Finite Group Databasebeta

← C2×#11726796 #13381223

Subgroups — C2×#11726796 #13381223

Order 1792.

1234 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90208C211yesmaximal, characteristic, complemented
2C2×#89911C211yesmaximal, characteristic
3C22×#6399C211yesmaximal, characteristic
4C2×#89778C211yesmaximal, characteristic
5C2×C7×#344C211yesmaximal, characteristic, complemented
6C2×#89352C211yesmaximal, characteristic, complemented
7C2×#89350C211yesmaximal, characteristic, complemented
8#11726796C218yesmaximal, direct product factor
9C22×#1157C2211yescharacteristic
10C22×C7×M16C2211yescharacteristic
11C22×C7×M16C2211yescharacteristic
12C2×C7×#117C2211yescharacteristic
13C2×#6489C2211yescharacteristic
14C2×#6489C2211yescharacteristic
15C22×C4×Dic7C2211yescharacteristic
16#90208—22no—
17#90208—22no—
18#90208—22no—
19#90208C2214yescomplemented
20C2×#6453—21no—
21C2×#6451—21no—
22C2×#6441—22no—
23C2×C4×Dic14—22no—
24#89911—22no—
25#89911C2214yes—
26C2×#6399—21no—
27C2×#6399—21no—
28C2×#6399—22no—
29C2×#6399—22no—
30C2×#6399C2214yes—
31#89778—22no—
32#89778C2214yes—
33C2×#6380—22no—
34C7×#344C2214yescomplemented
35#89352C2214yescomplemented
36#89350C2214yescomplemented
37C2×#2031—71nomaximal, Sylow
38C23×C4×C7C2311yescharacteristic
39C22×C22⋊D7—21no—
40C23×Dic7—21no—
41C2×#1157—21no—
42C2×#1157—21no—
43C2×#1157—21no—
44C2×#1157—21no—
45C2×#1157—21no—
46C2×#1157—21no—
47C2×#1157—21no—
48C2×#1157—21no—
49C2×#1157—21no—
50C2×#1157—21no—
51C2×#1157Q812yescomplemented
52C2×#1157C2312yes—
53C22×D28Q811yescharacteristic, complemented
54C22×C4×D7—21no—
55C22×Dic14—22no—
56C22×Dic14Q811yescharacteristic, complemented
57C2×C7×M16—21no—
58C2×C7×M16—21no—
59C2×C7×M16—21no—
60C2×C7×M16—21no—
61C2×C7×M16—21no—
62C2×C7×M16—21no—
63C2×C7×M16—21no—
64C2×C7×M16—21no—
65C2×C7×M16—21no—
66C2×C7×M16—21no—
67C2×C7×M16C2312yes—
68C2×C7×M16C2312yes—
69C22×C7×C8—21no—
70C22×C7×C8—21no—
71C7×#117—21no—
72C7×#117—21no—
73C7×#117D412yes—
74C7×#117C2312yes—
75C2×C7×C4⋊C4—21no—
76C2×C7×C22⋊C4D412yes—
77C2×C42×C7—21no—
78C2×C22⋊Dic7—21no—
79C2×C22⋊Dic7—21no—
80#6489—21no—
81#6489—21no—
82#6489—21no—
83#6489—21no—
84#6489—21no—
85#6489D412yes—
86#6489C2312yes—
87#6489C2312yes—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7—21no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—22no—
93C2×C4×Dic7—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7—21no—
97C2×C4×Dic7D412yes—
98C2×C4×Dic7D411yescharacteristic
99C2×C4×Dic7D411yescharacteristic
100C2×C4×Dic7D412yes—
101C2×C4×Dic7C2312yes—
102#6453—24no—
103#6453—24no—
104#6451—24no—
105#6451—24no—
106#6441—28no—
107#6441—28no—
108C4×Dic14—28no—
109C4×Dic14—28no—
110#6399—24no—
111#6399—24no—
112#6399—28no—
113#6380—28no—
114C2×#533—71no—
115C2×#421—71no—
116C22×#104—71no—
117C2×#410—71no—
118#2031—78no—
119C2×#344D711yescharacteristic, complemented
120C2×#339—71no—
121C2×H(3,ℤ/4)—71no—
122C24×C7C2×D411yescharacteristic
123C23×D7—21no—
124C22×C4×C7—22no—
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7C2×D411yescharacteristic
129C22×C4×C7C2×D411yescharacteristic
130C22×C4×C7C2×Q811yescharacteristic
131C22×C4×C7C2×Q811yescharacteristic
132C22×C4×C7#4111yescharacteristic
133C22×C4×C7#4111yescharacteristic
134C22×C4×C7#4111yescharacteristic
135C22×C4×C7#4111yescharacteristic
136C22×C4×C7#4111yescharacteristic
137C22×C4×C7#4111yescharacteristic
138C22×C4×C7C2411yescharacteristic
139C2×C22⋊D7—22no—
140C2×C22⋊D7—22no—
141C2×C22⋊D7—41no—
142C2×C22⋊D7—41no—
143C2×C22⋊D7—41no—
144C2×C22⋊D7—41no—
145C22×Dic7—21no—
146C22×Dic7—22no—
147C22×Dic7—21no—
148C22×Dic7—22no—
149C22×Dic7—21no—
150C22×Dic7—22no—
151C22×Dic7—44no—
152C22×Dic7—41no—
153#1157—22no—
154#1157—22no—
155#1157—22no—
156#1157—22no—
157#1157—22no—
158#1157—22no—
159#1157—22no—
160#1157—22no—
161#1157—41no—
162#1157—41no—
163#1157—41no—
164#1157—41no—
165#1157—41no—
166#1157—41no—
167#1157—41no—
168#1157—41no—
169C2×D28—21no—
170C2×D28—21no—
171C2×D28—21no—
172C2×D28—21no—
173C2×D28—21no—
174C2×D28C2×Q812yescomplemented
175C2×C4×D7—22no—
176C2×C4×D7—22no—
177C2×C4×D7—41no—
178C2×C4×D7—41no—
179C2×C4×D7—41no—
180C2×C4×D7—41no—
181C2×Dic14—21no—
182C2×Dic14—21no—
183C2×Dic14—21no—
184C2×Dic14—21no—
185C2×Dic14—28no—
186C2×Dic14—21no—
187C2×Dic14—48no—
188C2×Dic14C2×Q812yescomplemented
189C7×M16—22no—
190C7×M16—22no—
191C7×M16—22no—
192C7×M16—22no—
193C7×M16—41no—
194C7×M16—41no—
195C7×M16—41no—
196C7×M16—41no—
197C2×C7×C8—22no—
198C2×C7×C8—22no—
199C2×C7×C8—41no—
200C2×C7×C8—41no—
201C2×C7×C8—41no—
202C2×C7×C8—41no—
203C7×C4⋊C4—22no—
204C7×C4⋊C4—22no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4C2×D414yes—
207C42×C7—22no—
208C42×C7—22no—
209C22⋊Dic7—22no—
210C22⋊Dic7—22no—
211C22⋊Dic7—22no—
212C22⋊Dic7—41no—
213C4⋊Dic7—28no—
214C4⋊Dic7—22no—
215C4⋊Dic7—22no—
216C4⋊Dic7—22no—
217C4⋊Dic7—41no—
218Dic7⋊C4—28no—
219Dic7⋊C4—28no—
220C4×Dic7—22no—
221C4×Dic7—22no—
222C4×Dic7—21no—
223C4×Dic7—21no—
224C4×Dic7—22no—
225C4×Dic7—22no—
226C4×Dic7—41no—
227C4×Dic7C2×D414yes—
228C4×Dic7C2×D412yes—
229C4×Dic7C2×D412yes—
230C22×#41—71no—
231C22×M16C2×D711yescharacteristic
232C22×M16C2×D711yescharacteristic
233#533—74no—
234#533—142no—
235#533—142no—
236#533—142no—
237C2×C4⋊Q8—141no—
238C2×#125—141no—
239C2×C22⋊Q8—142no—
240C2×C4×Q8—142no—
241C2×#117—71no—
242C2×#117—71no—
243C2×#117C2×D711yescharacteristic
244C22×C42—71no—
245#421—74no—
246#421—142no—
247C2×#104—74no—
248C2×#104—141no—
249C2×#104—141no—
250C2×#104—142no—
251C2×#104—142no—
252#410—74no—
253#410—142no—
254C2×#99—142no—
255#344C2×D714yescomplemented
256#339—74no—
257H(3,ℤ/4)—74no—
258C23×C7—42no—
259C23×C7#12011yescharacteristic
260C23×C7#12011yescharacteristic
261C23×C7C22⋊Q811yescharacteristic
262C23×C7C22⋊Q811yescharacteristic
263C23×C7#12411yescharacteristic
264C23×C7#12411yescharacteristic
265C23×C7C22×D411yescharacteristic
266C22×D7—22no—
267C22×D7—41no—
268C22×D7—41no—
269C22×D7—82no—
270C2×C4×C7—24no—
271C2×C4×C7—44no—
272C2×C4×C7#12011yescharacteristic
273C2×C4×C7#12011yescharacteristic
274C2×C4×C7C22⋊Q811yescharacteristic
275C2×C4×C7C22⋊Q811yescharacteristic
276C2×C4×C7C22⋊Q811yescharacteristic
277C2×C4×C7C22⋊Q811yescharacteristic
278C2×C4×C7C22⋊Q811yescharacteristic
279C2×C4×C7C22⋊Q811yescharacteristic
280C2×C4×C7C22⋊Q811yescharacteristic
281C2×C4×C7C22⋊Q811yescharacteristic
282C2×C4×C7C22⋊Q811yescharacteristic
283C2×C4×C7C22⋊Q811yescharacteristic
284C2×C4×C7#12411yescharacteristic
285C2×C4×C7#12411yescharacteristic
286C2×C4×C7#12411yescharacteristic
287C2×C4×C7#12411yescharacteristic
288C2×C4×C7#12411yescharacteristic
289C2×C4×C7#12411yescharacteristic
290C2×C4×C7#12411yescharacteristic
291C2×C4×C7#12411yescharacteristic
292C2×C4×C7#12411yescharacteristic
293C2×C4×C7#12411yescharacteristic
294C2×C4×C7C22×D411yescharacteristic
295C2×C4×C7C22×D411yescharacteristic
296C2×C4×C7C22×Q811yescharacteristic
297C2×C4×C7C2×#4111yescharacteristic
298C2×C4×C7C2×#4111yescharacteristic
299C2×C4×C7C2×#4111yescharacteristic
300C22⋊D7—42no—
301C22⋊D7—42no—
302C22⋊D7—42no—
303C22⋊D7—42no—
304C2×Dic7—24no—
305C2×Dic7—22no—
306C2×Dic7—22no—
307C2×Dic7—24no—
308C2×Dic7—22no—
309C2×Dic7—44no—
310C2×Dic7—44no—
311C2×Dic7—44no—
312C2×Dic7—42no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—42no—
316C2×Dic7—82no—
317D28—22no—
318D28—22no—
319D28—41no—
320D28—41no—
321C4×D7—42no—
322C4×D7—42no—
323C4×D7—42no—
324C4×D7—42no—
325Dic14—22no—
326Dic14—22no—
327Dic14—416no—
328Dic14—41no—
329Dic14—41no—
330C7×C8—42no—
331C7×C8—42no—
332C2×#41—72no—
333C2×#41—72no—
334C2×#41—141no—
335C2×#41—141no—
336C2×#41—141no—
337C2×#41—141no—
338C2×#41—141no—
339C2×#41—141no—
340C2×#41—141no—
341C2×#41—141no—
342C2×#41—141no—
343C2×#41—141no—
344C22×Q8—71no—
345C22×Q8—142no—
346C22×D4—71no—
347C22×D4—141no—
348C23×C4—141no—
349C23×C4—141no—
350C23×C4C22×D711yescharacteristic
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16C22×D712yes—
362C2×M16C22×D712yes—
363C22×C8—21no—
364C22×C8—21no—
365C4⋊Q8—144no—
366C4⋊Q8—144no—
367#125—144no—
368#125—144no—
369C22⋊Q8—148no—
370C22⋊Q8—148no—
371C4×Q8—148no—
372C4×Q8—148no—
373#117—21no—
374#117—21no—
375#117—72no—
376#117—72no—
377#117—72no—
378#117—141no—
379#117—141no—
380#117—141no—
381#117—141no—
382#117—141no—
383#117D2812yes—
384#117C22×D712yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—142no—
387C2×C4⋊C4—142no—
388C2×C4⋊C4—142no—
389C2×C4⋊C4—141no—
390C2×C4⋊C4—141no—
391C2×C22⋊C4—141no—
392C2×C22⋊C4—141no—
393C2×C22⋊C4D2812yes—
394C2×C42—21no—
395C2×C42—72no—
396C2×C42—71no—
397C2×C42—71no—
398C2×C42—72no—
399C2×C42—72no—
400C2×C42—141no—
401C2×C42—141no—
402C2×C42—141no—
403C2×C42—141no—
404#104—144no—
405#104—144no—
406#104—148no—
407#99—148no—
408C22×C7—22no—
409C22×C7—22no—
410C22×C7—22no—
411C22×C7—41no—
412C22×C7—41no—
413C22×C7—41no—
414C22×C7—41no—
415C22×C7#39311yescharacteristic
416C22×C7#39311yescharacteristic
417C22×C7#39311yescharacteristic
418C22×C7#39311yescharacteristic
419C22×C7C2×#12011yescharacteristic
420C22×C7C2×C22⋊Q811yescharacteristic
421C22×C7C2×#12411yescharacteristic
422C2×D7—42no—
423C2×D7—82no—
424C2×D7—82no—
425C2×D7—82no—
426C4×C7—44no—
427C4×C7#39311yescharacteristic
428C4×C7#39311yescharacteristic
429C4×C7#39311yescharacteristic
430C4×C7#39311yescharacteristic
431C4×C7C2×C22⋊Q811yescharacteristic
432C4×C7C2×C22⋊Q811yescharacteristic
433C4×C7C2×#12411yescharacteristic
434C4×C7C2×#12411yescharacteristic
435Dic7—24no—
436Dic7—44no—
437Dic7—42no—
438Dic7—42no—
439Dic7—82no—
440C24—141no—
441C24C2×D2811yescharacteristic
442#41—142no—
443#41—142no—
444#41—142no—
445#41—142no—
446#41—142no—
447#41—142no—
448#41—142no—
449#41—142no—
450#41—281no—
451#41—281no—
452#41—281no—
453#41—281no—
454#41—281no—
455#41—281no—
456#41—281no—
457#41—281no—
458C2×Q8—72no—
459C2×Q8—148no—
460C2×Q8—141no—
461C2×Q8—141no—
462C2×Q8—141no—
463C2×Q8—141no—
464C2×Q8—141no—
465C2×Q8—288no—
466C2×D4—72no—
467C2×D4—142no—
468C2×D4—142no—
469C2×D4—141no—
470C2×D4—141no—
471C2×D4—141no—
472C2×D4—141no—
473C2×D4—141no—
474C2×D4—281no—
475C2×D4—281no—
476C2×D4—281no—
477C2×D4—281no—
478C22×C4—22no—
479C22×C4—141no—
480C22×C4—141no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—141no—
484C22×C4—142no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—284no—
488C22×C4—281no—
489C22×C4—281no—
490C22×C4—281no—
491C22×C4—281no—
492C22×C4—281no—
493C22×C4C2×D2811yescharacteristic
494C22×C4#115711yescharacteristic
495C22×C4#115711yescharacteristic
496C22×C4#115711yescharacteristic
497C22×C4#115711yescharacteristic
498C22×C4D4×D711yescharacteristic
499C22×C4D4×D711yescharacteristic
500C22×C4D4×D711yescharacteristic
501C22×C4D4×D711yescharacteristic
502C22×C4#115911yescharacteristic
503C22×C4#115911yescharacteristic
504C22×C4Q8×D711yescharacteristic
505C22×C4Q8×D711yescharacteristic
506C22×C4C23×D711yescharacteristic
507M16—22no—
508M16—22no—
509M16—22no—
510M16—22no—
511M16—41no—
512M16—41no—
513M16—41no—
514M16—41no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—148no—
524C4⋊C4—148no—
525C4⋊C4—148no—
526C4⋊C4—142no—
527C4⋊C4—142no—
528C4⋊C4—142no—
529C4⋊C4—281no—
530C22⋊C4—22no—
531C22⋊C4—142no—
532C22⋊C4—142no—
533C22⋊C4—142no—
534C22⋊C4—281no—
535C22⋊C4C2×D2814yes—
536C42—22no—
537C42—22no—
538C42—72no—
539C42—72no—
540C42—74no—
541C42—142no—
542C42—141no—
543C42—141no—
544C42—142no—
545C42—142no—
546C42—142no—
547C42—281no—
548C2×C7—21no—
549C2×C7—21no—
550C2×C7—21no—
551C2×C7—21no—
552C2×C7—21no—
553C2×C7—21no—
554C2×C7#203112yescomplemented
555C2×C7C2×#39311yescharacteristic
556D7—82no—
557C23—42no—
558C23—142no—
559C23—281no—
560C23—281no—
561C23—562no—
562C23#643811yescharacteristic
563C23#643811yescharacteristic
564C23#644511yescharacteristic
565C23#644511yescharacteristic
566C23#646011yescharacteristic
567C23#646011yescharacteristic
568C23C22×D2811yescharacteristic
569Q8—142no—
570Q8—142no—
571Q8—2816no—
572Q8—281no—
573Q8—281no—
574D4—142no—
575D4—142no—
576D4—282no—
577D4—282no—
578D4—282no—
579D4—282no—
580D4—281no—
581D4—281no—
582C2×C4—24no—
583C2×C4—44no—
584C2×C4—144no—
585C2×C4—142no—
586C2×C4—142no—
587C2×C4—144no—
588C2×C4—142no—
589C2×C4—284no—
590C2×C4—284no—
591C2×C4—282no—
592C2×C4—284no—
593C2×C4—281no—
594C2×C4—281no—
595C2×C4—282no—
596C2×C4—282no—
597C2×C4—282no—
598C2×C4—282no—
599C2×C4—282no—
600C2×C4—562no—
601C2×C4#643811yescharacteristic
602C2×C4#643811yescharacteristic
603C2×C4#644511yescharacteristic
604C2×C4#644511yescharacteristic
605C2×C4#644811yescharacteristic
606C2×C4#644811yescharacteristic
607C2×C4#644811yescharacteristic
608C2×C4#644811yescharacteristic
609C2×C4#644811yescharacteristic
610C2×C4#644811yescharacteristic
611C2×C4#644811yescharacteristic
612C2×C4#644811yescharacteristic
613C2×C4#645911yescharacteristic
614C2×C4#645911yescharacteristic
615C2×C4#645911yescharacteristic
616C2×C4#645911yescharacteristic
617C2×C4#645911yescharacteristic
618C2×C4#645911yescharacteristic
619C2×C4#645911yescharacteristic
620C2×C4#645911yescharacteristic
621C2×C4#646011yescharacteristic
622C2×C4#646011yescharacteristic
623C2×C4C2×#115711yescharacteristic
624C2×C4C2×#115711yescharacteristic
625C2×C4C2×D4×D711yescharacteristic
626C2×C4C2×D4×D711yescharacteristic
627C2×C4C2×#115911yescharacteristic
628C2×C4C2×Q8×D711yescharacteristic
629C8—42no—
630C8—42no—
631C7C2×#203111yescharacteristic, complemented, Sylow
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—282no—
640C22—562no—
641C22—562no—
642C22—562no—
643C22#8944511yescharacteristic
644C22#8944511yescharacteristic
645C22#8944511yescharacteristic
646C22#8944511yescharacteristic
647C22C2×#643811yescharacteristic
648C22C2×#644511yescharacteristic
649C22C2×#646011yescharacteristic
650C4—44no—
651C4—144no—
652C4—282no—
653C4—284no—
654C4—282no—
655C4—562no—
656C4#8944511yescharacteristic
657C4#8944511yescharacteristic
658C4#8944511yescharacteristic
659C4#8944511yescharacteristic
660C4C2×#644811yescharacteristic
661C4C2×#644811yescharacteristic
662C4C2×#645911yescharacteristic
663C4C2×#645911yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—562no—
671C2#1172679612yesdirect product factor
672C2C2×#8944511yescharacteristic
subgroupG/H
centerC2×C4#6448
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#344C2
socleC22×C7#393
prime radicalC22×#1157C22
hypercenterC2×#344D7
hypocenterC7C2×#2031
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#90208C2semidirect
5. C2×C7×#344C2semidirect
6. C2×#89352C2semidirect
7. C2×#89350C2semidirect
8. #11726796C2direct (N × H)
19. #90208C22semidirect
34. C7×#344C22semidirect
35. #89352C22semidirect
36. #89350C22semidirect
51. C2×#1157Q8semidirect
53. C22×D28Q8semidirect
56. C22×Dic14Q8semidirect
119. C2×#344D7semidirect
174. C2×D28C2×Q8semidirect
188. C2×Dic14C2×Q8semidirect
255. #344C2×D7semidirect
554. C2×C7#2031semidirect
631. C7C2×#2031semidirect
671. C2#11726796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902082
C2×#899112
C22×#63992
C2×#897782
C2×C7×#3442
C2×#893522
C2×#893502
#117267962
C2×#20317