Finite Group Databasebeta

← C2×#11743578 #14262237

Subgroups — C2×#11743578 #14262237

Order 1792.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#541C211yesmaximal, characteristic, complemented
2#11743578C2132yesmaximal, direct product factor
3C2×#90422C211yesmaximal, characteristic, complemented
4C2×D7×C4⋊Q8C211yesmaximal, characteristic, complemented
5C2×#90399C214yesmaximal, complemented
6C2×#90393C214yesmaximal, complemented
7C2×#90384C214yesmaximal, complemented
8C2×#90388C211yesmaximal, characteristic, complemented
9C2×#90376C214yesmaximal, complemented
10C2×#90379C211yesmaximal, characteristic, complemented
11C2×#90319C212yesmaximal
12C2×#90313C212yesmaximal, complemented
13C2×#90269C212yesmaximal, complemented
14C2×#90263C212yesmaximal, complemented
15C2×#90209C211yesmaximal, characteristic, complemented
16C2×#90213C211yesmaximal, characteristic
17C22×Q8×D7C2212yes—
18C22×#1157C2211yescharacteristic
19C7×#541C22116yescomplemented
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#126C2214yes—
22C2×C7×#125C2211yescharacteristic
23C2×C7×#125C2214yes—
24C2×C7×C22⋊Q8C2212yes—
25C2×C4×C7×Q8C2212yes—
26C2×C7×#117C2211yescharacteristic
27C2×#6509C2212yes—
28C2×Q8×Dic7C2212yes—
29C2×#6507C2212yes—
30C2×#6487C2212yes—
31C22×C4×Dic7C2211yescharacteristic
32#90422C22116yescomplemented
33D7×C4⋊Q8C22116yescomplemented
34#90399C22164yescomplemented
35#90393C22164yescomplemented
36#90388C22116yescomplemented
37#90384C22164yescomplemented
38#90379C22116yescomplemented
39#90376C22164yescomplemented
40#90319C22132yes—
41#90313C22132yescomplemented
42#90269C22132yescomplemented
43#90263C22132yescomplemented
44#90213C22116yes—
45#90209C22116yescomplemented
46C2×#6461C2214yes—
47C2×#6461C2214yes—
48C2×#6460C2212yes—
49C2×#6459C2214yes—
50C2×#6459C2214yes—
51C2×#6457C2214yes—
52C2×#6456C2212yes—
53C2×#6455C2212yes—
54C2×#6455C2214yes—
55C2×D7×C4⋊C4C2214yes—
56C2×#6453C2214yes—
57C2×#6452C2214yes—
58C2×#6452C2214yes—
59C2×#6452C2214yes—
60C2×#6452C2214yes—
61C2×#6451C2214yes—
62C2×#6451C2212yes—
63C2×#6451C2214yes—
64C2×#6450C2212yes—
65C2×#6450C2214yes—
66C2×#6450C2212yes—
67C2×#6450C2214yes—
68C2×#6450C2214yes—
69C2×#6448C2214yes—
70C2×#6446C2214yes—
71C2×(C22⋊D7)⋊C4C2212yes—
72C2×(C22⋊D7)⋊C4C2212yes—
73C2×#6442C2214yes—
74C2×#6441C2214yes—
75C2×#6440C2214yes—
76C2×#6435C2211yescharacteristic
77C2×#6435C2211yescharacteristic
78C2×#6435C2214yes—
79C2×#6435C2214yes—
80C2×C42×D7C2211yescharacteristic
81C2×C42×D7C2211yescharacteristic
82C2×#6433C2211yescharacteristic
83C2×#6432C2211yescharacteristic
84C2×C4×Dic14C2212yes—
85C2×C4×Dic14C2214yes—
86C2×C4×Dic14C2214yes—
87C2×#3509—71nomaximal, Sylow
88C22×C7×Q8C2312yes—
89C23×C4×C7C2311yescharacteristic
90C22×C22⋊D7C2311yescharacteristic
91C22×C22⋊D7C2311yescharacteristic
92C23×Dic7C2312yes—
93C2×Q8×D7—216no—
94C2×Q8×D7C23116yes—
95C2×#1157—28no—
96C2×#1157C2318yes—
97C22×D28C2311yescharacteristic
98C22×C4×D7C2312yes—
99C22×C4×D7C2311yescharacteristic
100C22×C4×D7C2312yes—
101C22×C4×D7C2314yes—
102C22×C4×D7C2311yescharacteristic
103C22×Dic14C2312yes—
104C22×Dic14C2314yes—
105C22×Dic14C2314yes—
106C22×Dic14C2311yescharacteristic
107C7×C4⋊Q8C2318yes—
108C7×#126C23132yes—
109C7×#125C23132yes—
110C7×#125C2318yes—
111C7×C22⋊Q8C23116yes—
112C4×C7×Q8C23116yes—
113C7×#117C2318yes—
114C2×C7×C4⋊C4C2314yes—
115C2×C7×C4⋊C4C2312yes—
116C2×C7×C4⋊C4C2312yes—
117C2×C7×C4⋊C4C2314yes—
118C2×C7×C4⋊C4C2314yes—
119C2×C7×C4⋊C4C2314yes—
120C2×C7×C22⋊C4C2314yes—
121C2×C7×C22⋊C4C2312yes—
122C2×C42×C7C2311yescharacteristic
123C2×C42×C7C2314yes—
124C2×C42×C7C2311yescharacteristic
125C2×C22⋊Dic7C2314yes—
126#6509C23116yes—
127Q8×Dic7C23116yes—
128#6507C23116yes—
129C2×(C2×D7)⋊C4C2312yes—
130C2×(C2×D7)⋊C4C2312yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×C4⋊Dic7C2312yes—
135C2×C4⋊Dic7C2314yes—
136C2×C4⋊Dic7C2314yes—
137C2×C4⋊Dic7C2314yes—
138#6487C23116yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2312yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×Dic7⋊C4C2312yes—
148C2×Dic7⋊C4C2314yes—
149C2×C4×Dic7C2312yes—
150C2×C4×Dic7C2314yes—
151C2×C4×Dic7C2314yes—
152C2×C4×Dic7C2314yes—
153C2×C4×Dic7C2311yescharacteristic
154C2×C4×Dic7C2312yes—
155C2×C4×Dic7C2311yescharacteristic
156C2×C4×Dic7C2314yes—
157C2×C4×Dic7C2312yes—
158C2×C4×Dic7C2318yes—
159#6461C23132yes—
160#6461C23132yes—
161#6460C23116yes—
162#6459C23132yes—
163#6459C23132yes—
164#6457C23132yes—
165#6456C23116yes—
166#6455C23116yes—
167#6455C23132yes—
168D7×C4⋊C4C23132yes—
169#6453C23132yes—
170#6452C23132yes—
171#6452C23132yes—
172#6452C23132yes—
173#6452C23132yes—
174#6451C23132yes—
175#6451C23132yes—
176#6451C23116yes—
177#6450C23116yes—
178#6450C23132yes—
179#6450C23132yes—
180#6450C23132yes—
181#6450C23116yes—
182#6448C23132yes—
183#6446C23132yes—
184(C22⋊D7)⋊C4C23116yes—
185(C22⋊D7)⋊C4C23116yes—
186#6442C23132yes—
187#6441C23132yes—
188#6440C23132yes—
189#6435C23132yes—
190#6435C23132yes—
191#6435C2318yes—
192#6435C2318yes—
193C42×D7C2318yes—
194C42×D7C2318yes—
195#6433C2318yes—
196#6432C2318yes—
197C4×Dic14C23132yes—
198C4×Dic14C23132yes—
199C4×Dic14C23116yes—
200#3509—732no—
201C2×#557—74no—
202C2×#556—74no—
203C2×#552—74no—
204C2×#552—74no—
205C2×#541—71no—
206C2×#541—71no—
207C2×#541—71no—
208C2×#541D711yescharacteristic, complemented
209C2×#536—72no—
210C2×#533—71no—
211C2×#533—72no—
212C2×#533—72no—
213C22×C4⋊Q8—71no—
214C2×#519—72no—
215C2×C4×#41—71no—
216C24×C7C2411yescharacteristic
217C23×D7C2411yescharacteristic
218C23×D7C2411yescharacteristic
219C2×C7×Q8—28no—
220C2×C7×Q8C2418yes—
221C22×C4×C7—24no—
222C22×C4×C7C2412yes—
223C22×C4×C7C2411yescharacteristic
224C22×C4×C7C2414yes—
225C22×C4×C7C2414yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2414yes—
228C22×C4×C7C2411yescharacteristic
229C2×C22⋊D7—24no—
230C2×C22⋊D7—24no—
231C2×C22⋊D7C2414yes—
232C2×C22⋊D7C2414yes—
233C22×Dic7—28no—
234C22×Dic7C2418yes—
235C22×Dic7C2412yes—
236C22×Dic7C2414yes—
237C22×Dic7C2411yescharacteristic
238C22×Dic7C2414yes—
239C22×Dic7C2411yescharacteristic
240C22×Dic7C2412yes—
241Q8×D7—264no—
242#1157—232no—
243C2×D28—24no—
244C2×D28C2414yes—
245C2×C4×D7—216no—
246C2×C4×D7—24no—
247C2×C4×D7—28no—
248C2×C4×D7—28no—
249C2×C4×D7#4118yes—
250C2×C4×D7C2418yes—
251C2×C4×D7C2414yes—
252C2×C4×D7C2418yes—
253C2×C4×D7C24116yes—
254C2×C4×D7C2414yes—
255C2×Dic14—28no—
256C2×Dic14—24no—
257C2×Dic14—216no—
258C2×Dic14—216no—
259C2×Dic14C2418yes—
260C2×Dic14C24116yes—
261C2×Dic14C24116yes—
262C2×Dic14C2414yes—
263C7×C4⋊C4C24116yes—
264C7×C4⋊C4C2418yes—
265C7×C4⋊C4C2418yes—
266C7×C4⋊C4C24116yes—
267C7×C4⋊C4C24116yes—
268C7×C4⋊C4C24116yes—
269C7×C22⋊C4C24116yes—
270C7×C22⋊C4C2418yes—
271C42×C7C2414yes—
272C42×C7C24116yes—
273C42×C7C2414yes—
274C22⋊Dic7C24116yes—
275(C2×D7)⋊C4C2418yes—
276(C2×D7)⋊C4C2418yes—
277(C2×D7)⋊C4C24116yes—
278(C2×D7)⋊C4C24116yes—
279(C2×D7)⋊C4C24116yes—
280C4⋊Dic7C2418yes—
281C4⋊Dic7C24116yes—
282C4⋊Dic7C24116yes—
283C4⋊Dic7C24116yes—
284Dic7⋊C4C24116yes—
285Dic7⋊C4C2418yes—
286Dic7⋊C4C24116yes—
287Dic7⋊C4C24116yes—
288Dic7⋊C4C24116yes—
289Dic7⋊C4C24116yes—
290Dic7⋊C4C24116yes—
291Dic7⋊C4C24116yes—
292Dic7⋊C4C2418yes—
293Dic7⋊C4C24116yes—
294C4×Dic7C2418yes—
295C4×Dic7C24116yes—
296C4×Dic7C24116yes—
297C4×Dic7C24116yes—
298C4×Dic7C2414yes—
299C4×Dic7C2418yes—
300C4×Dic7C2414yes—
301C4×Dic7C24116yes—
302C4×Dic7C2418yes—
303C22×#41—71no—
304C23×Q8—72no—
305#557—764no—
306#556—764no—
307#552—764no—
308#552—764no—
309#541—716no—
310#541—716no—
311#541—716no—
312#541C2×D7116yescomplemented
313#536—732no—
314#533—716no—
315#533—732no—
316#533—732no—
317C2×C4⋊Q8—72no—
318C2×C4⋊Q8—716no—
319C2×C4⋊Q8—74no—
320C2×C4⋊Q8—72no—
321C2×C4⋊Q8—74no—
322C2×C4⋊Q8—71no—
323C2×C4⋊Q8C2×D711yescharacteristic
324C2×#126—74no—
325C2×#126—74no—
326C2×#126—74no—
327C2×#126C2×D714yes—
328C2×#125—74no—
329C2×#125—74no—
330C2×#125—74no—
331C2×#125—74no—
332C2×#125—74no—
333C2×#125—71no—
334C2×#125C2×D711yescharacteristic
335C2×#125C2×D714yes—
336C2×#124—74no—
337C2×#123—74no—
338C2×#123—74no—
339C2×C22⋊Q8—72no—
340C2×C22⋊Q8—72no—
341C2×C22⋊Q8—74no—
342C2×C22⋊Q8—74no—
343C2×C22⋊Q8—72no—
344C2×C22⋊Q8—74no—
345C2×C22⋊Q8C2×D712yes—
346#519—732no—
347C4×#41—716no—
348C2×C4×Q8—72no—
349C2×C4×Q8—72no—
350C2×C4×Q8—72no—
351C2×C4×Q8—74no—
352C2×C4×Q8—74no—
353C2×C4×Q8—74no—
354C2×C4×Q8—72no—
355C2×C4×Q8—74no—
356C2×C4×Q8—74no—
357C2×C4×Q8C2×D712yes—
358C2×C4×D4—72no—
359C2×C4×D4—72no—
360C2×C4×D4—72no—
361C2×#117—72no—
362C2×#117—74no—
363C2×#117—74no—
364C2×#117—71no—
365C2×#117—71no—
366C2×#117—74no—
367C2×#117—74no—
368C2×#117C2×D711yescharacteristic
369C22×C4⋊C4—74no—
370C22×C42—71no—
371C22×C42—71no—
372C22×C42—71no—
373C23×C7—22no—
374C23×C7—24no—
375C23×C7C2512yes—
376C23×C7C2511yescharacteristic
377C22×D7—24no—
378C22×D7—22no—
379C22×D7—24no—
380C22×D7C2×#4114yes—
381C22×D7C2512yes—
382C22×D7C2512yes—
383C7×Q8—216no—
384C2×C4×C7—28no—
385C2×C4×C7—22no—
386C2×C4×C7—28no—
387C2×C4×C7—24no—
388C2×C4×C7—24no—
389C2×C4×C7—28no—
390C2×C4×C7C2×#4114yes—
391C2×C4×C7C2514yes—
392C2×C4×C7C2512yes—
393C2×C4×C7C2518yes—
394C2×C4×C7C2514yes—
395C2×C4×C7C2518yes—
396C2×C4×C7C2512yes—
397C22⋊D7—28no—
398C22⋊D7—28no—
399C2×Dic7—28no—
400C2×Dic7—22no—
401C2×Dic7—28no—
402C2×Dic7—24no—
403C2×Dic7—216no—
404C2×Dic7C2×#4114yes—
405C2×Dic72−1+418yes—
406C2×Dic7C2514yes—
407C2×Dic7C2518yes—
408C2×Dic7C2512yes—
409C2×Dic7C2518yes—
410C2×Dic7C2512yes—
411C2×Dic7C2514yes—
412D28—28no—
413C4×D7—232no—
414C4×D7—28no—
415C4×D7—216no—
416C4×D7—216no—
417C4×D7C2×#41116yes—
418Dic14—216no—
419Dic14—28no—
420Dic14—232no—
421Dic14—232no—
422C2×#41—78no—
423C2×#41—148no—
424C22×Q8—716no—
425C22×Q8—74no—
426C22×Q8—72no—
427C22×Q8—74no—
428C22×Q8—71no—
429C22×Q8—1416no—
430C22×Q8C22×D712yes—
431C22×D4—71no—
432C22×D4—71no—
433C22×D4—71no—
434C23×C4—71no—
435C23×C4—72no—
436C23×C4—74no—
437C23×C4—72no—
438C23×C4—72no—
439C23×C4—71no—
440C23×C4C22×D711yescharacteristic
441C4⋊Q8—716no—
442C4⋊Q8—732no—
443C4⋊Q8—716no—
444C4⋊Q8—732no—
445C4⋊Q8—78no—
446C4⋊Q8C22×D718yes—
447#126—732no—
448#126—732no—
449#126—732no—
450#126C22×D7132yes—
451#125—732no—
452#125—732no—
453#125—732no—
454#125—732no—
455#125—732no—
456#125—78no—
457#125C22×D718yes—
458#125C22×D7132yes—
459#124—732no—
460#123—732no—
461#123—732no—
462C22⋊Q8—716no—
463C22⋊Q8—716no—
464C22⋊Q8—716no—
465C22⋊Q8—732no—
466C22⋊Q8—732no—
467C22⋊Q8—732no—
468C22⋊Q8C22×D7116yes—
469C4×Q8—716no—
470C4×Q8—716no—
471C4×Q8—716no—
472C4×Q8—732no—
473C4×Q8—732no—
474C4×Q8—732no—
475C4×Q8—716no—
476C4×Q8—732no—
477C4×Q8—732no—
478C4×Q8C22×D7116yes—
479C4×D4—716no—
480C4×D4—716no—
481C4×D4—716no—
482#117—716no—
483#117—732no—
484#117—732no—
485#117—78no—
486#117—78no—
487#117—732no—
488#117—732no—
489#117C22×D718yes—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—74no—
492C2×C4⋊C4—74no—
493C2×C4⋊C4—74no—
494C2×C4⋊C4—72no—
495C2×C4⋊C4—72no—
496C2×C4⋊C4—72no—
497C2×C4⋊C4—74no—
498C2×C4⋊C4—74no—
499C2×C4⋊C4—74no—
500C2×C4⋊C4—74no—
501C2×C4⋊C4—74no—
502C2×C4⋊C4—74no—
503C2×C4⋊C4—74no—
504C2×C4⋊C4—732no—
505C2×C4⋊C4C22×D714yes—
506C2×C4⋊C4C22×D712yes—
507C2×C4⋊C4C22×D714yes—
508C2×C4⋊C4C22×D712yes—
509C2×C4⋊C4C22×D714yes—
510C2×C4⋊C4C22×D714yes—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—72no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—72no—
515C2×C22⋊C4—74no—
516C2×C22⋊C4—74no—
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D712yes—
519C2×C42—71no—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—74no—
524C2×C42—72no—
525C2×C42—72no—
526C2×C42—72no—
527C2×C42—78no—
528C2×C42—71no—
529C2×C42—78no—
530C2×C42—78no—
531C2×C42C22×D714yes—
532C2×C42C22×D711yescharacteristic
533C2×C42C22×D711yescharacteristic
534C22×C7—22no—
535C22×C7—24no—
536C22×C7—44no—
537C22×C7C22×#4112yes—
538C22×C7C2×2−1+414yes—
539C22×C7C2611yescharacteristic
540C2×D7—24no—
541C2×D7—28no—
542C2×D7—22no—
543C2×D7—24no—
544C2×D7—44no—
545C2×D7C22×#4114yes—
546C4×C7—28no—
547C4×C7—22no—
548C4×C7—28no—
549C4×C7—24no—
550C4×C7—24no—
551C4×C7C22×#4114yes—
552Dic7—28no—
553Dic7—22no—
554Dic7—28no—
555Dic7—24no—
556Dic7C22×#4114yes—
557Dic7C2×2−1+418yes—
558C24—71no—
559C24—71no—
560C24C23×D711yescharacteristic
561#41—1432no—
562C2×Q8—28no—
563C2×Q8—716no—
564C2×Q8—78no—
565C2×Q8—716no—
566C2×Q8—74no—
567C2×Q8—1416no—
568C2×Q8—1416no—
569C2×Q8—144no—
570C2×Q8—1464no—
571C2×Q8—148no—
572C2×Q8C23×D718yes—
573C2×D4—74no—
574C2×D4—74no—
575C2×D4—74no—
576C2×D4—144no—
577C2×D4—144no—
578C2×D4—144no—
579C22×C4—24no—
580C22×C4—71no—
581C22×C4—72no—
582C22×C4—78no—
583C22×C4—74no—
584C22×C4—78no—
585C22×C4—72no—
586C22×C4—74no—
587C22×C4—74no—
588C22×C4—71no—
589C22×C4—78no—
590C22×C4—78no—
591C22×C4—74no—
592C22×C4—716no—
593C22×C4—148no—
594C22×C4—148no—
595C22×C4—1416no—
596C22×C4—148no—
597C22×C4—144no—
598C22×C4C23×D714yes—
599C22×C4C23×D712yes—
600C22×C4C23×D714yes—
601C22×C4C23×D711yescharacteristic
602C22×C4C23×D712yes—
603C22×C4C23×D714yes—
604C22×C4C23×D711yescharacteristic
605C4⋊C4—716no—
606C4⋊C4—716no—
607C4⋊C4—716no—
608C4⋊C4—78no—
609C4⋊C4—78no—
610C4⋊C4—716no—
611C4⋊C4—716no—
612C4⋊C4—716no—
613C4⋊C4—716no—
614C4⋊C4—716no—
615C4⋊C4—716no—
616C4⋊C4—78no—
617C4⋊C4—716no—
618C4⋊C4—716no—
619C4⋊C4C23×D7116yes—
620C4⋊C4C23×D718yes—
621C4⋊C4C23×D7116yes—
622C4⋊C4C23×D718yes—
623C4⋊C4C23×D7116yes—
624C4⋊C4C23×D7116yes—
625C22⋊C4—716no—
626C22⋊C4—78no—
627C22⋊C4—716no—
628C22⋊C4—78no—
629C22⋊C4—716no—
630C22⋊C4—716no—
631C22⋊C4C23×D7116yes—
632C22⋊C4C23×D718yes—
633C42—74no—
634C42—74no—
635C42—78no—
636C42—78no—
637C42—78no—
638C42—716no—
639C42—716no—
640C42—716no—
641C42—716no—
642C42C23×D714yes—
643C42C23×D714yes—
644C42C23×D7116yes—
645C2×C7—42no—
646C2×C7#350914yescomplemented
647C2×C7C23×#4111yescharacteristic
648C2×C7C22×2−1+412yes—
649D7—24no—
650D7—42no—
651C23—22no—
652C23—24no—
653C23—72no—
654C23—74no—
655C23—72no—
656C23—144no—
657C23—142no—
658C23—144no—
659C23C24×D712yes—
660C23C24×D711yescharacteristic
661Q8—216no—
662Q8—1432no—
663Q8—1432no—
664Q8—148no—
665Q8—1416no—
666D4—148no—
667D4—148no—
668D4—148no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—72no—
676C2×C4—74no—
677C2×C4—74no—
678C2×C4—78no—
679C2×C4—716no—
680C2×C4—74no—
681C2×C4—78no—
682C2×C4—78no—
683C2×C4—72no—
684C2×C4—1416no—
685C2×C4—1416no—
686C2×C4—1432no—
687C2×C4—1416no—
688C2×C4—142no—
689C2×C4—148no—
690C2×C4—144no—
691C2×C4—148no—
692C2×C4—148no—
693C2×C4D7×#4114yes—
694C2×C4C24×D714yes—
695C2×C4C24×D718yes—
696C2×C4C24×D712yes—
697C2×C4C24×D714yes—
698C2×C4C24×D718yes—
699C2×C4C24×D712yes—
700C7C2×#350911yescharacteristic, complemented, Sylow
701C22—22no—
702C22—24no—
703C22—44no—
704C22—74no—
705C22—144no—
706C22—148no—
707C22—142no—
708C22—144no—
709C22—284no—
710C22C2×D7×#4112yes—
711C22D7×2−1+414yes—
712C22C25×D711yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—74no—
719C4—78no—
720C4—142no—
721C4—148no—
722C4—144no—
723C4—148no—
724C4C2×D7×#4114yes—
725C2—42no—
726C2—144no—
727C2—282no—
728C2#1174357814yesdirect product factor
729C2C22×D7×#4111yescharacteristic
730C2C2×D7×2−1+412yes—
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#541C2
socleC23×C7C25
prime radicalC22×#1157C22
hypercenterC2×#541D7
hypocenterC7C2×#3509
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×C7×#541C2semidirect
2. #11743578C2direct (N × H)
3. C2×#90422C2semidirect
4. C2×D7×C4⋊Q8C2semidirect
5. C2×#90399C2semidirect
6. C2×#90393C2semidirect
7. C2×#90384C2semidirect
8. C2×#90388C2semidirect
9. C2×#90376C2semidirect
10. C2×#90379C2semidirect
12. C2×#90313C2semidirect
13. C2×#90269C2semidirect
14. C2×#90263C2semidirect
15. C2×#90209C2semidirect
19. C7×#541C22semidirect
32. #90422C22semidirect
33. D7×C4⋊Q8C22semidirect
34. #90399C22semidirect
35. #90393C22semidirect
36. #90388C22semidirect
37. #90384C22semidirect
38. #90379C22semidirect
39. #90376C22semidirect
41. #90313C22semidirect
42. #90269C22semidirect
43. #90263C22semidirect
45. #90209C22semidirect
208. C2×#541D7semidirect
312. #541C2×D7semidirect
646. C2×C7#3509semidirect
700. C7C2×#3509semidirect
728. C2#11743578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5412
#117435782
C2×#904222
C2×D7×C4⋊Q82
C2×#903992
C2×#903932
C2×#903842
C2×#903882
C2×#903762
C2×#903792
C2×#903192
C2×#903132
C2×#902692
C2×#902632
C2×#902092
C2×#902132
C2×#35097