Finite Group Databasebeta

← C2×#11743301 #14261158

Subgroups — C2×#11743301 #14261158

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×#532C211yesmaximal, characteristic, complemented
2C2×#90515C214yesmaximal, complemented
3#11743301C2132yesmaximal, direct product factor
4C2×#90420C212yesmaximal, complemented
5C2×#90410C212yesmaximal, complemented
6C2×#90363C212yesmaximal, complemented
7C2×#90375C212yesmaximal, complemented
8C2×#90309C212yesmaximal, complemented
9C2×#90302C212yesmaximal, complemented
10C2×#90293C212yesmaximal, complemented
11C2×#90288C212yesmaximal, complemented
12C2×#90249C212yesmaximal, complemented
13C2×#90230C212yesmaximal, complemented
14C2×#90255C214yesmaximal, complemented
15C2×#90170C211yesmaximal, characteristic, complemented
16C22×#6433C211yesmaximal, characteristic, complemented
17C22×C7×#41C2212yes—
18C22×#1159C2214yes—
19C7×#532C22116yescomplemented
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#127C2211yescharacteristic
22C2×C7×#124C2212yes—
23C2×C7×#121C2212yes—
24C2×C7×#121C2212yes—
25C2×C4×C7×D4C2212yes—
26C2×C4×C7×D4C2212yes—
27C22×C42×C7C2211yescharacteristic
28#90515C22164yescomplemented
29C2×#6509C2214yes—
30C2×#6507C2214yes—
31C2×#6502C2214yes—
32C2×#6502C2214yes—
33C2×#6502C2214yes—
34C2×#6501C2212yes—
35C2×#6501C2212yes—
36C2×#6498C2214yes—
37C2×#6498C2214yes—
38C2×#6498C2214yes—
39C2×D4×Dic7C2214yes—
40C2×D4×Dic7C2212yes—
41C2×D4×Dic7C2212yes—
42C2×#6493C2211yescharacteristic
43C2×#6492C2212yes—
44C2×#6492C2214yes—
45C2×C4×C22⋊D7C2212yes—
46C2×C4×C22⋊D7C2214yes—
47C22×C4⋊Dic7C2211yescharacteristic
48C22×C4⋊Dic7C2211yescharacteristic
49C2×#6487C2211yescharacteristic
50C2×#6487C2214yes—
51C22×Dic7⋊C4C2212yes—
52C22×Dic7⋊C4C2212yes—
53C22×Dic7⋊C4C2214yes—
54#90420C22132yescomplemented
55#90410C22132yescomplemented
56#90375C22132yescomplemented
57#90363C22132yescomplemented
58#90309C22132yescomplemented
59#90302C22132yescomplemented
60#90293C22132yescomplemented
61#90288C22132yescomplemented
62#90255C22164yescomplemented
63#90249C22132yescomplemented
64#90230C22132yescomplemented
65C2×#6459C2214yes—
66C2×#6455C2212yes—
67C2×D7×C4⋊C4C2212yes—
68C2×#6453C2212yes—
69C2×#6452C2214yes—
70C2×#6451C2212yes—
71C2×#6449C2214yes—
72C2×#6447C2214yes—
73C2×#6446C2214yes—
74C2×#6442C2214yes—
75C2×#6442C2214yes—
76C2×#6441C2214yes—
77C2×#6441C2214yes—
78C2×#6441C2214yes—
79#90170C22116yescomplemented
80C2×#6439C2212yes—
81C2×#6438C2211yescharacteristic
82C2×C4×D28C2211yescharacteristic
83C2×#6435C2212yes—
84C2×#6433C2212yes—
85C2×#6433C2212yes—
86C2×#6433C2212yes—
87C2×#6433C2212yes—
88C2×#6433C2211yescharacteristic
89C2×#6433C22116yescomplemented
90C2×C4×Dic14C2211yescharacteristic
91C2×#3559—71nomaximal, Sylow
92C2×C7×#41—48no—
93C2×C7×#41C23116yes—
94C22×C7×Q8C2312yes—
95C22×C7×D4C2314yes—
96C22×C7×D4C2312yes—
97C22×C7×D4C2312yes—
98C22×C7×D4C2312yes—
99C23×C4×C7C2311yescharacteristic
100C23×C4×C7C2311yescharacteristic
101C23×C4×C7C2314yes—
102C23×C4×C7C2311yescharacteristic
103C22×C22⋊D7C2312yes—
104C22×C22⋊D7C2314yes—
105C22×C22⋊D7C2314yes—
106C23×Dic7C2312yes—
107C23×Dic7C2314yes—
108C23×Dic7C2314yes—
109C23×Dic7C2312yes—
110C2×#1159—416no—
111C2×#1159C23132yes—
112C22×D28C2311yescharacteristic
113C22×C4×D7C2312yes—
114C22×C4×D7C2314yes—
115C22×Dic14C2311yescharacteristic
116C22×Dic14C2314yes—
117C7×C4⋊Q8C2318yes—
118C7×#127C2318yes—
119C7×#124C23116yes—
120C7×#121C23116yes—
121C7×#121C23116yes—
122C4×C7×D4C23116yes—
123C4×C7×D4C23116yes—
124C2×C7×C4⋊C4C2312yes—
125C2×C7×C4⋊C4C2312yes—
126C2×C7×C22⋊C4C2314yes—
127C2×C7×C22⋊C4C2314yes—
128C2×C42×C7C2311yescharacteristic
129C2×C42×C7C2311yescharacteristic
130C2×C42×C7C2311yescharacteristic
131C2×C42×C7C2311yescharacteristic
132C2×C42×C7C2318yes—
133C2×C22⋊Dic7C2314yes—
134C2×C22⋊Dic7C2314yes—
135C2×C22⋊Dic7C2314yes—
136C2×C22⋊Dic7C2314yes—
137C2×C22⋊Dic7C2312yes—
138#6509C23132yes—
139#6507C23132yes—
140#6502C23132yes—
141#6502C23132yes—
142#6502C23132yes—
143#6501C23116yes—
144#6501C23116yes—
145#6498C23132yes—
146#6498C23132yes—
147#6498C23132yes—
148D4×Dic7C23116yes—
149D4×Dic7C23116yes—
150D4×Dic7C23132yes—
151#6493C2318yes—
152#6492C23116yes—
153#6492C23132yes—
154C4×C22⋊D7C23116yes—
155C4×C22⋊D7C23132yes—
156C2×(C2×D7)⋊C4C2312yes—
157C2×(C2×D7)⋊C4C2312yes—
158C2×(C2×D7)⋊C4C2312yes—
159C2×(C2×D7)⋊C4C2312yes—
160C2×(C2×D7)⋊C4C2314yes—
161C2×C4⋊Dic7C2311yescharacteristic
162C2×C4⋊Dic7C2312yes—
163C2×C4⋊Dic7C2312yes—
164C2×C4⋊Dic7C2312yes—
165C2×C4⋊Dic7C2312yes—
166C2×C4⋊Dic7C2311yescharacteristic
167C2×C4⋊Dic7C2318yes—
168C2×C4⋊Dic7C2318yes—
169C2×C4⋊Dic7C2314yes—
170#6487C2318yes—
171#6487C23132yes—
172C2×Dic7⋊C4C2312yes—
173C2×Dic7⋊C4C2314yes—
174C2×Dic7⋊C4C2314yes—
175C2×Dic7⋊C4C2314yes—
176C2×Dic7⋊C4C2314yes—
177C2×Dic7⋊C4C2312yes—
178C2×Dic7⋊C4C2312yes—
179C2×Dic7⋊C4C23116yes—
180C2×Dic7⋊C4C23116yes—
181C2×Dic7⋊C4C2312yes—
182C2×Dic7⋊C4C2314yes—
183C2×Dic7⋊C4C2314yes—
184C2×Dic7⋊C4C2314yes—
185C2×Dic7⋊C4C23132yes—
186C2×C4×Dic7C2312yes—
187C2×C4×Dic7C2314yes—
188#6459C23132yes—
189#6455C23116yes—
190D7×C4⋊C4C23116yes—
191#6453C23116yes—
192#6452C23132yes—
193#6451C23116yes—
194#6449C23132yes—
195#6447C23132yes—
196#6446C23132yes—
197#6442C23132yes—
198#6442C23132yes—
199#6441C23132yes—
200#6441C23132yes—
201#6441C23132yes—
202#6439C23116yes—
203#6438C2318yes—
204C4×D28C2318yes—
205#6435C23116yes—
206#6433C23116yes—
207#6433C23116yes—
208#6433C23116yes—
209#6433C23116yes—
210#6433C2318yes—
211C4×Dic14C2318yes—
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—72no—
223C2×#539—74no—
224C2×#537—72no—
225C2×#532D711yescharacteristic, complemented
226C2×#529—71no—
227C22×#125—71no—
228C24×C7C2414yes—
229C24×C7C2411yescharacteristic
230C23×D7C2412yes—
231C7×#41—432no—
232C2×C7×Q8—44no—
233C2×C7×Q8C2418yes—
234C2×C7×D4—216no—
235C2×C7×D4—28no—
236C2×C7×D4—44no—
237C2×C7×D4—44no—
238C2×C7×D4C2418yes—
239C2×C7×D4C24116yes—
240C2×C7×D4C2418yes—
241C2×C7×D4C2418yes—
242C22×C4×C7—24no—
243C22×C4×C7—24no—
244C22×C4×C7—42no—
245C22×C4×C7—48no—
246C22×C4×C7C2414yes—
247C22×C4×C7C2411yescharacteristic
248C22×C4×C7C2411yescharacteristic
249C22×C4×C7C2411yescharacteristic
250C22×C4×C7C2411yescharacteristic
251C22×C4×C7C2414yes—
252C22×C4×C7C2411yescharacteristic
253C22×C4×C7C2414yes—
254C22×C4×C7C2414yes—
255C22×C4×C7C24116yes—
256C22×C4×C7C2411yescharacteristic
257C2×C22⋊D7—28no—
258C2×C22⋊D7—48no—
259C2×C22⋊D7—48no—
260C2×C22⋊D7C2418yes—
261C2×C22⋊D7C24116yes—
262C2×C22⋊D7C24116yes—
263C22×Dic7—28no—
264C22×Dic7—48no—
265C22×Dic7—48no—
266C22×Dic7—44no—
267C22×Dic7C2412yes—
268C22×Dic7C2414yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2414yes—
272C22×Dic7C2418yes—
273C22×Dic7C24116yes—
274C22×Dic7C24116yes—
275C22×Dic7C2418yes—
276#1159—464no—
277C2×D28—42no—
278C2×D28C2414yes—
279C2×C4×D7—28no—
280C2×C4×D7—48no—
281C2×C4×D7C2418yes—
282C2×C4×D7C24116yes—
283C2×Dic14—42no—
284C2×Dic14—48no—
285C2×Dic14C2414yes—
286C2×Dic14C24116yes—
287C7×C4⋊C4C2418yes—
288C7×C4⋊C4C2418yes—
289C7×C22⋊C4C24116yes—
290C7×C22⋊C4C24116yes—
291C42×C7C2414yes—
292C42×C7C2414yes—
293C42×C7C2414yes—
294C42×C7C2414yes—
295C22⋊Dic7C24116yes—
296C22⋊Dic7C24116yes—
297C22⋊Dic7C24116yes—
298C22⋊Dic7C24116yes—
299C22⋊Dic7C2418yes—
300(C2×D7)⋊C4C2418yes—
301(C2×D7)⋊C4C2418yes—
302(C2×D7)⋊C4C2418yes—
303(C2×D7)⋊C4C2418yes—
304(C2×D7)⋊C4C24116yes—
305C4⋊Dic7C2414yes—
306C4⋊Dic7C2418yes—
307C4⋊Dic7C2418yes—
308C4⋊Dic7C2418yes—
309C4⋊Dic7C2418yes—
310C4⋊Dic7C2414yes—
311C4⋊Dic7C24116yes—
312Dic7⋊C4C2418yes—
313Dic7⋊C4C24116yes—
314Dic7⋊C4C24116yes—
315Dic7⋊C4C24116yes—
316Dic7⋊C4C24116yes—
317Dic7⋊C4C2418yes—
318Dic7⋊C4C2418yes—
319Dic7⋊C4C2418yes—
320Dic7⋊C4C24116yes—
321Dic7⋊C4C24116yes—
322Dic7⋊C4C24116yes—
323C4×Dic7C2418yes—
324C4×Dic7C24116yes—
325C22×#41—74no—
326C22×#41C2×D712yes—
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—732no—
337#539—764no—
338#537—732no—
339#532C2×D7116yescomplemented
340C2×C4⋊Q8—74no—
341C2×C4⋊Q8—72no—
342C2×C4⋊Q8C2×D711yescharacteristic
343C2×#127C2×D711yescharacteristic
344#529—716no—
345C2×#126—74no—
346C2×#126—74no—
347C2×#126—72no—
348C2×#125—74no—
349C2×#125—72no—
350C2×#125—72no—
351C2×#125—72no—
352C2×#125—72no—
353C2×#125—72no—
354C2×#125—71no—
355C2×#125—716no—
356C2×#124—71no—
357C2×#124C2×D712yes—
358C2×#123—74no—
359C2×#123—74no—
360C2×#123—74no—
361C2×#123—72no—
362C2×#123—74no—
363C2×#123—74no—
364C2×#123—74no—
365C2×C22⋊Q8—74no—
366C2×C22⋊Q8—71no—
367C2×C22⋊Q8—74no—
368C2×C22⋊Q8—74no—
369C2×C22⋊Q8—74no—
370C2×C22⋊Q8—74no—
371C2×C22⋊Q8—74no—
372C2×#121—74no—
373C2×#121—74no—
374C2×#121—72no—
375C2×#121—72no—
376C2×#121—74no—
377C2×#121—71no—
378C2×#121—74no—
379C2×#121C2×D712yes—
380C2×#121C2×D712yes—
381C2×C4×Q8—71no—
382C2×C4×D4—74no—
383C2×C4×D4—72no—
384C2×C4×D4—72no—
385C2×C4×D4—72no—
386C2×C4×D4—74no—
387C2×C4×D4—71no—
388C2×C4×D4C2×D712yes—
389C2×C4×D4C2×D712yes—
390C2×#117—72no—
391C2×#117—72no—
392C22×C4⋊C4—72no—
393C22×C4⋊C4—72no—
394C22×C4⋊C4—74no—
395C22×C4⋊C4—71no—
396C22×C4⋊C4—71no—
397C22×C4⋊C4—72no—
398C22×C42C2×D711yescharacteristic
399C23×C7—22no—
400C23×C7—22no—
401C23×C7—28no—
402C23×C7—28no—
403C23×C7—28no—
404C23×C7H(5,𝔽2)14yes—
405C23×C7C2518yes—
406C23×C7C2512yes—
407C23×C7C2511yescharacteristic
408C22×D7—24no—
409C22×D7—24no—
410C22×D7—24no—
411C22×D7C2514yes—
412C7×Q8—48no—
413C7×D4—232no—
414C7×D4—216no—
415C7×D4—48no—
416C7×D4—48no—
417C2×C4×C7—28no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—28no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—28no—
425C2×C4×C7—44no—
426C2×C4×C7—416no—
427C2×C4×C72−1+414yes—
428C2×C4×C7C2518yes—
429C2×C4×C7C2512yes—
430C2×C4×C7C2512yes—
431C2×C4×C7C2512yes—
432C2×C4×C7C2512yes—
433C2×C4×C7C2512yes—
434C2×C4×C7C2512yes—
435C22⋊D7—216no—
436C22⋊D7—416no—
437C22⋊D7—416no—
438C2×Dic7—24no—
439C2×Dic7—28no—
440C2×Dic7—216no—
441C2×Dic7—24no—
442C2×Dic7—24no—
443C2×Dic7—28no—
444C2×Dic7—416no—
445C2×Dic7—416no—
446C2×Dic7—48no—
447C2×Dic7C2514yes—
448C2×Dic7C2518yes—
449C2×Dic7C2514yes—
450C2×Dic7C2514yes—
451C2×Dic7C2518yes—
452D28—44no—
453C4×D7—216no—
454C4×D7—416no—
455Dic14—44no—
456Dic14—416no—
457C2×#41—48no—
458C2×#41—732no—
459C2×#41—2816no—
460C2×#41C22×D7116yes—
461C22×Q8—71no—
462C22×Q8—74no—
463C22×Q8C22×D712yes—
464C22×D4—72no—
465C22×D4—74no—
466C22×D4—74no—
467C22×D4—71no—
468C22×D4C22×D712yes—
469C22×D4C22×D714yes—
470C22×D4C22×D712yes—
471C22×D4C22×D712yes—
472C23×C4—72no—
473C23×C4—72no—
474C23×C4—74no—
475C23×C4—74no—
476C23×C4—72no—
477C23×C4—74no—
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D714yes—
482C4⋊Q8—732no—
483C4⋊Q8—716no—
484C4⋊Q8C22×D718yes—
485#127C22×D718yes—
486#126—732no—
487#126—732no—
488#126—716no—
489#125—732no—
490#125—716no—
491#125—716no—
492#125—716no—
493#125—716no—
494#125—716no—
495#125—78no—
496#124—78no—
497#124C22×D7116yes—
498#123—732no—
499#123—732no—
500#123—732no—
501#123—716no—
502#123—732no—
503#123—732no—
504#123—732no—
505C22⋊Q8—732no—
506C22⋊Q8—78no—
507C22⋊Q8—732no—
508C22⋊Q8—732no—
509C22⋊Q8—732no—
510C22⋊Q8—732no—
511C22⋊Q8—732no—
512#121—732no—
513#121—732no—
514#121—716no—
515#121—732no—
516#121—716no—
517#121—78no—
518#121—732no—
519#121C22×D7116yes—
520#121C22×D7116yes—
521C4×Q8—78no—
522C4×D4—732no—
523C4×D4—716no—
524C4×D4—716no—
525C4×D4—716no—
526C4×D4—732no—
527C4×D4—78no—
528C4×D4C22×D7116yes—
529C4×D4C22×D7116yes—
530#117—716no—
531#117—716no—
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—732no—
549C2×C4⋊C4—72no—
550C2×C4⋊C4—72no—
551C2×C4⋊C4—74no—
552C2×C4⋊C4—72no—
553C2×C4⋊C4—71no—
554C2×C4⋊C4—71no—
555C2×C4⋊C4—716no—
556C2×C4⋊C4C22×D712yes—
557C2×C4⋊C4C22×D712yes—
558C2×C22⋊C4—72no—
559C2×C22⋊C4—74no—
560C2×C22⋊C4—74no—
561C2×C22⋊C4—74no—
562C2×C22⋊C4—74no—
563C2×C22⋊C4—72no—
564C2×C22⋊C4—74no—
565C2×C22⋊C4—72no—
566C2×C22⋊C4—72no—
567C2×C22⋊C4—72no—
568C2×C22⋊C4C22×D714yes—
569C2×C22⋊C4C22×D714yes—
570C2×C42—72no—
571C2×C42—74no—
572C2×C42C22×D711yescharacteristic
573C2×C42C22×D711yescharacteristic
574C2×C42C22×D711yescharacteristic
575C2×C42C22×D711yescharacteristic
576C2×C42C22×D718yes—
577C22×C7—22no—
578C22×C7—22no—
579C22×C7—28no—
580C22×C7—28no—
581C22×C7—28no—
582C22×C7—28no—
583C22×C7—416no—
584C22×C7C2×H(5,𝔽2)14yes—
585C22×C7C2×H(5,𝔽2)12yes—
586C22×C7C2×2−1+412yes—
587C22×C7#58512yes—
588C22×C7C2611yescharacteristic
589C2×D7—24no—
590C2×D7—24no—
591C2×D7—24no—
592C2×D7—48no—
593C4×C7—28no—
594C4×C7—22no—
595C4×C7—22no—
596C4×C7—22no—
597C4×C7—22no—
598C4×C7—22no—
599C4×C7C2×2−1+414yes—
600Dic7—24no—
601Dic7—28no—
602Dic7—24no—
603Dic7—24no—
604Dic7—28no—
605C24—72no—
606C24C23×D714yes—
607C24C23×D711yescharacteristic
608#41—432no—
609#41—2864no—
610C2×Q8—44no—
611C2×Q8—74no—
612C2×Q8—716no—
613C2×Q8—282no—
614C2×Q8—288no—
615C2×Q8C23×D718yes—
616C2×D4—216no—
617C2×D4—28no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—78no—
621C2×D4—716no—
622C2×D4—716no—
623C2×D4—74no—
624C2×D4—148no—
625C2×D4—282no—
626C2×D4—288no—
627C2×D4—288no—
628C2×D4C23×D718yes—
629C2×D4C23×D7116yes—
630C2×D4C23×D718yes—
631C2×D4C23×D718yes—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—42no—
635C22×C4—48no—
636C22×C4—78no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—74no—
640C22×C4—72no—
641C22×C4—74no—
642C22×C4—78no—
643C22×C4—716no—
644C22×C4—716no—
645C22×C4—78no—
646C22×C4—716no—
647C22×C4—148no—
648C22×C4—148no—
649C22×C4—288no—
650C22×C4—284no—
651C22×C4—288no—
652C22×C4—288no—
653C22×C4C23×D714yes—
654C22×C4C23×D714yes—
655C22×C4C23×D714yes—
656C22×C4C23×D711yescharacteristic
657C22×C4C23×D711yescharacteristic
658C22×C4C23×D711yescharacteristic
659C22×C4C23×D711yescharacteristic
660C22×C4C23×D711yescharacteristic
661C22×C4C23×D714yes—
662C22×C4C23×D7116yes—
663C22×C4C23×D711yescharacteristic
664C4⋊C4—716no—
665C4⋊C4—78no—
666C4⋊C4—716no—
667C4⋊C4—716no—
668C4⋊C4—716no—
669C4⋊C4—716no—
670C4⋊C4—716no—
671C4⋊C4—716no—
672C4⋊C4—78no—
673C4⋊C4—78no—
674C4⋊C4—78no—
675C4⋊C4—78no—
676C4⋊C4—78no—
677C4⋊C4—78no—
678C4⋊C4—78no—
679C4⋊C4—716no—
680C4⋊C4—74no—
681C4⋊C4—74no—
682C4⋊C4C23×D718yes—
683C4⋊C4C23×D718yes—
684C22⋊C4—78no—
685C22⋊C4—716no—
686C22⋊C4—716no—
687C22⋊C4—716no—
688C22⋊C4—716no—
689C22⋊C4—78no—
690C22⋊C4—716no—
691C22⋊C4—78no—
692C22⋊C4—78no—
693C22⋊C4—78no—
694C22⋊C4C23×D7116yes—
695C22⋊C4C23×D7116yes—
696C42—78no—
697C42—716no—
698C42C23×D714yes—
699C42C23×D714yes—
700C42C23×D714yes—
701C42C23×D714yes—
702C2×C7—24no—
703C2×C7—48no—
704C2×C7#355914yescomplemented
705C2×C7C22×H(5,𝔽2)11yescharacteristic
706C2×C7C22×2−1+411yescharacteristic
707C2×C7C2×#58511yescharacteristic
708D7—44no—
709C23—22no—
710C23—22no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—74no—
715C23—144no—
716C23—144no—
717C23—144no—
718C23#654814yes—
719C23C24×D718yes—
720C23C24×D712yes—
721C23C24×D711yescharacteristic
722Q8—48no—
723Q8—284no—
724Q8—2816no—
725D4—232no—
726D4—216no—
727D4—48no—
728D4—48no—
729D4—1416no—
730D4—284no—
731D4—2816no—
732D4—2816no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—44no—
742C2×C4—416no—
743C2×C4—74no—
744C2×C4—74no—
745C2×C4—78no—
746C2×C4—74no—
747C2×C4—78no—
748C2×C4—148no—
749C2×C4—1416no—
750C2×C4—144no—
751C2×C4—144no—
752C2×C4—148no—
753C2×C4—144no—
754C2×C4—1416no—
755C2×C4—2816no—
756C2×C4—288no—
757C2×C4—2816no—
758C2×C4—2816no—
759C2×C4#655414yes—
760C2×C4C24×D718yes—
761C2×C4C24×D712yes—
762C2×C4C24×D712yes—
763C2×C4C24×D712yes—
764C2×C4C24×D712yes—
765C2×C4C24×D712yes—
766C2×C4C24×D712yes—
767C7C2×#355911yescharacteristic, complemented, Sylow
768C22—22no—
769C22—22no—
770C22—28no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—416no—
775C22—144no—
776C22—144no—
777C22—144no—
778C22—288no—
779C22C2×#654814yes—
780C22C2×#654812yes—
781C22C2×#655412yes—
782C22#9061612yes—
783C22C25×D711yescharacteristic
784C4—22no—
785C4—22no—
786C4—28no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—148no—
791C4—144no—
792C4—144no—
793C4—148no—
794C4—144no—
795C4C2×#655414yes—
796C2—24no—
797C2—48no—
798C2—284no—
799C2#1174330114yesdirect product factor
800C2C22×#654811yescharacteristic
801C2C22×#655411yescharacteristic
802C2C2×#9061611yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#532C2
socleC23×C7C25
hypercenterC2×#532D7
hypocenterC7C2×#3559
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×C7×#532C2semidirect
2. C2×#90515C2semidirect
3. #11743301C2direct (N × H)
4. C2×#90420C2semidirect
5. C2×#90410C2semidirect
6. C2×#90363C2semidirect
7. C2×#90375C2semidirect
8. C2×#90309C2semidirect
9. C2×#90302C2semidirect
10. C2×#90293C2semidirect
11. C2×#90288C2semidirect
12. C2×#90249C2semidirect
13. C2×#90230C2semidirect
14. C2×#90255C2semidirect
15. C2×#90170C2semidirect
16. C22×#6433C2semidirect
19. C7×#532C22semidirect
28. #90515C22semidirect
54. #90420C22semidirect
55. #90410C22semidirect
56. #90375C22semidirect
57. #90363C22semidirect
58. #90309C22semidirect
59. #90302C22semidirect
60. #90293C22semidirect
61. #90288C22semidirect
62. #90255C22semidirect
63. #90249C22semidirect
64. #90230C22semidirect
79. #90170C22semidirect
89. C2×#6433C22semidirect
225. C2×#532D7semidirect
339. #532C2×D7semidirect
704. C2×C7#3559semidirect
767. C7C2×#3559semidirect
799. C2#11743301direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5322
C2×#905152
#117433012
C2×#904202
C2×#904102
C2×#903632
C2×#903752
C2×#903092
C2×#903022
C2×#902932
C2×#902882
C2×#902492
C2×#902302
C2×#902552
C2×#901702
C22×#64332
C2×#35597