Finite Group Databasebeta

← C2×#11739183 #14223045

Subgroups — C2×#11739183 #14223045

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90415C211yesmaximal, characteristic
2C2×#90380C211yesmaximal, characteristic, complemented
3C2×C7×#491C211yesmaximal, characteristic, complemented
4C2×#89853C211yesmaximal, characteristic, complemented
5C2×#89840C211yesmaximal, characteristic, complemented
6#11739183C2116yesmaximal, direct product factor
7C2×#89575C211yesmaximal, characteristic
8C2×#89574C211yesmaximal, characteristic, complemented
9C2×#89576C211yesmaximal, characteristic
10C2×D7×#103C211yesmaximal, characteristic, complemented
11C2×#89569C211yesmaximal, characteristic, complemented
12C2×#89567C211yesmaximal, characteristic, complemented
13C2×#89572C211yesmaximal, characteristic, complemented
14C2×#89564C211yesmaximal, characteristic, complemented
15C2×#89486C211yesmaximal, characteristic, complemented
16C2×#89480C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C22×Q8×D7C2211yescharacteristic
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#125C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×#6507C2211yescharacteristic
23C22×#1131C2211yescharacteristic
24C22×C8×D7C2211yescharacteristic
25#90415—24no—
26#90415C2218yes—
27#90380—24no—
28#90380C2218yescomplemented
29C2×#6460—21no—
30C2×#6459—21no—
31C2×#6459—21no—
32C2×#6459—21no—
33C2×#6457—21no—
34C2×#6457—21no—
35C2×#6455C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6453C2211yescharacteristic
38C2×#6452—21no—
39C2×#6451—21no—
40C2×#6451C2211yescharacteristic
41C2×#6438C2211yescharacteristic
42C2×#6435C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C7×#491C2218yescomplemented
45C2×C7×#103C2211yescharacteristic
46C2×C7×#103C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58C2×#6389C2211yescharacteristic
59C2×C8×Dic7C2211yescharacteristic
60#89853C2218yescomplemented
61#89840C2218yescomplemented
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×C4×C7⋊C8C2211yescharacteristic
67#89576C2218yes—
68#89575C2218yes—
69#89574C2218yescomplemented
70D7×#103C2218yescomplemented
71#89572C2218yescomplemented
72#89569C2218yescomplemented
73#89567C2218yescomplemented
74#89564C2218yescomplemented
75#89486C2218yescomplemented
76#89480C2218yescomplemented
77C2×#3137—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C2×#1161—22no—
81C2×#1161—24no—
82C2×#1161—24no—
83C2×#1161C2314yes—
84C2×Q8×D7—22no—
85C2×Q8×D7—24no—
86C2×Q8×D7—24no—
87C2×Q8×D7C2314yes—
88C22×D28—21no—
89C22×D28C2311yescharacteristic
90C22×C4×D7—21no—
91C22×C4×D7—21no—
92C22×C4×D7—21no—
93C22×C4×D7C2311yescharacteristic
94C22×Dic14—21no—
95C22×Dic14—21no—
96C22×Dic14—21no—
97C22×Dic14C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C7×C4⋊Q8—22no—
101C7×C4⋊Q8C2314yes—
102C7×#125—22no—
103C7×#125C2314yes—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C42×C7C2311yescharacteristic
111#6510—22no—
112#6510C2314yes—
113#6507—22no—
114#6507C2314yes—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4D411yescharacteristic
121C2×(C2×D7)⋊C4D411yescharacteristic
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4D411yescharacteristic
132C2×Dic7⋊C4D411yescharacteristic
133C2×C4×Dic7—21no—
134C2×C4×Dic7C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C2×#1131—24no—
138C2×#1131C2314yes—
139C2×C8×D7—24no—
140C2×C8×D7C2314yes—
141#6460—28no—
142#6459—28no—
143#6459—28no—
144#6459—28no—
145#6457—28no—
146#6457—28no—
147#6455—22no—
148#6455C2314yes—
149D7×C4⋊C4—22no—
150D7×C4⋊C4C2314yes—
151#6453—22no—
152#6453C2314yes—
153#6452—28no—
154#6451—28no—
155#6451—22no—
156#6451C2314yes—
157#6438—22no—
158#6438C2314yes—
159#6435D414yes—
160#6435C2314yes—
161#6432—22no—
162#6432C2314yes—
163C7×#103C2314yes—
164C7×#103C2314yes—
165C7×#103C2314yes—
166C7×#103C2314yes—
167C7×#97C2314yes—
168#6409C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6395C2314yes—
173#6395C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176#6389C2314yes—
177C8×Dic7C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6383C2314yes—
181#6383C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#544—71no—
184C2×#536—71no—
185#3137—716no—
186C2×#491—71no—
187C2×#491D711yescharacteristic, complemented
188C2×#489—71no—
189C2×#489—71no—
190C2×#488—71no—
191C2×#488—71no—
192C2×#487—71no—
193C2×#487—71no—
194C2×#417—71no—
195C2×#419—71no—
196C2×#416—71no—
197C22×#103—71no—
198C2×#405—71no—
199C23×D7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8—22no—
207C2×C7×Q8C2412yes—
208C2×C7×Q8C2412yes—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2411yescharacteristic
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C22×Dic7C2×D411yescharacteristic
222#1161—28no—
223#1161—28no—
224#1161—48no—
225Q8×D7—28no—
226Q8×D7—28no—
227Q8×D7—48no—
228C2×D28—22no—
229C2×D28—22no—
230C2×D28—24no—
231C2×D28—21no—
232C2×D28—44no—
233C2×D28C2412yes—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—44no—
238C2×C4×D7—44no—
239C2×C4×D7—82no—
240C2×C4×D7C2×D412yes—
241C2×C4×D7#4114yes—
242C2×C4×D7#4114yes—
243C2×C4×D7C2412yes—
244C2×Dic14—22no—
245C2×Dic14—22no—
246C2×Dic14—21no—
247C2×Dic14—24no—
248C2×Dic14—24no—
249C2×Dic14—24no—
250C2×Dic14—44no—
251C2×Dic14—82no—
252C2×Dic14—82no—
253C2×Dic14C2412yes—
254C2×C7×C8—22no—
255C2×C7×C8—22no—
256C2×C7×C8C2412yes—
257C2×C7×C8C2412yes—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—24no—
260C7×C4⋊C4—24no—
261C7×C4⋊C4—21no—
262C7×C4⋊C4—24no—
263C7×C4⋊C4—24no—
264C7×C4⋊C4C2412yes—
265C7×C4⋊C4C2412yes—
266C42×C7C2×D412yes—
267C42×C7C2412yes—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4C2×D414yes—
274(C2×D7)⋊C4C2×D414yes—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7—24no—
279C4⋊Dic7C2412yes—
280C4⋊Dic7C2412yes—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4C2×D414yes—
287Dic7⋊C4C2×D414yes—
288C4×Dic7—24no—
289C4×Dic7C2×D412yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295#1131—28no—
296C8×D7—28no—
297C22×#41—71no—
298C23×Q8—71no—
299C22×M16—71no—
300C23×C8—71no—
301#544—78no—
302#544—144no—
303#536—78no—
304#536—144no—
305C2×C4⋊Q8—71no—
306C2×C4⋊Q8—71no—
307C2×C4⋊Q8—71no—
308C2×C4⋊Q8—141no—
309C2×C4⋊Q8C2×D711yescharacteristic
310C2×#125—71no—
311C2×#125—141no—
312C2×#125C2×D711yescharacteristic
313C2×#124—71no—
314C2×#124—71no—
315C2×#123—141no—
316C2×#123—141no—
317C2×C22⋊Q8—141no—
318C2×C22⋊Q8—141no—
319C2×C22⋊Q8—141no—
320C2×C22⋊Q8—141no—
321C2×#117—71no—
322C2×#117—71no—
323C22×C4⋊C4—71no—
324#491—78no—
325#491C2×D718yescomplemented
326#489—78no—
327#489—78no—
328#488—78no—
329#488—78no—
330#487—78no—
331#487—78no—
332#419—78no—
333#417—78no—
334#416—78no—
335C2×#103—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103—78no—
344C2×#103C2×D711yescharacteristic
345C2×#103C2×D711yescharacteristic
346C2×#103C2×D711yescharacteristic
347C2×#103C2×D711yescharacteristic
348C2×#102—71no—
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352#405—78no—
353C2×#97—71no—
354C2×#97C2×D711yescharacteristic
355C2×C4×C8—71no—
356C2×C4×C8—71no—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7#12414yes—
365C22×D7C22×D412yes—
366C7×Q8—22no—
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—22no—
370C7×Q8—42no—
371C7×Q8—42no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C2×#4112yes—
386C2×C4×C7C2×#4112yes—
387C2×C4×C7C2511yescharacteristic
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7#12414yes—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400D28—22no—
401D28—22no—
402D28—48no—
403D28—42no—
404C4×D7—48no—
405C4×D7—48no—
406C4×D7—84no—
407C4×D7#12418yes—
408C4×D7C2×#4114yes—
409C4×D7C2×#4114yes—
410Dic14—22no—
411Dic14—22no—
412Dic14—42no—
413Dic14—48no—
414Dic14—84no—
415Dic14—84no—
416C7×C8—22no—
417C7×C8—22no—
418C7⋊C8—22no—
419C7⋊C8—22no—
420C2×#41—74no—
421C2×#41—142no—
422C2×#41—144no—
423C2×#41—144no—
424C22×Q8—74no—
425C22×Q8—71no—
426C22×Q8—141no—
427C22×Q8—141no—
428C22×Q8—142no—
429C22×Q8—144no—
430C22×Q8—144no—
431C22×Q8—141no—
432C22×Q8C22×D711yescharacteristic
433C22×Q8C22×D711yescharacteristic
434C22×D4—71no—
435C22×D4—141no—
436C23×C4—71no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4—141no—
440C2×M16—74no—
441C2×M16—144no—
442C22×C8—71no—
443C22×C8—71no—
444C22×C8—74no—
445C22×C8—144no—
446C22×C8C22×D711yescharacteristic
447C22×C8C22×D711yescharacteristic
448C4⋊Q8—22no—
449C4⋊Q8—74no—
450C4⋊Q8—74no—
451C4⋊Q8—74no—
452C4⋊Q8—142no—
453C4⋊Q8—142no—
454C4⋊Q8—148no—
455C4⋊Q8—142no—
456C4⋊Q8C22×D714yes—
457#125—22no—
458#125—74no—
459#125—142no—
460#125—148no—
461#125C22×D714yes—
462#124—74no—
463#124—74no—
464#124—142no—
465#124—142no—
466#123—148no—
467#123—148no—
468C22⋊Q8—148no—
469C22⋊Q8—148no—
470C22⋊Q8—148no—
471C22⋊Q8—148no—
472#117—74no—
473#117—74no—
474#117—74no—
475#117—142no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—142no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4C22×D711yescharacteristic
494C2×C4⋊C4C22×D711yescharacteristic
495C2×C22⋊C4—71no—
496C2×C22⋊C4—71no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C42—71no—
503C2×C42—141no—
504C2×C42C22×D711yescharacteristic
505#103—74no—
506#103—74no—
507#103—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103—74no—
513#103C22×D714yes—
514#103C22×D714yes—
515#103C22×D714yes—
516#103C22×D714yes—
517#102—74no—
518#102—74no—
519#102—74no—
520#102—74no—
521#97—74no—
522#97C22×D714yes—
523C4×C8—74no—
524C4×C8—74no—
525C22×C7C2×#12412yes—
526C22×C7#57712yes—
527C22×C7#57812yes—
528C22×C7C23×D411yescharacteristic
529C2×D7—28no—
530C2×D7—22no—
531C2×D7—22no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—84no—
536C2×D7C2×#12414yes—
537C4×C7—22no—
538C4×C7—22no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7C2×#12412yes—
544C4×C7C22×#4111yescharacteristic
545C4×C7C22×#4111yescharacteristic
546Dic7—22no—
547Dic7—22no—
548Dic7—42no—
549Dic7—42no—
550Dic7—42no—
551Dic7C2×#12414yes—
552C24—71no—
553C24—141no—
554#41—148no—
555#41—148no—
556#41—288no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—72no—
564C2×Q8—144no—
565C2×Q8—144no—
566C2×Q8—148no—
567C2×Q8—148no—
568C2×Q8—141no—
569C2×Q8—144no—
570C2×Q8—142no—
571C2×Q8—142no—
572C2×Q8—284no—
573C2×Q8—288no—
574C2×Q8—562no—
575C2×Q8—562no—
576C2×Q8C23×D712yes—
577C2×Q8C23×D712yes—
578C2×D4—72no—
579C2×D4—144no—
580C2×D4—141no—
581C2×D4—142no—
582C2×D4—142no—
583C2×D4—284no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—71no—
589C22×C4—72no—
590C22×C4—74no—
591C22×C4—74no—
592C22×C4—72no—
593C22×C4—71no—
594C22×C4—71no—
595C22×C4—144no—
596C22×C4—144no—
597C22×C4—144no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—284no—
602C22×C4—284no—
603C22×C4—562no—
604C22×C4D4×D711yescharacteristic
605C22×C4D4×D711yescharacteristic
606C22×C4C23×D711yescharacteristic
607M16—148no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—72no—
611C2×C8—72no—
612C2×C8—148no—
613C2×C8—142no—
614C2×C8—142no—
615C2×C8C23×D712yes—
616C2×C8C23×D712yes—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—74no—
624C4⋊C4—74no—
625C4⋊C4—72no—
626C4⋊C4—72no—
627C4⋊C4—144no—
628C4⋊C4—144no—
629C4⋊C4—144no—
630C4⋊C4—144no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—141no—
634C4⋊C4—141no—
635C4⋊C4—144no—
636C4⋊C4C23×D712yes—
637C4⋊C4C23×D712yes—
638C22⋊C4—74no—
639C22⋊C4—74no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C22⋊C4—144no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C42—72no—
646C42—72no—
647C42—144no—
648C42D4×D712yes—
649C42C23×D712yes—
650C2×C7#313714yescomplemented
651C2×C7C22×#12411yescharacteristic
652C2×C7C2×#57711yescharacteristic
653C2×C7C2×#57811yescharacteristic
654D7—24no—
655D7—82no—
656C23—72no—
657C23—74no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—282no—
662C23—282no—
663C23—282no—
664C23C2×D4×D711yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—22no—
669Q8—42no—
670Q8—42no—
671Q8—142no—
672Q8—142no—
673Q8—288no—
674Q8—282no—
675Q8—564no—
676Q8—564no—
677D4—142no—
678D4—142no—
679D4—288no—
680D4—282no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—72no—
692C2×C4—74no—
693C2×C4—74no—
694C2×C4—74no—
695C2×C4—78no—
696C2×C4—72no—
697C2×C4—72no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—288no—
704C2×C4—288no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—282no—
708C2×C4—564no—
709C2×C4C2×D4×D712yes—
710C2×C4C2×D4×D712yes—
711C2×C4C2×D4×D711yescharacteristic
712C2×C4D7×#4112yes—
713C2×C4D7×#4112yes—
714C2×C4C24×D711yescharacteristic
715C8—22no—
716C8—22no—
717C8—142no—
718C8—142no—
719C7C2×#313711yescharacteristic, complemented, Sylow
720C22—74no—
721C22—142no—
722C22—142no—
723C22—148no—
724C22—282no—
725C22—282no—
726C22—282no—
727C22—564no—
728C22D7×#12412yes—
729C22#9046912yes—
730C22#9047012yes—
731C22C22×D4×D711yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—74no—
739C4—142no—
740C4—142no—
741C4—282no—
742C4—282no—
743C4—282no—
744C4D7×#12412yes—
745C4C2×D7×#4111yescharacteristic
746C4C2×D7×#4111yescharacteristic
747C2—144no—
748C2—562no—
749C2#1173918314yesdirect product factor
750C2C2×D7×#12411yescharacteristic
751C2C2×#9046911yescharacteristic
752C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#491C2
socleC23×C7C22×D4
prime radicalC22×#1161C22
hypercenterC2×#491D7
hypocenterC7C2×#3137
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
2. C2×#90380C2semidirect
3. C2×C7×#491C2semidirect
4. C2×#89853C2semidirect
5. C2×#89840C2semidirect
6. #11739183C2direct (N × H)
8. C2×#89574C2semidirect
10. C2×D7×#103C2semidirect
11. C2×#89569C2semidirect
12. C2×#89567C2semidirect
13. C2×#89572C2semidirect
14. C2×#89564C2semidirect
15. C2×#89486C2semidirect
16. C2×#89480C2semidirect
28. #90380C22semidirect
44. C7×#491C22semidirect
60. #89853C22semidirect
61. #89840C22semidirect
69. #89574C22semidirect
70. D7×#103C22semidirect
71. #89572C22semidirect
72. #89569C22semidirect
73. #89567C22semidirect
74. #89564C22semidirect
75. #89486C22semidirect
76. #89480C22semidirect
187. C2×#491D7semidirect
325. #491C2×D7semidirect
650. C2×C7#3137semidirect
719. C7C2×#3137semidirect
749. C2#11739183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904152
C2×#903802
C2×C7×#4912
C2×#898532
C2×#898402
#117391832
C2×#895752
C2×#895742
C2×#895762
C2×D7×#1032
C2×#895692
C2×#895672
C2×#895722
C2×#895642
C2×#894862
C2×#894802
C2×#31377