Finite Group Databasebeta

← C2×#11739126 #14223041

Subgroups — C2×#11739126 #14223041

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×#90420C211yesmaximal, characteristic, complemented
2C2×#90366C211yesmaximal, characteristic
3C2×C7×#489C211yesmaximal, characteristic, complemented
4C2×#89865C211yesmaximal, characteristic, complemented
5C2×#89828C211yesmaximal, characteristic, complemented
6#11739126C2116yesmaximal, direct product factor
7C2×#89574C211yesmaximal, characteristic, complemented
8C2×D7×#103C211yesmaximal, characteristic, complemented
9C2×#89569C211yesmaximal, characteristic, complemented
10C2×#89564C211yesmaximal, characteristic, complemented
11C2×#89543C211yesmaximal, characteristic
12C2×#89544C211yesmaximal, characteristic
13C2×#89537C211yesmaximal, characteristic, complemented
14C2×#89540C211yesmaximal, characteristic, complemented
15C2×#89475C211yesmaximal, characteristic, complemented
16C2×#89480C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C22×#1159C2211yescharacteristic
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#124C2211yescharacteristic
21C2×#6509—21no—
22C2×#6507—21no—
23C2×#6507C2211yescharacteristic
24C2×#6499C2211yescharacteristic
25C22×#1131C2211yescharacteristic
26C22×C8×D7C2211yescharacteristic
27#90420—24no—
28#90420C2218yescomplemented
29#90366—24no—
30#90366C2218yes—
31C2×#6459—21no—
32C2×#6455C2211yescharacteristic
33C2×D7×C4⋊C4C2211yescharacteristic
34C2×#6453C2211yescharacteristic
35C2×#6452—21no—
36C2×#6451C2211yescharacteristic
37C2×#6446—21no—
38C2×#6446—21no—
39C2×#6441—21no—
40C2×#6441—21no—
41C2×#6435C2211yescharacteristic
42C2×#6433C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C7×#489C2218yescomplemented
45C2×C7×#103C2211yescharacteristic
46C2×C7×#103C2211yescharacteristic
47C2×C7×#102C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×#6390C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58C2×#6389C2211yescharacteristic
59C2×C8×Dic7C2211yescharacteristic
60#89865C2218yescomplemented
61#89828C2218yescomplemented
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×C4×C7⋊C8C2211yescharacteristic
67#89574C2218yescomplemented
68D7×#103C2218yescomplemented
69#89569C2218yescomplemented
70#89564C2218yescomplemented
71#89544C2218yes—
72#89543C2218yes—
73#89540C2218yescomplemented
74#89537C2218yescomplemented
75#89480C2218yescomplemented
76#89475C2218yescomplemented
77C2×#3137—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C22×C22⋊D7—21no—
82C23×Dic7—21no—
83C2×Q8×D7—22no—
84C2×Q8×D7—24no—
85C2×Q8×D7—24no—
86C2×Q8×D7C2314yes—
87C2×#1159—22no—
88C2×#1159—24no—
89C2×#1159—24no—
90C2×#1159C2314yes—
91C22×C4×D7—21no—
92C22×C4×D7—21no—
93C22×C4×D7C2311yescharacteristic
94C22×Dic14—21no—
95C22×Dic14—21no—
96C22×Dic14C2311yescharacteristic
97C22×Dic14C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C7×C4⋊Q8—22no—
101C7×C4⋊Q8C2314yes—
102C7×#124—22no—
103C7×#124C2314yes—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—21no—
109C2×C42×C7C2311yescharacteristic
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112#6509—28no—
113#6507—28no—
114#6507—22no—
115#6507C2314yes—
116#6499—22no—
117#6499C2314yes—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4D411yescharacteristic
120C2×(C2×D7)⋊C4D411yescharacteristic
121C2×C4⋊Dic7—21no—
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⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4D411yescharacteristic
134C2×Dic7⋊C4D411yescharacteristic
135C2×C4×Dic7—21no—
136C2×C4×Dic7C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C2×#1131—24no—
140C2×#1131C2314yes—
141C2×C8×D7—24no—
142C2×C8×D7C2314yes—
143#6459—28no—
144#6455—22no—
145#6455C2314yes—
146D7×C4⋊C4—22no—
147D7×C4⋊C4C2314yes—
148#6453—22no—
149#6453C2314yes—
150#6452—28no—
151#6451—22no—
152#6451C2314yes—
153#6446—28no—
154#6446—28no—
155#6441—28no—
156#6441—28no—
157#6435D414yes—
158#6435C2314yes—
159#6433—22no—
160#6433C2314yes—
161#6432—22no—
162#6432C2314yes—
163C7×#103C2314yes—
164C7×#103C2314yes—
165C7×#102C2314yes—
166C7×#102C2314yes—
167C7×#97C2314yes—
168#6409C2314yes—
169#6409C2314yes—
170#6406C2314yes—
171#6406C2314yes—
172#6390C2314yes—
173#6390C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176#6389C2314yes—
177C8×Dic7C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6384C2314yes—
181#6384C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#544—71no—
184C2×#536—71no—
185#3137—716no—
186C2×#491—71no—
187C2×#491—71no—
188C2×#489—71no—
189C2×#489D711yescharacteristic, complemented
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—
199C24×C7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—24no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—82no—
206C2×C7×Q8C2412yes—
207C2×C7×D4—21no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4C2412yes—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—24no—
218C2×C22⋊D7—44no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—24no—
224C22×Dic7—44no—
225C22×Dic7C2×D411yescharacteristic
226C22×Dic7C2×D411yescharacteristic
227C22×Dic7C2×D411yescharacteristic
228Q8×D7—28no—
229Q8×D7—28no—
230Q8×D7—48no—
231#1159—28no—
232#1159—28no—
233#1159—48no—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—44no—
237C2×C4×D7—82no—
238C2×C4×D7C2×D412yes—
239C2×C4×D7#4114yes—
240C2×C4×D7#4114yes—
241C2×C4×D7C2412yes—
242C2×Dic14—22no—
243C2×Dic14—22no—
244C2×Dic14—22no—
245C2×Dic14—22no—
246C2×Dic14—21no—
247C2×Dic14—21no—
248C2×Dic14—24no—
249C2×Dic14—24no—
250C2×Dic14—44no—
251C2×Dic14—82no—
252C2×Dic14C2412yes—
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—21no—
261C7×C4⋊C4C2412yes—
262C7×C4⋊C4C2412yes—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—24no—
265C42×C7C2×D412yes—
266C42×C7C2412yes—
267C22⋊Dic7—24no—
268C22⋊Dic7—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4C2×D414yes—
271(C2×D7)⋊C4C2×D414yes—
272C4⋊Dic7—24no—
273C4⋊Dic7—24no—
274C4⋊Dic7—21no—
275C4⋊Dic7—21no—
276C4⋊Dic7—24no—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
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—71no—
312C2×#125—141no—
313C2×#124—71no—
314C2×#124C2×D711yescharacteristic
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#491—78no—
326#489—78no—
327#489C2×D718yescomplemented
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—71no—
344C2×#103—71no—
345C2×#103—78no—
346C2×#103C2×D711yescharacteristic
347C2×#103C2×D711yescharacteristic
348C2×#102—71no—
349C2×#102—71no—
350C2×#102C2×D711yescharacteristic
351C2×#102C2×D711yescharacteristic
352#405—78no—
353C2×#97—71no—
354C2×#97C2×D711yescharacteristic
355C2×C4×C8—71no—
356C2×C4×C8—71no—
357C23×C7—22no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D411yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7#12414yes—
365C22×D7C22×D412yes—
366C7×Q8—22no—
367C7×Q8—22no—
368C7×Q8—42no—
369C7×Q8—84no—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—42no—
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×C7C22×D412yes—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C2×#4112yes—
385C2×C4×C7C2×#4112yes—
386C2×C4×C7C2511yescharacteristic
387C22⋊D7—48no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—48no—
399C2×Dic7#12414yes—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403C4×D7—48no—
404C4×D7—84no—
405C4×D7#12418yes—
406C4×D7C2×#4114yes—
407C4×D7C2×#4114yes—
408Dic14—22no—
409Dic14—22no—
410Dic14—22no—
411Dic14—22no—
412Dic14—42no—
413Dic14—42no—
414Dic14—48no—
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—21no—
425C22×Q8—74no—
426C22×Q8—71no—
427C22×Q8—71no—
428C22×Q8—141no—
429C22×Q8—141no—
430C22×Q8—142no—
431C22×Q8—144no—
432C22×Q8—144no—
433C22×Q8C22×D711yescharacteristic
434C22×D4—141no—
435C22×D4C22×D711yescharacteristic
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—74no—
458#125—74no—
459#125—142no—
460#125—148no—
461#125—142no—
462#124—22no—
463#124—74no—
464#124—142no—
465#124C22×D714yes—
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—71no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—71no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
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—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—71no—
498C2×C22⋊C4—71no—
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#103—74no—
514#103—74no—
515#103C22×D714yes—
516#103C22×D714yes—
517#102—74no—
518#102—74no—
519#102C22×D714yes—
520#102C22×D714yes—
521#97—74no—
522#97C22×D714yes—
523C4×C8—74no—
524C4×C8—74no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7—84no—
529C22×C7C2×#12412yes—
530C22×C7#57712yes—
531C22×C7#57812yes—
532C22×C7C23×D411yescharacteristic
533C2×D7—28no—
534C2×D7—22no—
535C2×D7—22no—
536C2×D7C2×#12414yes—
537C4×C7—22no—
538C4×C7—22no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7C2×#12412yes—
543C4×C7C22×#4111yescharacteristic
544C4×C7C22×#4111yescharacteristic
545Dic7—22no—
546Dic7—22no—
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550Dic7—42no—
551Dic7C2×#12414yes—
552C24—21no—
553C24—71no—
554#41—148no—
555#41—148no—
556#41—288no—
557C2×Q8—21no—
558C2×Q8—24no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—72no—
562C2×Q8—72no—
563C2×Q8—82no—
564C2×Q8—144no—
565C2×Q8—144no—
566C2×Q8—148no—
567C2×Q8—148no—
568C2×Q8—141no—
569C2×Q8—141no—
570C2×Q8—142no—
571C2×Q8—142no—
572C2×Q8—142no—
573C2×Q8—142no—
574C2×Q8—284no—
575C2×Q8—288no—
576C2×Q8—562no—
577C2×Q8C23×D712yes—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—144no—
582C2×D4—284no—
583C2×D4C23×D712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—71no—
588C22×C4—72no—
589C22×C4—74no—
590C22×C4—74no—
591C22×C4—72no—
592C22×C4—71no—
593C22×C4—71no—
594C22×C4—144no—
595C22×C4—144no—
596C22×C4—144no—
597C22×C4—141no—
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—21no—
619C4⋊C4—21no—
620C4⋊C4—74no—
621C4⋊C4—74no—
622C4⋊C4—72no—
623C4⋊C4—72no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—144no—
629C4⋊C4—144no—
630C4⋊C4—144no—
631C4⋊C4—144no—
632C4⋊C4—141no—
633C4⋊C4—141no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4C23×D712yes—
637C4⋊C4C23×D712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—74no—
641C22⋊C4—74no—
642C22⋊C4—144no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C42—72no—
646C42—72no—
647C42—144no—
648C42D4×D712yes—
649C42C23×D712yes—
650C2×C7—82no—
651C2×C7#313714yescomplemented
652C2×C7C22×#12411yescharacteristic
653C2×C7C2×#57711yescharacteristic
654C2×C7C2×#57811yescharacteristic
655D7—24no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—72no—
661C23—74no—
662C23—142no—
663C23—142no—
664C23C2×D4×D711yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—42no—
668Q8—84no—
669Q8—142no—
670Q8—142no—
671Q8—142no—
672Q8—142no—
673Q8—288no—
674Q8—282no—
675Q8—282no—
676Q8—564no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—288no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—72no—
690C2×C4—74no—
691C2×C4—74no—
692C2×C4—74no—
693C2×C4—78no—
694C2×C4—72no—
695C2×C4—72no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—288no—
703C2×C4—288no—
704C2×C4—282no—
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—42no—
721C22—42no—
722C22—42no—
723C22—74no—
724C22—84no—
725C22—142no—
726C22—142no—
727C22—148no—
728C22D7×#12412yes—
729C22#9046612yes—
730C22#9047012yes—
731C22C22×D4×D711yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—74no—
738C4—142no—
739C4—142no—
740C4—282no—
741C4—282no—
742C4—282no—
743C4—282no—
744C4D7×#12412yes—
745C4C2×D7×#4111yescharacteristic
746C4C2×D7×#4111yescharacteristic
747C2—82no—
748C2—144no—
749C2#1173912614yesdirect product factor
750C2C2×D7×#12411yescharacteristic
751C2C2×#9046611yescharacteristic
752C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#489C2
socleC23×C7C22×D4
prime radicalC22×#1159C22
hypercenterC2×#489D7
hypocenterC7C2×#3137
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#90420C2semidirect
3. C2×C7×#489C2semidirect
4. C2×#89865C2semidirect
5. C2×#89828C2semidirect
6. #11739126C2direct (N × H)
7. C2×#89574C2semidirect
8. C2×D7×#103C2semidirect
9. C2×#89569C2semidirect
10. C2×#89564C2semidirect
13. C2×#89537C2semidirect
14. C2×#89540C2semidirect
15. C2×#89475C2semidirect
16. C2×#89480C2semidirect
28. #90420C22semidirect
44. C7×#489C22semidirect
60. #89865C22semidirect
61. #89828C22semidirect
67. #89574C22semidirect
68. D7×#103C22semidirect
69. #89569C22semidirect
70. #89564C22semidirect
73. #89540C22semidirect
74. #89537C22semidirect
75. #89480C22semidirect
76. #89475C22semidirect
189. C2×#489D7semidirect
327. #489C2×D7semidirect
651. C2×C7#3137semidirect
719. C7C2×#3137semidirect
749. C2#11739126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904202
C2×#903662
C2×C7×#4892
C2×#898652
C2×#898282
#117391262
C2×#895742
C2×D7×#1032
C2×#895692
C2×#895642
C2×#895432
C2×#895442
C2×#895372
C2×#895402
C2×#894752
C2×#894802
C2×#31377