Finite Group Databasebeta

← C2×#11743208 #14261165

Subgroups — C2×#11743208 #14261165

Order 1792.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#529C211yesmaximal, characteristic, complemented
2#11743208C2132yesmaximal, direct product factor
3C2×#90398C214yesmaximal, complemented
4C2×#90390C212yesmaximal, complemented
5C2×#90375C212yesmaximal, complemented
6C2×#90346C214yesmaximal, complemented
7C2×#90336C212yesmaximal, complemented
8C2×#90288C212yesmaximal, complemented
9C2×#90270C212yesmaximal, complemented
10C2×#90256C212yesmaximal, complemented
11C2×#90256C212yesmaximal, complemented
12C2×#90246C212yesmaximal, complemented
13C2×#90226C212yesmaximal, complemented
14C2×#90210C212yesmaximal, complemented
15C2×#90168C211yesmaximal, characteristic, complemented
16C22×#6433C211yesmaximal, characteristic, complemented
17C22×#1159C2214yes—
18C22×#1157C2212yes—
19C7×#529C22116yescomplemented
20C2×C7×#126C2212yes—
21C2×C7×#125C2211yescharacteristic
22C2×C7×#124C2211yescharacteristic
23C2×C7×#123C2212yes—
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×#121C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×D4C2212yes—
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117C2212yes—
30C22×C42×C7C2211yescharacteristic
31C2×#6509C2214yes—
32C2×#6502C2214yes—
33C2×#6502C2214yes—
34C2×#6493C2212yes—
35C2×#6493C2212yes—
36C2×#6493C2212yes—
37C2×#6493C2212yes—
38C2×#6489C2212yes—
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×C4⋊Dic7C2212yes—
42C22×Dic7⋊C4C2212yes—
43C22×Dic7⋊C4C2212yes—
44#90398C22164yescomplemented
45#90390C22132yescomplemented
46#90375C22132yescomplemented
47#90346C22164yescomplemented
48#90336C22132yescomplemented
49#90288C22132yescomplemented
50#90270C22132yescomplemented
51#90256C22132yescomplemented
52#90256C22132yescomplemented
53#90246C22132yescomplemented
54#90226C22132yescomplemented
55#90210C22132yescomplemented
56C2×#6461C2214yes—
57C2×#6461C2214yes—
58C2×#6460C2214yes—
59C2×#6459C2214yes—
60C2×#6459C2214yes—
61C2×#6457C2214yes—
62C2×#6457C2214yes—
63C2×D7×C4⋊C4C2214yes—
64C2×#6453C2214yes—
65C2×#6451C2214yes—
66C2×#6449C2214yes—
67C2×#6449C2214yes—
68C2×#6447C2214yes—
69C2×#6447C2214yes—
70C2×#6446C2214yes—
71C2×#6446C2214yes—
72C2×(C22⋊D7)⋊C4C2214yes—
73C2×(C22⋊D7)⋊C4C2214yes—
74C2×#6441C2214yes—
75C2×#6441C2214yes—
76#90168C22116yescomplemented
77C2×#6438C2212yes—
78C2×#6437C2211yescharacteristic
79C2×C4×D28C2212yes—
80C2×C4×D28C2212yes—
81C2×C4×D28C2212yes—
82C2×C4×D28C2212yes—
83C2×#6433C2212yes—
84C2×#6433C2212yes—
85C2×#6433C2212yes—
86C2×#6433C2212yes—
87C2×#6433C2212yes—
88C2×#6433C22116yescomplemented
89C2×#6432C2211yescharacteristic
90C2×#6432C2212yes—
91C2×#3559—71nomaximal, Sylow
92C22×C7×Q8C2311yescharacteristic
93C22×C7×D4C2312yes—
94C22×C7×D4C2311yescharacteristic
95C23×C4×C7C2311yescharacteristic
96C23×C4×C7C2311yescharacteristic
97C23×C4×C7C2312yes—
98C23×C4×C7C2311yescharacteristic
99C22×C22⋊D7C2314yes—
100C22×C22⋊D7C2314yes—
101C22×C22⋊D7C2314yes—
102C23×Dic7C2312yes—
103C23×Dic7C2314yes—
104C23×Dic7C2312yes—
105C2×#1159—416no—
106C2×#1159C23132yes—
107C2×#1157—48no—
108C2×#1157C23116yes—
109C22×D28C2312yes—
110C22×D28C2312yes—
111C22×D28C2312yes—
112C22×C4×D7C2314yes—
113C22×C4×D7C2314yes—
114C22×C4×D7C2314yes—
115C22×Dic14C2312yes—
116C22×Dic14C2314yes—
117C7×#126C23116yes—
118C7×#125C2318yes—
119C7×#124C2318yes—
120C7×#123C23116yes—
121C7×C22⋊Q8C2318yes—
122C7×#121C2318yes—
123C4×C7×Q8C2318yes—
124C4×C7×D4C23116yes—
125C4×C7×D4C2318yes—
126C7×#117C23116yes—
127C2×C7×C4⋊C4C2312yes—
128C2×C7×C4⋊C4C2312yes—
129C2×C7×C4⋊C4C2312yes—
130C2×C7×C4⋊C4C2311yescharacteristic
131C2×C7×C4⋊C4C2312yes—
132C2×C7×C4⋊C4C2311yescharacteristic
133C2×C7×C22⋊C4C2312yes—
134C2×C7×C22⋊C4C2312yes—
135C2×C7×C22⋊C4C2312yes—
136C2×C7×C22⋊C4C2312yes—
137C2×C7×C22⋊C4C2312yes—
138C2×C42×C7C2311yescharacteristic
139C2×C42×C7C2312yes—
140C2×C42×C7C2311yescharacteristic
141C2×C42×C7C2311yescharacteristic
142C2×C42×C7C2311yescharacteristic
143C2×C42×C7C2318yes—
144C2×C22⋊Dic7C2314yes—
145#6509C23132yes—
146#6502C23132yes—
147#6502C23132yes—
148#6493C23116yes—
149#6493C23116yes—
150#6493C23116yes—
151#6493C23116yes—
152C2×(C2×D7)⋊C4C2314yes—
153C2×(C2×D7)⋊C4C2314yes—
154C2×(C2×D7)⋊C4C2314yes—
155C2×(C2×D7)⋊C4C2314yes—
156C2×(C2×D7)⋊C4C2314yes—
157C2×(C2×D7)⋊C4C2314yes—
158#6489C23116yes—
159C2×C4⋊Dic7C2312yes—
160C2×C4⋊Dic7C2312yes—
161C2×C4⋊Dic7C2312yes—
162C2×C4⋊Dic7C2314yes—
163C2×C4⋊Dic7C2312yes—
164C2×C4⋊Dic7C2312yes—
165C2×C4⋊Dic7C2312yes—
166C2×C4⋊Dic7C2318yes—
167C2×C4⋊Dic7C2318yes—
168C2×C4⋊Dic7C2314yes—
169C2×C4⋊Dic7C23116yes—
170C2×Dic7⋊C4C2314yes—
171C2×Dic7⋊C4C2314yes—
172C2×Dic7⋊C4C2314yes—
173C2×Dic7⋊C4C2314yes—
174C2×Dic7⋊C4C2314yes—
175C2×Dic7⋊C4C2314yes—
176C2×Dic7⋊C4C23116yes—
177C2×Dic7⋊C4C23116yes—
178C2×C4×Dic7C2314yes—
179#6461C23132yes—
180#6461C23132yes—
181#6460C23132yes—
182#6459C23132yes—
183#6459C23132yes—
184#6457C23132yes—
185#6457C23132yes—
186D7×C4⋊C4C23132yes—
187#6453C23132yes—
188#6451C23132yes—
189#6449C23132yes—
190#6449C23132yes—
191#6447C23132yes—
192#6447C23132yes—
193#6446C23132yes—
194#6446C23132yes—
195(C22⋊D7)⋊C4C23132yes—
196(C22⋊D7)⋊C4C23132yes—
197#6441C23132yes—
198#6441C23132yes—
199#6438C23116yes—
200#6437C2318yes—
201C4×D28C23116yes—
202C4×D28C23116yes—
203C4×D28C23116yes—
204C4×D28C23116yes—
205#6433C23116yes—
206#6433C23116yes—
207#6433C23116yes—
208#6433C23116yes—
209#6433C23116yes—
210#6432C2318yes—
211#6432C23116yes—
212#3559—732no—
213C2×#563—72no—
214C2×#562—72no—
215C2×#554—72no—
216C2×#553—72no—
217C2×#553—72no—
218C2×#547—74no—
219C2×#547—72no—
220C2×#544—72no—
221C2×#540—72no—
222C2×#539—74no—
223C2×#539—72no—
224C2×#537—72no—
225C2×#532—71no—
226C2×#529D711yescharacteristic, complemented
227C22×#125—71no—
228C24×C7C2412yes—
229C24×C7C2411yescharacteristic
230C23×D7C2414yes—
231C2×C7×Q8—42no—
232C2×C7×Q8C2414yes—
233C2×C7×D4—28no—
234C2×C7×D4—42no—
235C2×C7×D4C2418yes—
236C2×C7×D4C2414yes—
237C22×C4×C7—24no—
238C22×C4×C7—24no—
239C22×C4×C7—28no—
240C22×C4×C7—42no—
241C22×C4×C7C2412yes—
242C22×C4×C7C2411yescharacteristic
243C22×C4×C7C2411yescharacteristic
244C22×C4×C7C2411yescharacteristic
245C22×C4×C7C2411yescharacteristic
246C22×C4×C7C2414yes—
247C22×C4×C7C2412yes—
248C22×C4×C7C2412yes—
249C22×C4×C7C2411yescharacteristic
250C22×C4×C7C2414yes—
251C22×C4×C7C2418yes—
252C22×C4×C7C2414yes—
253C22×C4×C7C2411yescharacteristic
254C2×C22⋊D7—216no—
255C2×C22⋊D7—48no—
256C2×C22⋊D7—48no—
257C2×C22⋊D7C24116yes—
258C2×C22⋊D7C24116yes—
259C2×C22⋊D7C24116yes—
260C22×Dic7—28no—
261C22×Dic7—48no—
262C22×Dic7—44no—
263C22×Dic7C2418yes—
264C22×Dic7C2414yes—
265C22×Dic7C2414yes—
266C22×Dic7C2414yes—
267C22×Dic7C24116yes—
268C22×Dic7C2418yes—
269#1159—464no—
270#1157—432no—
271C2×D28—28no—
272C2×D28—44no—
273C2×D28—44no—
274C2×D28C2418yes—
275C2×D28C2418yes—
276C2×D28C2418yes—
277C2×C4×D7—48no—
278C2×C4×D7—48no—
279C2×C4×D7—48no—
280C2×C4×D7C24116yes—
281C2×C4×D7C24116yes—
282C2×C4×D7C24116yes—
283C2×Dic14—44no—
284C2×Dic14—48no—
285C2×Dic14C2418yes—
286C2×Dic14C24116yes—
287C7×C4⋊C4C2418yes—
288C7×C4⋊C4C2418yes—
289C7×C4⋊C4C2418yes—
290C7×C4⋊C4C2414yes—
291C7×C4⋊C4C2418yes—
292C7×C4⋊C4C2414yes—
293C7×C22⋊C4C2418yes—
294C7×C22⋊C4C2418yes—
295C7×C22⋊C4C2418yes—
296C7×C22⋊C4C2418yes—
297C7×C22⋊C4C2418yes—
298C42×C7C2414yes—
299C42×C7C2418yes—
300C42×C7C2414yes—
301C42×C7C2414yes—
302C42×C7C2414yes—
303C22⋊Dic7C24116yes—
304(C2×D7)⋊C4C24116yes—
305(C2×D7)⋊C4C24116yes—
306(C2×D7)⋊C4C24116yes—
307(C2×D7)⋊C4C24116yes—
308(C2×D7)⋊C4C24116yes—
309(C2×D7)⋊C4C24116yes—
310C4⋊Dic7C2418yes—
311C4⋊Dic7C2418yes—
312C4⋊Dic7C2418yes—
313C4⋊Dic7C24116yes—
314C4⋊Dic7C2418yes—
315C4⋊Dic7C2418yes—
316C4⋊Dic7C2418yes—
317C4⋊Dic7C24116yes—
318Dic7⋊C4C24116yes—
319Dic7⋊C4C24116yes—
320Dic7⋊C4C24116yes—
321Dic7⋊C4C24116yes—
322Dic7⋊C4C24116yes—
323Dic7⋊C4C24116yes—
324C4×Dic7C24116yes—
325C22×#41—74no—
326C22×#41—72no—
327#563—732no—
328#562—732no—
329#554—732no—
330#553—732no—
331#553—732no—
332#547—764no—
333#547—732no—
334#544—732no—
335#540—732no—
336#539—764no—
337#539—732no—
338#537—732no—
339#532—716no—
340C2×C4⋊Q8—74no—
341C2×C4⋊Q8—71no—
342C2×C4⋊Q8—72no—
343C2×#127—71no—
344#529C2×D7116yescomplemented
345C2×#126—74no—
346C2×#126—74no—
347C2×#126C2×D712yes—
348C2×#125—74no—
349C2×#125—72no—
350C2×#125—72no—
351C2×#125—72no—
352C2×#125—72no—
353C2×#125—72no—
354C2×#125—716no—
355C2×#125C2×D711yescharacteristic
356C2×#124—72no—
357C2×#124C2×D711yescharacteristic
358C2×#123—74no—
359C2×#123—74no—
360C2×#123—74no—
361C2×#123—74no—
362C2×#123—74no—
363C2×#123—74no—
364C2×#123C2×D712yes—
365C2×C22⋊Q8—74no—
366C2×C22⋊Q8—74no—
367C2×C22⋊Q8—74no—
368C2×C22⋊Q8—74no—
369C2×C22⋊Q8—74no—
370C2×C22⋊Q8—74no—
371C2×C22⋊Q8C2×D711yescharacteristic
372C2×#121—74no—
373C2×#121—74no—
374C2×#121—72no—
375C2×#121—72no—
376C2×#121—72no—
377C2×#121—72no—
378C2×#121—74no—
379C2×#121—74no—
380C2×#121C2×D711yescharacteristic
381C2×C4×Q8C2×D711yescharacteristic
382C2×C4×D4—74no—
383C2×C4×D4—74no—
384C2×C4×D4—72no—
385C2×C4×D4—72no—
386C2×C4×D4—72no—
387C2×C4×D4—72no—
388C2×C4×D4C2×D712yes—
389C2×C4×D4C2×D711yescharacteristic
390C2×#117—72no—
391C2×#117C2×D712yes—
392C22×C4⋊C4—72no—
393C22×C4⋊C4—72no—
394C22×C4⋊C4—71no—
395C22×C4⋊C4—71no—
396C22×C4⋊C4—72no—
397C22×C4⋊C4—74no—
398C22×C42C2×D711yescharacteristic
399C23×C7—22no—
400C23×C7—22no—
401C23×C7—24no—
402C23×C7—24no—
403C23×C7—24no—
404C23×C7H(5,𝔽2)14yes—
405C23×C7C2514yes—
406C23×C7C2512yes—
407C23×C7C2511yescharacteristic
408C22×D7—28no—
409C22×D7—28no—
410C22×D7—28no—
411C22×D7C2518yes—
412C7×Q8—44no—
413C7×D4—216no—
414C7×D4—44no—
415C2×C4×C7—24no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—28no—
419C2×C4×C7—24no—
420C2×C4×C7—22no—
421C2×C4×C7—24no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—28no—
425C2×C4×C7—216no—
426C2×C4×C7—44no—
427C2×C4×C72−1+414yes—
428C2×C4×C7C2514yes—
429C2×C4×C7C2512yes—
430C2×C4×C7C2512yes—
431C2×C4×C7C2512yes—
432C2×C4×C7C2512yes—
433C2×C4×C7C2514yes—
434C2×C4×C7C2514yes—
435C2×C4×C7C2512yes—
436C2×C4×C7C2512yes—
437C22⋊D7—232no—
438C22⋊D7—416no—
439C22⋊D7—416no—
440C2×Dic7—28no—
441C2×Dic7—28no—
442C2×Dic7—216no—
443C2×Dic7—28no—
444C2×Dic7—416no—
445C2×Dic7—48no—
446C2×Dic7C2518yes—
447C2×Dic7C2518yes—
448C2×Dic7C2518yes—
449D28—216no—
450D28—48no—
451D28—48no—
452C4×D7—416no—
453C4×D7—416no—
454C4×D7—416no—
455Dic14—48no—
456Dic14—416no—
457C2×#41—732no—
458C2×#41—716no—
459C2×#41—288no—
460C2×#41—2816no—
461C22×Q8—74no—
462C22×Q8—72no—
463C22×Q8C22×D711yescharacteristic
464C22×D4—74no—
465C22×D4—74no—
466C22×D4—74no—
467C22×D4—72no—
468C22×D4—72no—
469C22×D4—72no—
470C22×D4C22×D712yes—
471C22×D4C22×D711yescharacteristic
472C23×C4—72no—
473C23×C4—72no—
474C23×C4—74no—
475C23×C4—74no—
476C23×C4—74no—
477C23×C4—74no—
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D712yes—
481C23×C4C22×D711yescharacteristic
482C4⋊Q8—732no—
483C4⋊Q8—78no—
484C4⋊Q8—716no—
485#127—78no—
486#126—732no—
487#126—732no—
488#126C22×D7116yes—
489#125—732no—
490#125—716no—
491#125—716no—
492#125—716no—
493#125—716no—
494#125—716no—
495#125C22×D718yes—
496#124—716no—
497#124C22×D718yes—
498#123—732no—
499#123—732no—
500#123—732no—
501#123—732no—
502#123—732no—
503#123—732no—
504#123C22×D7116yes—
505C22⋊Q8—732no—
506C22⋊Q8—732no—
507C22⋊Q8—732no—
508C22⋊Q8—732no—
509C22⋊Q8—732no—
510C22⋊Q8—732no—
511C22⋊Q8C22×D718yes—
512#121—732no—
513#121—732no—
514#121—716no—
515#121—716no—
516#121—716no—
517#121—716no—
518#121—732no—
519#121—732no—
520#121C22×D718yes—
521C4×Q8C22×D718yes—
522C4×D4—732no—
523C4×D4—732no—
524C4×D4—716no—
525C4×D4—716no—
526C4×D4—716no—
527C4×D4—716no—
528C4×D4C22×D7116yes—
529C4×D4C22×D718yes—
530#117—716no—
531#117C22×D7116yes—
532C2×C4⋊C4—72no—
533C2×C4⋊C4—74no—
534C2×C4⋊C4—72no—
535C2×C4⋊C4—72no—
536C2×C4⋊C4—74no—
537C2×C4⋊C4—74no—
538C2×C4⋊C4—74no—
539C2×C4⋊C4—74no—
540C2×C4⋊C4—72no—
541C2×C4⋊C4—74no—
542C2×C4⋊C4—74no—
543C2×C4⋊C4—72no—
544C2×C4⋊C4—716no—
545C2×C4⋊C4—716no—
546C2×C4⋊C4—78no—
547C2×C4⋊C4—78no—
548C2×C4⋊C4—716no—
549C2×C4⋊C4—72no—
550C2×C4⋊C4—74no—
551C2×C4⋊C4—732no—
552C2×C4⋊C4C22×D712yes—
553C2×C4⋊C4C22×D712yes—
554C2×C4⋊C4C22×D712yes—
555C2×C4⋊C4C22×D712yes—
556C2×C4⋊C4C22×D711yescharacteristic
557C2×C4⋊C4C22×D711yescharacteristic
558C2×C22⋊C4—74no—
559C2×C22⋊C4—74no—
560C2×C22⋊C4—74no—
561C2×C22⋊C4—74no—
562C2×C22⋊C4—74no—
563C2×C22⋊C4—74no—
564C2×C22⋊C4—74no—
565C2×C22⋊C4C22×D712yes—
566C2×C22⋊C4C22×D712yes—
567C2×C22⋊C4C22×D712yes—
568C2×C22⋊C4C22×D712yes—
569C2×C22⋊C4C22×D712yes—
570C2×C42—74no—
571C2×C42C22×D711yescharacteristic
572C2×C42C22×D712yes—
573C2×C42C22×D711yescharacteristic
574C2×C42C22×D711yescharacteristic
575C2×C42C22×D711yescharacteristic
576C2×C42C22×D718yes—
577C22×C7—22no—
578C22×C7—22no—
579C22×C7—28no—
580C22×C7—24no—
581C22×C7—24no—
582C22×C7—24no—
583C22×C7—48no—
584C22×C7C2×H(5,𝔽2)14yes—
585C22×C7C2×H(5,𝔽2)12yes—
586C22×C7C2×2−1+412yes—
587C22×C7#58512yes—
588C22×C7C2611yescharacteristic
589C2×D7—28no—
590C2×D7—28no—
591C2×D7—28no—
592C2×D7—416no—
593C4×C7—24no—
594C4×C7—22no—
595C4×C7—22no—
596C4×C7—24no—
597C4×C7—22no—
598C4×C7—24no—
599C4×C7—22no—
600C4×C7—22no—
601C4×C7C2×2−1+414yes—
602Dic7—28no—
603Dic7—28no—
604Dic7—28no—
605C24—74no—
606C24C23×D712yes—
607C24C23×D711yescharacteristic
608#41—2832no—
609#41—2864no—
610C2×Q8—42no—
611C2×Q8—716no—
612C2×Q8—78no—
613C2×Q8—284no—
614C2×Q8—288no—
615C2×Q8C23×D714yes—
616C2×D4—28no—
617C2×D4—42no—
618C2×D4—716no—
619C2×D4—716no—
620C2×D4—716no—
621C2×D4—78no—
622C2×D4—78no—
623C2×D4—78no—
624C2×D4—1416no—
625C2×D4—148no—
626C2×D4—284no—
627C2×D4—284no—
628C2×D4—288no—
629C2×D4—288no—
630C2×D4C23×D718yes—
631C2×D4C23×D714yes—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—28no—
635C22×C4—42no—
636C22×C4—78no—
637C22×C4—74no—
638C22×C4—74no—
639C22×C4—74no—
640C22×C4—78no—
641C22×C4—716no—
642C22×C4—716no—
643C22×C4—716no—
644C22×C4—716no—
645C22×C4—148no—
646C22×C4—288no—
647C22×C4—288no—
648C22×C4—288no—
649C22×C4—284no—
650C22×C4—288no—
651C22×C4C23×D714yes—
652C22×C4C23×D714yes—
653C22×C4C23×D718yes—
654C22×C4C23×D712yes—
655C22×C4C23×D711yescharacteristic
656C22×C4C23×D711yescharacteristic
657C22×C4C23×D711yescharacteristic
658C22×C4C23×D711yescharacteristic
659C22×C4C23×D711yescharacteristic
660C22×C4C23×D712yes—
661C22×C4C23×D712yes—
662C22×C4C23×D714yes—
663C22×C4C23×D711yescharacteristic
664C4⋊C4—716no—
665C4⋊C4—716no—
666C4⋊C4—716no—
667C4⋊C4—716no—
668C4⋊C4—716no—
669C4⋊C4—716no—
670C4⋊C4—78no—
671C4⋊C4—78no—
672C4⋊C4—78no—
673C4⋊C4—78no—
674C4⋊C4—716no—
675C4⋊C4—716no—
676C4⋊C4—78no—
677C4⋊C4—78no—
678C4⋊C4C23×D718yes—
679C4⋊C4C23×D718yes—
680C4⋊C4C23×D718yes—
681C4⋊C4C23×D718yes—
682C4⋊C4C23×D714yes—
683C4⋊C4C23×D714yes—
684C22⋊C4—716no—
685C22⋊C4—716no—
686C22⋊C4—716no—
687C22⋊C4—716no—
688C22⋊C4—716no—
689C22⋊C4—716no—
690C22⋊C4—716no—
691C22⋊C4C23×D718yes—
692C22⋊C4C23×D718yes—
693C22⋊C4C23×D718yes—
694C22⋊C4C23×D718yes—
695C22⋊C4C23×D718yes—
696C42—716no—
697C42C23×D714yes—
698C42C23×D714yes—
699C42C23×D714yes—
700C42C23×D714yes—
701C42C23×D718yes—
702C2×C7—24no—
703C2×C7—44no—
704C2×C7#355914yescomplemented
705C2×C7C22×H(5,𝔽2)11yescharacteristic
706C2×C7C22×2−1+411yescharacteristic
707C2×C7C2×#58511yescharacteristic
708D7—48no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—78no—
715C23—148no—
716C23—148no—
717C23—148no—
718C23#655314yes—
719C23C24×D714yes—
720C23C24×D712yes—
721C23C24×D711yescharacteristic
722Q8—44no—
723Q8—288no—
724Q8—2816no—
725D4—216no—
726D4—44no—
727D4—1432no—
728D4—1416no—
729D4—288no—
730D4—288no—
731D4—2816no—
732D4—2816no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—216no—
744C2×C4—44no—
745C2×C4—78no—
746C2×C4—78no—
747C2×C4—78no—
748C2×C4—148no—
749C2×C4—1416no—
750C2×C4—148no—
751C2×C4—148no—
752C2×C4—2816no—
753C2×C4—2816no—
754C2×C4—2816no—
755C2×C4—288no—
756C2×C4—2816no—
757C2×C4#655414yes—
758C2×C4C24×D714yes—
759C2×C4C24×D712yes—
760C2×C4C24×D712yes—
761C2×C4C24×D712yes—
762C2×C4C24×D712yes—
763C2×C4C24×D712yes—
764C2×C4C24×D714yes—
765C2×C4C24×D714yes—
766C2×C4C24×D712yes—
767C7C2×#355911yescharacteristic, complemented, Sylow
768C22—22no—
769C22—22no—
770C22—28no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—48no—
775C22—148no—
776C22—148no—
777C22—148no—
778C22—2816no—
779C22C2×#655314yes—
780C22C2×#655312yes—
781C22C2×#655412yes—
782C22#9061612yes—
783C22C25×D711yescharacteristic
784C4—24no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—24no—
789C4—22no—
790C4—22no—
791C4—24no—
792C4—148no—
793C4—148no—
794C4—148no—
795C4C2×#655414yes—
796C2—24no—
797C2—44no—
798C2—288no—
799C2#1174320814yesdirect product factor
800C2C22×#655411yescharacteristic
801C2C22×#655311yescharacteristic
802C2C2×#9061611yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#529C2
socleC23×C7C25
hypercenterC2×#529D7
hypocenterC7C2×#3559
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C7×#529C2semidirect
2. #11743208C2direct (N × H)
3. C2×#90398C2semidirect
4. C2×#90390C2semidirect
5. C2×#90375C2semidirect
6. C2×#90346C2semidirect
7. C2×#90336C2semidirect
8. C2×#90288C2semidirect
9. C2×#90270C2semidirect
10. C2×#90256C2semidirect
11. C2×#90256C2semidirect
12. C2×#90246C2semidirect
13. C2×#90226C2semidirect
14. C2×#90210C2semidirect
15. C2×#90168C2semidirect
16. C22×#6433C2semidirect
19. C7×#529C22semidirect
44. #90398C22semidirect
45. #90390C22semidirect
46. #90375C22semidirect
47. #90346C22semidirect
48. #90336C22semidirect
49. #90288C22semidirect
50. #90270C22semidirect
51. #90256C22semidirect
52. #90256C22semidirect
53. #90246C22semidirect
54. #90226C22semidirect
55. #90210C22semidirect
76. #90168C22semidirect
88. C2×#6433C22semidirect
226. C2×#529D7semidirect
344. #529C2×D7semidirect
704. C2×C7#3559semidirect
767. C7C2×#3559semidirect
799. C2#11743208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5292
#117432082
C2×#903982
C2×#903902
C2×#903752
C2×#903462
C2×#903362
C2×#902882
C2×#902702
C2×#902562
C2×#902462
C2×#902262
C2×#902102
C2×#901682
C22×#64332
C2×#35597