—
403C2×C22⋊Q8—74no—
404C2×C22⋊Q8—72no—
405C2×C22⋊Q8—72no—
406C2×C22⋊Q8—74no—
407C2×#121—71no—
408C2×#121—71no—
409C2×#120—72no—
410#520—716no—
411#519—716no—
412C2×C4×Q8—72no—
413C2×C4×Q8—72no—
414C2×C4×Q8—72no—
415C2×C4×Q8—72no—
416C2×C4×Q8—72no—
417C2×C4×Q8—74no—
418C2×C4×D4—72no—
419C2×C4×D4—72no—
420C2×C4×D4—74no—
421C2×C4×D4—74no—
422C2×C4×D4—72no—
423C2×#117—71no—
424C2×#117—74no—
425C2×#117—72no—
426C2×#117—74no—
427C2×#117—74no—
428C2×#117C2×D711yescharacteristic
429C2×#117C2×D711yescharacteristic
430C2×#117C2×D712yes—
431C2×#117C2×D711yescharacteristic
432C2×#117C2×D712yes—
433C2×#117C2×D711yescharacteristic
434C2×#117C2×D7116yescomplemented
435C22×C4⋊C4—71no—
436C22×C4⋊C4—72no—
437C22×C4⋊C4—72no—
438C22×C4⋊C4C2×D711yescharacteristic
439C22×C4⋊C4C2×D711yescharacteristic
440C22×C22⋊C4—72no—
441C22×C22⋊C4C2×D712yes—
442C22×C42C2×D712yes—
443C23×C7—22no—
444C23×C7—22no—
445C23×C7—22no—
446C23×C7—22no—
447C23×C7—28no—
448C23×C7—22no—
449C23×C7—28no—
450C23×C7—22no—
451C23×C7—22no—
452C23×C7—44no—
453C23×C7—416no—
454C23×C7C2×#4114yes—
455C23×C72−1+414yes—
456C23×C7C2512yes—
457C23×C7C2512yes—
458C23×C7C2512yes—
459C23×C7C2511yescharacteristic
460C22×D7—24no—
461C22×D7—24no—
462C22×D7—24no—
463C22×D7C2514yes—
464C2×C4×C7—28no—
465C2×C4×C7—22no—
466C2×C4×C7—22no—
467C2×C4×C7—216no—
468C2×C4×C7—24no—
469C2×C4×C7—24no—
470C2×C4×C7—24no—
471C2×C4×C7—24no—
472C2×C4×C7—28no—
473C2×C4×C7—28no—
474C2×C4×C7—28no—
475C2×C4×C7—28no—
476C2×C4×C7—48no—
477C2×C4×C7C2×#4114yes—
478C2×C4×C7C2×#4114yes—
479C2×C4×C7C2×#41116yes—
480C2×C4×C7C2514yes—
481C2×C4×C7C2514yes—
482C2×C4×C7C2512yes—
483C2×C4×C7C2512yes—
484C2×C4×C7C2514yes—
485C2×C4×C7C2514yes—
486C2×C4×C7C2512yes—
487C2×C4×C7C2512yes—
488C22⋊D7—216no—
489C22⋊D7—216no—
490C22⋊D7—48no—
491C2×Dic7—216no—
492C2×Dic7—28no—
493C2×Dic7—24no—
494C2×Dic7—24no—
495C2×Dic7—24no—
496C2×Dic7—28no—
497C2×Dic7—48no—
498C2×Dic7C2514yes—
499C2×Dic7C2514yes—
500C2×Dic7C2514yes—
501C2×Dic7C2518yes—
502C2×Dic7C2518yes—
503D28—28no—
504C4×D7—216no—
505C4×D7—416no—
506Dic14—216no—
507Dic14—216no—
508Dic14—28no—
509Dic14—416no—
510C25C22×D711yescharacteristic
511C2×#41—78no—
512C2×#41—148no—
513C22×Q8—72no—
514C22×Q8—72no—
515C22×Q8—71no—
516C22×Q8—78no—
517C22×Q8—74no—
518C22×Q8—148no—
519C22×D4—72no—
520C22×D4—72no—
521C22×D4—72no—
522C22×D4—71no—
523C23×C4—28no—
524C23×C4—72no—
525C23×C4—72no—
526C23×C4—72no—
527C23×C4—74no—
528C23×C4C22×D712yes—
529C23×C4C22×D711yescharacteristic
530C23×C4C22×D711yescharacteristic
531C23×C4C22×D711yescharacteristic
532C23×C4C22×D711yescharacteristic
533C23×C4C22×D718yes—
534C23×C4C22×D711yescharacteristic
535C23×C4C22×D712yes—
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—732no—
545#125—732no—
546#125—716no—
547#125—716no—
548#125—732no—
549#124—732no—
550#124—716no—
551#123—716no—
552#123—732no—
553#123—732no—
554#123—732no—
555C22⋊Q8—716no—
556C22⋊Q8—716no—
557C22⋊Q8—716no—
558C22⋊Q8—716no—
559C22⋊Q8—78no—
560C22⋊Q8—78no—
561C22⋊Q8—732no—
562C22⋊Q8—716no—
563C22⋊Q8—716no—
564C22⋊Q8—732no—
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—716no—
574C4×Q8—732no—
575C4×D4—716no—
576C4×D4—716no—
577C4×D4—732no—
578C4×D4—732no—
579C4×D4—716no—
580#117—78no—
581#117—732no—
582#117—716no—
583#117—732no—
584#117—732no—
585#117C22×D718yes—
586#117C22×D718yes—
587#117C22×D7116yes—
588#117C22×D718yes—
589#117C22×D7116yes—
590#117C22×D718yes—
591C2×C4⋊C4—72no—
592C2×C4⋊C4—74no—
593C2×C4⋊C4—72no—
594C2×C4⋊C4—74no—
595C2×C4⋊C4—78no—
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—716no—
610C2×C4⋊C4C22×D711yescharacteristic
611C2×C4⋊C4C22×D711yescharacteristic
612C2×C4⋊C4C22×D712yes—
613C2×C4⋊C4C22×D711yescharacteristic
614C2×C4⋊C4C22×D711yescharacteristic
615C2×C4⋊C4C22×D712yes—
616C2×C4⋊C4C22×D718yes—
617C2×C4⋊C4C22×D718yes—
618C2×C22⋊C4—74no—
619C2×C22⋊C4—74no—
620C2×C22⋊C4—716no—
621C2×C22⋊C4—72no—
622C2×C22⋊C4—72no—
623C2×C22⋊C4—72no—
624C2×C22⋊C4—72no—
625C2×C22⋊C4—74no—
626C2×C22⋊C4—74no—
627C2×C22⋊C4—72no—
628C2×C22⋊C4—74no—
629C2×C22⋊C4C22×D712yes—
630C2×C22⋊C4C22×D712yes—
631C2×C22⋊C4C22×D712yes—
632C2×C22⋊C4C22×D712yes—
633C2×C22⋊C4C22×D7116yes—
634C2×C42—74no—
635C2×C42—74no—
636C2×C42—74no—
637C2×C42—72no—
638C2×C42C22×D712yes—
639C2×C42C22×D712yes—
640C2×C42C22×D712yes—
641C2×C42C22×D712yes—
642C2×C42C22×D7116yes—
643C22×C7—22no—
644C22×C7—22no—
645C22×C7—22no—
646C22×C7—22no—
647C22×C7—28no—
648C22×C7—28no—
649C22×C7—22no—
650C22×C7—22no—
651C22×C7—22no—
652C22×C7—416no—
653C22×C7—44no—
654C22×C7C22×#4114yes—
655C22×C7C22×#4112yes—
656C22×C7C2×2−1+414yes—
657C22×C7C2×2−1+412yes—
658C22×C7#58512yes—
659C22×C7C2611yescharacteristic
660C2×D7—24no—
661C2×D7—24no—
662C2×D7—24no—
663C2×D7—48no—
664C4×C7—22no—
665C4×C7—22no—
666C4×C7—24no—
667C4×C7—24no—
668C4×C7—24no—
669C4×C7—24no—
670C4×C7C22×#4114yes—
671C4×C7C22×#4114yes—
672Dic7—28no—
673Dic7—24no—
674Dic7—24no—
675Dic7—24no—
676Dic7—28no—
677C24—24no—
678C24—24no—
679C24—42no—
680C24—72no—
681C24C23×D711yescharacteristic
682C24C23×D714yes—
683C24C23×D711yescharacteristic
684C24C23×D711yescharacteristic
685#41—1432no—
686C2×Q8—78no—
687C2×Q8—78no—
688C2×Q8—74no—
689C2×Q8—716no—
690C2×Q8—148no—
691C2×Q8—148no—
692C2×Q8—1432no—
693C2×Q8—144no—
694C2×Q8—288no—
695C2×D4—78no—
696C2×D4—78no—
697C2×D4—78no—
698C2×D4—74no—
699C2×D4—148no—
700C2×D4—148no—
701C2×D4—144no—
702C2×D4—284no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—232no—
710C22×C4—44no—
711C22×C4—78no—
712C22×C4—72no—
713C22×C4—72no—
714C22×C4—74no—
715C22×C4—72no—
716C22×C4—74no—
717C22×C4—78no—
718C22×C4—78no—
719C22×C4—716no—
720C22×C4—148no—
721C22×C4—148no—
722C22×C4—288no—
723C22×C4—284no—
724C22×C4#115718yes—
725C22×C4C23×D714yes—
726C22×C4C23×D718yes—
727C22×C4C23×D714yes—
728C22×C4C23×D714yes—
729C22×C4C23×D714yes—
730C22×C4C23×D714yes—
731C22×C4C23×D712yes—
732C22×C4C23×D712yes—
733C22×C4C23×D711yescharacteristic
734C22×C4C23×D712yes—
735C22×C4C23×D712yes—
736C22×C4C23×D711yescharacteristic
737C22×C4C23×D718yes—
738C22×C4C23×D714yes—
739C22×C4C23×D711yescharacteristic
740C22×C4C23×D711yescharacteristic
741C4⋊C4—716no—
742C4⋊C4—716no—
743C4⋊C4—716no—
744C4⋊C4—716no—
745C4⋊C4—716no—
746C4⋊C4—716no—
747C4⋊C4—78no—
748C4⋊C4—78no—
749C4⋊C4—716no—
750C4⋊C4—78no—
751C4⋊C4—78no—
752C4⋊C4—74no—
753C4⋊C4—74no—
754C4⋊C4—716no—
755C4⋊C4—716no—
756C4⋊C4—716no—
757C4⋊C4C23×D714yes—
758C4⋊C4C23×D714yes—
759C4⋊C4C23×D718yes—
760C4⋊C4C23×D714yes—
761C4⋊C4C23×D714yes—
762C4⋊C4C23×D718yes—
763C22⋊C4—716no—
764C22⋊C4—716no—
765C22⋊C4—78no—
766C22⋊C4—78no—
767C22⋊C4—78no—
768C22⋊C4—78no—
769C22⋊C4—716no—
770C22⋊C4—716no—
771C22⋊C4—78no—
772C22⋊C4—716no—
773C22⋊C4C23×D718yes—
774C22⋊C4C23×D718yes—
775C22⋊C4C23×D718yes—
776C22⋊C4C23×D718yes—
777C42—716no—
778C42—716no—
779C42—716no—
780C42—78no—
781C42C23×D718yes—
782C42C23×D718yes—
783C42C23×D718yes—
784C42C23×D718yes—
785C2×C7—24no—
786C2×C7—24no—
787C2×C7—42no—
788C2×C7#349514yescomplemented
789C2×C7C23×#4111yescharacteristic
790C2×C7C22×2−1+411yescharacteristic
791C2×C7C2×#58511yescharacteristic
792D7—44no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—28no—
798C23—22no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—44no—
803C23—416no—
804C23—74no—
805C23—144no—
806C23—144no—
807C23—144no—
808C23C2×#115714yes—
809C23#655414yes—
810C23C24×D712yes—
811C23C24×D712yes—
812C23C24×D712yes—
813C23C24×D711yescharacteristic
814Q8—1416no—
815Q8—1416no—
816Q8—148no—
817Q8—2816no—
818D4—1416no—
819D4—1416no—
820D4—148no—
821D4—288no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—216no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—48no—
835C2×C4—74no—
836C2×C4—74no—
837C2×C4—78no—
838C2×C4—74no—
839C2×C4—78no—
840C2×C4—144no—
841C2×C4—1416no—
842C2×C4—148no—
843C2×C4—144no—
844C2×C4—148no—
845C2×C4—144no—
846C2×C4—1416no—
847C2×C4—2816no—
848C2×C4—288no—
849C2×C4C2×#115714yes—
850C2×C4C2×#115714yes—
851C2×C4C2×#1157116yes—
852C2×C4C24×D714yes—
853C2×C4C24×D714yes—
854C2×C4C24×D712yes—
855C2×C4C24×D714yes—
856C2×C4C24×D714yes—
857C2×C4C24×D712yes—
858C2×C4C24×D712yes—
859C2×C4C24×D712yes—
860C7C2×#349511yescharacteristic, complemented, Sylow
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—28no—
866C22—28no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—144no—
873C22—144no—
874C22—144no—
875C22—288no—
876C22C22×#115714yes—
877C22C22×#115712yes—
878C22C2×#655414yes—
879C22C2×#655412yes—
880C22#9061612yes—
881C22C25×D711yescharacteristic
882C4—22no—
883C4—22no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—144no—
889C4—148no—
890C4—144no—
891C4—148no—
892C4—144no—
893C4C22×#115714yes—
894C4C22×#115714yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—284no—
899C2#1174279514yesdirect product factor
900C2C23×#115711yescharacteristic
901C2C22×#655411yescharacteristic
902C2C2×#9061611yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC22×C7×#117C2
socleC23×C7C25
prime radicalC2×#90482C2
hypercenterC22×#117D7
hypocenterC7C2×#3495
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×C7×#117C2semidirect
3. C22×#6487C2semidirect
4. C2×#90224C2semidirect
5. C2×#90220C2semidirect
6. C2×#90225C2semidirect
7. C2×#90214C2semidirect
8. #11742795C2direct (N × H)
9. C2×#90222C2semidirect
10. C2×#90210C2semidirect
11. C2×#90209C2semidirect
12. C2×#90217C2semidirect
13. C2×#90207C2semidirect
14. C2×#90202C2semidirect
15. C2×#90204C2semidirect
16. C2×#90186C2semidirect
17. C2×#90170C2semidirect
18. C2×#90161C2semidirect
28. C2×C7×#117C22semidirect
53. C2×#6487C22semidirect
55. #90225C22semidirect
56. #90224C22semidirect
57. #90222C22semidirect
58. #90220C22semidirect
59. #90217C22semidirect
60. #90214C22semidirect
61. #90210C22semidirect
62. #90209C22semidirect
63. #90207C22semidirect
64. #90204C22semidirect
65. C2×#6461C22semidirect
66. #90202C22semidirect
67. C2×#6460C22semidirect
68. C2×#6460C22semidirect
69. C2×#6459C22semidirect
70. C2×#6455C22semidirect
71. C2×D7×C4⋊C4C22semidirect
72. C2×#6453C22semidirect
73. C2×#6452C22semidirect
74. C2×#6452C22semidirect
75. C2×#6451C22semidirect
76. C2×#6450C22semidirect
77. C2×#6450C22semidirect
78. #90186C22semidirect
87. #90170C22semidirect
88. C2×#6439C22semidirect
89. C2×#6438C22semidirect
90. C2×C4×D28C22semidirect
91. C2×#6435C22semidirect
92. #90161C22semidirect
93. C2×#6433C22semidirect
94. C2×#6433C22semidirect
95. C2×#6432C22semidirect
96. C2×#6432C22semidirect
97. C2×C4×Dic14C22semidirect
98. C2×C4×Dic14C22semidirect
99. C2×C4×Dic14C22semidirect
100. C2×C4×Dic14C22semidirect
203. #6461C23semidirect
204. #6460C23semidirect
205. #6460C23semidirect
206. #6459C23semidirect
207. #6455C23semidirect
208. D7×C4⋊C4C23semidirect
209. #6453C23semidirect
210. #6452C23semidirect
211. #6452C23semidirect
212. #6451C23semidirect
213. #6450C23semidirect
214. #6450C23semidirect
223. #6439C23semidirect
224. #6438C23semidirect
225. C4×D28C23semidirect
226. #6435C23semidirect
227. #6433C23semidirect
228. #6433C23semidirect
229. #6432C23semidirect
230. #6432C23semidirect
231. C4×Dic14C23semidirect
232. C4×Dic14C23semidirect
233. C4×Dic14C23semidirect
234. C4×Dic14C23semidirect
252. C22×#117D7semidirect
434. C2×#117C2×D7semidirect
788. C2×C7#3495semidirect
860. C7C2×#3495semidirect
899. C2#11742795direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1172
C2×#904822
C22×#64872
C2×#902242
C2×#902202
C2×#902252
C2×#902142
#117427952
C2×#902222
C2×#902102
C2×#902092
C2×#902172
C2×#902072
C2×#902022
C2×#902042
C2×#901862
C2×#901702
C2×#901612
C2×#34957