Finite Group Databasebeta

← C2×#11738654 #14222066

Subgroups — C2×#11738654 #14222066

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90388C211yesmaximal, characteristic, complemented
2C2×#90265C211yesmaximal, characteristic
3C2×C7×#479C211yesmaximal, characteristic, complemented
4C2×#89838C211yesmaximal, characteristic, complemented
5C2×#89803C211yesmaximal, characteristic, complemented
6#11738654C2116yesmaximal, direct product factor
7C2×#89656C211yesmaximal, characteristic, complemented
8C2×#89661C211yesmaximal, characteristic, complemented
9C2×#89634C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89613C211yesmaximal, characteristic, complemented
12C2×#89612C211yesmaximal, characteristic, complemented
13C2×#89582C211yesmaximal, characteristic
14C2×#89582C211yesmaximal, characteristic
15C2×#89561C211yesmaximal, characteristic, complemented
16C2×#89562C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C2×C7×#125C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C22×#1144C2211yescharacteristic
22C22×#1144C2211yescharacteristic
23C22×#1132C2211yescharacteristic
24C22×#1132C2211yescharacteristic
25#90388—24no—
26#90388C2218yescomplemented
27#90265—24no—
28#90265C2218yes—
29C2×#6461—21no—
30C2×#6461—21no—
31C2×#6460C2211yescharacteristic
32C2×#6460C2211yescharacteristic
33C2×#6456—21no—
34C2×#6456C2211yescharacteristic
35C2×D7×C4⋊C4—21no—
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6453—21no—
38C2×#6453—21no—
39C2×#6450C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×C4×D28—21no—
42C2×C4×D28C2211yescharacteristic
43C2×#6435—21no—
44C2×#6435C2211yescharacteristic
45C2×#6432C2211yescharacteristic
46C7×#479C2218yescomplemented
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#103C2211yescharacteristic
52C2×(C2×D7)⋊C8C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×#6390C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6389C2211yescharacteristic
57C2×C8×Dic7C2211yescharacteristic
58#89838C2218yescomplemented
59#89803C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89661C2218yescomplemented
68#89656C2218yescomplemented
69#89634C2218yescomplemented
70#89624C2218yescomplemented
71#89613C2218yescomplemented
72#89612C2218yescomplemented
73#89582C2218yes—
74#89582C2218yes—
75#89562C2218yescomplemented
76#89561C2218yescomplemented
77C2×#3120—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C2×#1161—24no—
80C2×#1161—24no—
81C2×#1161—22no—
82C2×#1161C2314yes—
83C22×D28—21no—
84C22×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7C2311yescharacteristic
90C22×Dic14C2311yescharacteristic
91C22×Dic14C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×#125—22no—
95C7×#125C2314yes—
96C4×C7×Q8—22no—
97C4×C7×Q8C2314yes—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106Q8×Dic7—22no—
107Q8×Dic7C2314yes—
108C2×#1144—24no—
109C2×#1144—24no—
110C2×#1144C2314yes—
111C2×#1144C2314yes—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4D411yescharacteristic
117C2×(C2×D7)⋊C4D411yescharacteristic
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7C2311yescharacteristic
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4D411yescharacteristic
128C2×Dic7⋊C4D411yescharacteristic
129C2×C4×Dic7—21no—
130C2×C4×Dic7—21no—
131C2×C4×Dic7—21no—
132C2×C4×Dic7C2311yescharacteristic
133C22×C7⋊C8C2311yescharacteristic
134C22×C7⋊C8C2311yescharacteristic
135C2×#1132—24no—
136C2×#1132—24no—
137C2×#1132C2314yes—
138C2×#1132C2314yes—
139#6461—28no—
140#6461—28no—
141#6460—22no—
142#6460—22no—
143#6460C2314yes—
144#6460C2314yes—
145#6456—28no—
146#6456—22no—
147#6456C2314yes—
148D7×C4⋊C4—22no—
149D7×C4⋊C4—28no—
150D7×C4⋊C4C2314yes—
151#6453—28no—
152#6453—28no—
153#6450—22no—
154#6450—22no—
155#6450C2314yes—
156#6450C2314yes—
157C4×D28—22no—
158C4×D28—28no—
159C4×D28C2314yes—
160#6435—28no—
161#6435D414yes—
162#6435C2314yes—
163#6432—22no—
164#6432C2314yes—
165C7×#107C2314yes—
166C7×#106C2314yes—
167C7×C4⋊C8C2314yes—
168C7×#103C2314yes—
169C7×#103C2314yes—
170(C2×D7)⋊C8C2314yes—
171(C2×D7)⋊C8C2314yes—
172#6390C2314yes—
173#6390C2314yes—
174#6389C2314yes—
175C8×Dic7C2314yes—
176#6384C2314yes—
177#6384C2314yes—
178#6383C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#541—71no—
184C2×#520—71no—
185#3120—716no—
186C2×#484—71no—
187C2×#483—71no—
188C2×#479D711yescharacteristic, complemented
189C2×#478—71no—
190C2×#462—71no—
191C2×#461—71no—
192C2×#452—71no—
193C2×#452—71no—
194C2×#441—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C23×D7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—22no—
203C2×C7×Q8#4114yes—
204C2×C7×Q8C2412yes—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2411yescharacteristic
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7C2×D411yescharacteristic
216C22×Dic7C2×D411yescharacteristic
217C22×Dic7C2×D411yescharacteristic
218#1161—216no—
219#1161—28no—
220#1161—28no—
221C2×D28—28no—
222C2×D28—24no—
223C2×D28—21no—
224C2×D28—22no—
225C2×D28#4114yes—
226C2×D28C2412yes—
227C2×C4×D7—28no—
228C2×C4×D7—22no—
229C2×C4×D7—22no—
230C2×C4×D7—24no—
231C2×C4×D7—24no—
232C2×C4×D7—24no—
233C2×C4×D7—24no—
234C2×C4×D7—82no—
235C2×C4×D7—82no—
236C2×C4×D7—82no—
237C2×C4×D7C2×D412yes—
238C2×C4×D7C2412yes—
239C2×Dic14—22no—
240C2×Dic14—22no—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14—21no—
245C2×Dic14C2412yes—
246C2×Dic14C2412yes—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4C2412yes—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C42×C7—24no—
261C42×C7C2×D412yes—
262C42×C7C2412yes—
263#1144—28no—
264#1144—28no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4C2×D414yes—
270(C2×D7)⋊C4C2×D414yes—
271C4⋊Dic7—24no—
272C4⋊Dic7—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7—24no—
275C4⋊Dic7—24no—
276C4⋊Dic7—24no—
277C4⋊Dic7C2412yes—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4C2×D414yes—
282Dic7⋊C4C2×D414yes—
283C4×Dic7—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7C2×D412yes—
287C4×Dic7C2412yes—
288C2×C7⋊C8—22no—
289C2×C7⋊C8—22no—
290C2×C7⋊C8C2412yes—
291C2×C7⋊C8C2412yes—
292#1132—28no—
293#1132—28no—
294C22×#41—71no—
295C22×Q16—71no—
296C22×Q16—71no—
297C22×SD16—71no—
298C22×SD16—71no—
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#126—141no—
304C2×#125—141no—
305C2×#125—141no—
306C2×#125C2×D711yescharacteristic
307C2×C22⋊Q8—71no—
308C2×C22⋊Q8—71no—
309#520—78no—
310#520—144no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8—71no—
314C2×C4×Q8C2×D711yescharacteristic
315C2×C4×D4—71no—
316C2×C4×D4—71no—
317C2×C4×D4—141no—
318C2×C4×D4—141no—
319C2×#117—71no—
320C2×#117—141no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—141no—
323#484—78no—
324#483—78no—
325#479C2×D718yescomplemented
326#478—78no—
327#462—78no—
328#461—78no—
329#452—78no—
330#452—78no—
331#441—78no—
332#440—78no—
333C4×Q16—78no—
334C4×SD16—78no—
335#433—78no—
336C2×#107—71no—
337C2×#107C2×D711yescharacteristic
338C2×#106—71no—
339C2×#106C2×D711yescharacteristic
340C2×C4⋊C8—71no—
341C2×C4⋊C8C2×D711yescharacteristic
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103C2×D711yescharacteristic
347C2×#103C2×D711yescharacteristic
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8—71no—
351C2×C22⋊C8—71no—
352C2×#97—71no—
353C2×C4×C8—71no—
354C23×C7C22×D411yescharacteristic
355C22×D7—22no—
356C22×D7—24no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7C22×D412yes—
363C7×Q8—24no—
364C7×Q8—22no—
365C7×Q8C2×#4114yes—
366C2×C4×C7—24no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D411yescharacteristic
379C2×C4×C7C2×#4112yes—
380C2×C4×C7C2×#4112yes—
381C2×C4×C7C2511yescharacteristic
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7C22×D412yes—
392C2×Dic7C22×D412yes—
393C2×Dic7C22×D412yes—
394D28—216no—
395D28—24no—
396D28—22no—
397D28C2×#4114yes—
398C4×D7—216no—
399C4×D7—24no—
400C4×D7—22no—
401C4×D7—22no—
402C4×D7—84no—
403C4×D7—84no—
404C4×D7—84no—
405Dic14—22no—
406Dic14—22no—
407Dic14—22no—
408Dic14—22no—
409Dic14—42no—
410Dic14—42no—
411C7×C8—22no—
412C7×C8—22no—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C2×#41—74no—
416C2×#41—142no—
417C2×#41—144no—
418C2×#41—144no—
419C22×Q8—71no—
420C22×Q8—71no—
421C22×Q8C22×D711yescharacteristic
422C22×D4—71no—
423C22×D4—141no—
424C23×C4—71no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4—141no—
428C23×C4—141no—
429C2×Q16—74no—
430C2×Q16—74no—
431C2×Q16—144no—
432C2×Q16—144no—
433C2×SD16—74no—
434C2×SD16—74no—
435C2×SD16—144no—
436C2×SD16—144no—
437C22×C8—71no—
438C22×C8—71no—
439C22×C8C22×D711yescharacteristic
440C22×C8C22×D711yescharacteristic
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443#126—148no—
444#126—148no—
445#125—22no—
446#125—148no—
447#125—148no—
448#125C22×D714yes—
449C22⋊Q8—74no—
450C22⋊Q8—74no—
451C22⋊Q8—142no—
452C22⋊Q8—142no—
453C4×Q8—22no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—142no—
458C4×Q8—142no—
459C4×Q8—142no—
460C4×Q8C22×D714yes—
461C4×D4—74no—
462C4×D4—74no—
463C4×D4—148no—
464C4×D4—142no—
465C4×D4—148no—
466C4×D4—142no—
467#117—74no—
468#117—74no—
469#117—148no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—148no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4C22×D711yescharacteristic
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C22⋊C4—71no—
491C2×C22⋊C4—71no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C42—21no—
497C2×C42—71no—
498C2×C42—141no—
499C2×C42—141no—
500C2×C42—141no—
501C2×C42C22×D711yescharacteristic
502#107—74no—
503#107C22×D714yes—
504#106—74no—
505#106C22×D714yes—
506C4⋊C8—74no—
507C4⋊C8C22×D714yes—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103C22×D714yes—
513#103C22×D714yes—
514#102—74no—
515#102—74no—
516C22⋊C8—74no—
517C22⋊C8—74no—
518#97—74no—
519C4×C8—74no—
520C22×C7#52512yes—
521C22×C7#57712yes—
522C22×C7#57812yes—
523C22×C7C23×D411yescharacteristic
524C2×D7—22no—
525C2×D7—24no—
526C2×D7—22no—
527C2×D7—22no—
528C2×D7—44no—
529C2×D7—48no—
530C2×D7—42no—
531C2×D7—42no—
532C4×C7—24no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7—42no—
538C4×C7#52512yes—
539C4×C7C22×#4111yescharacteristic
540C4×C7C22×#4111yescharacteristic
541Dic7—22no—
542Dic7—22no—
543Dic7—22no—
544Dic7—42no—
545Dic7—42no—
546Dic7—42no—
547C24—71no—
548C24—141no—
549#41—148no—
550#41—1416no—
551#41—148no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—72no—
555C2×Q8—72no—
556C2×Q8—141no—
557C2×Q8—141no—
558C2×Q8—142no—
559C2×Q8—142no—
560C2×Q8—142no—
561C2×Q8—142no—
562C2×Q8#116114yes—
563C2×Q8C23×D712yes—
564C2×D4—74no—
565C2×D4—72no—
566C2×D4—144no—
567C2×D4—148no—
568C2×D4—141no—
569C2×D4—142no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—71no—
575C22×C4—71no—
576C22×C4—71no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—144no—
580C22×C4—144no—
581C22×C4—148no—
582C22×C4—144no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—144no—
589C22×C4—562no—
590C22×C4—562no—
591C22×C4—562no—
592C22×C4D4×D711yescharacteristic
593C22×C4D4×D711yescharacteristic
594C22×C4C23×D711yescharacteristic
595Q16—148no—
596Q16—148no—
597SD16—148no—
598SD16—148no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—72no—
602C2×C8—72no—
603C2×C8—142no—
604C2×C8—142no—
605C2×C8C23×D712yes—
606C2×C8C23×D712yes—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—74no—
614C4⋊C4—74no—
615C4⋊C4—72no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—141no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4C23×D712yes—
626C4⋊C4C23×D712yes—
627C4⋊C4C23×D712yes—
628C22⋊C4—74no—
629C22⋊C4—74no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C42—24no—
635C42—72no—
636C42—72no—
637C42—144no—
638C42—144no—
639C42—144no—
640C42D4×D712yes—
641C42C23×D712yes—
642C2×C7#312014yescomplemented
643C2×C7C2×#52511yescharacteristic
644C2×C7C2×#57711yescharacteristic
645C2×C7C2×#57811yescharacteristic
646D7—42no—
647D7—44no—
648C23—72no—
649C23—142no—
650C23—142no—
651C23—144no—
652C23—142no—
653C23—142no—
654C23—282no—
655C23—282no—
656C23C2×D4×D711yescharacteristic
657Q8—24no—
658Q8—22no—
659Q8—142no—
660Q8—142no—
661Q8—142no—
662Q8—142no—
663Q8—282no—
664Q8—282no—
665Q8C2×#116114yes—
666D4—74no—
667D4—1416no—
668D4—144no—
669D4—142no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—72no—
681C2×C4—72no—
682C2×C4—72no—
683C2×C4—1416no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—144no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—564no—
697C2×C4—564no—
698C2×C4—564no—
699C2×C4C2×D4×D712yes—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4C2×#116112yes—
703C2×C4D7×#4112yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—142no—
708C8—142no—
709C7C2×#312011yescharacteristic, complemented, Sylow
710C22—142no—
711C22—144no—
712C22—142no—
713C22—142no—
714C22—282no—
715C22—284no—
716C22—288no—
717C22—282no—
718C22#9031812yes—
719C22#9046112yes—
720C22#9047012yes—
721C22C22×D4×D711yescharacteristic
722C4—22no—
723C4—24no—
724C4—22no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—142no—
729C4—142no—
730C4—142no—
731C4—282no—
732C4—282no—
733C4—282no—
734C4#9031812yes—
735C4C22×#116111yescharacteristic
736C4C2×D7×#4111yescharacteristic
737C2—282no—
738C2—284no—
739C2#1173865414yesdirect product factor
740C2C2×#9031811yescharacteristic
741C2C2×#9046111yescharacteristic
742C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#479C2
socleC23×C7C22×D4
prime radicalC22×#1161C22
hypercenterC2×#479D7
hypocenterC7C2×#3120
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#90388C2semidirect
3. C2×C7×#479C2semidirect
4. C2×#89838C2semidirect
5. C2×#89803C2semidirect
6. #11738654C2direct (N × H)
7. C2×#89656C2semidirect
8. C2×#89661C2semidirect
9. C2×#89634C2semidirect
10. C2×#89624C2semidirect
11. C2×#89613C2semidirect
12. C2×#89612C2semidirect
15. C2×#89561C2semidirect
16. C2×#89562C2semidirect
26. #90388C22semidirect
46. C7×#479C22semidirect
58. #89838C22semidirect
59. #89803C22semidirect
67. #89661C22semidirect
68. #89656C22semidirect
69. #89634C22semidirect
70. #89624C22semidirect
71. #89613C22semidirect
72. #89612C22semidirect
75. #89562C22semidirect
76. #89561C22semidirect
188. C2×#479D7semidirect
325. #479C2×D7semidirect
642. C2×C7#3120semidirect
709. C7C2×#3120semidirect
739. C2#11738654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903882
C2×#902652
C2×C7×#4792
C2×#898382
C2×#898032
#117386542
C2×#896562
C2×#896612
C2×#896342
C2×#896242
C2×#896132
C2×#896122
C2×#895822
C2×#895612
C2×#895622
C2×#31207