Finite Group Databasebeta

← C2×#11738914 #14221599

Subgroups — C2×#11738914 #14221599

Order 1792.

2326 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C22⋊Q8C211yesmaximal, characteristic
2C22×#6455C211yesmaximal, characteristic
3C2×C7×#484C211yesmaximal, characteristic, complemented
4C2×#89815C211yesmaximal, characteristic, complemented
5C2×#89742C211yesmaximal, characteristic, complemented
6#11738914C2116yesmaximal, direct product factor
7C2×#89660C212yesmaximal, complemented
8C2×#89653C212yesmaximal, complemented
9C2×#89587C212yesmaximal, complemented
10C2×#89574C212yesmaximal, complemented
11C2×#89498C211yesmaximal, characteristic
12C2×#89493C211yesmaximal, characteristic, complemented
13C22×Q8×D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C2×C7×C22⋊Q8C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C2×#6509C2211yescharacteristic
18C22×(C2×D7)⋊C4—21no—
19C22×C4⋊Dic7C2211yescharacteristic
20C2×#6487C2211yescharacteristic
21C22×C4×Dic7—21no—
22C22×#1131C2212yes—
23D7×C22⋊Q8—24no—
24D7×C22⋊Q8C2218yes—
25C2×#6460C2211yescharacteristic
26C2×#6459—21no—
27C2×#6455—21no—
28C2×#6455—21no—
29C2×#6455—24no—
30C2×#6455C2212yes—
31C2×#6455C2212yes—
32C2×#6455C2218yes—
33C2×D7×C4⋊C4—21no—
34C2×D7×C4⋊C4C2211yescharacteristic
35C2×D7×C22⋊C4—21no—
36C2×#6441—21no—
37C7×#484C2218yescomplemented
38C2×C7×#107C2212yescomplemented
39C2×C7×#103C2212yescomplemented
40C2×C7×C22⋊C8C2211yescharacteristic
41C2×#6409C2212yescomplemented
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43C2×(C2×D7)⋊C8C2212yes—
44C2×#6391C2212yescomplemented
45C2×#6390C2212yescomplemented
46#89815C2218yescomplemented
47#89742C2218yescomplemented
48C2×#6384C2212yescomplemented
49C2×#6382C2212yescomplemented
50C2×#6381C2212yescomplemented
51#89660C22116yescomplemented
52#89653C22116yescomplemented
53#89587C22116yescomplemented
54#89574C22116yescomplemented
55#89498C2218yes—
56#89493C2218yescomplemented
57C2×#3095—71nomaximal, Sylow
58C24×D7D411yescharacteristic
59C22×C7×Q8C2311yescharacteristic
60C23×C4×C7—21no—
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—21no—
63C23×Dic7D411yescharacteristic
64C2×Q8×D7—22no—
65C2×Q8×D7—28no—
66C2×Q8×D7C2314yes—
67C22×C4×D7—28no—
68C22×C4×D7—21no—
69C22×C4×D7—21no—
70C22×C4×D7D411yescharacteristic
71C22×C4×D7D411yescharacteristic
72C22×C4×D7D414yes—
73C22×C4×D7C2311yescharacteristic
74C22×C4×D7C2314yes—
75C22×C4×D7C2311yescharacteristic
76C22×Dic14—21no—
77C22×Dic14C2311yescharacteristic
78C22×C7×C8C2312yes—
79C7×C22⋊Q8—22no—
80C7×C22⋊Q8C2314yes—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4C2314yes—
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C4⋊C4C2312yes—
87C2×C7×C22⋊C4—21no—
88C2×C22⋊Dic7—21no—
89#6509—22no—
90#6509C2314yes—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—28no—
95C2×(C2×D7)⋊C4—22no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7C2312yes—
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2314yes—
102#6487—22no—
103#6487C2314yes—
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×C4×Dic7—28no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C22×C7⋊C8C2312yes—
111C2×#1131—28no—
112C2×#1131C2318yes—
113#6460—22no—
114#6460C2314yes—
115#6459—28no—
116#6455—28no—
117#6455—28no—
118#6455—24no—
119#6455—24no—
120#6455C2318yes—
121#6455C2318yes—
122D7×C4⋊C4—28no—
123D7×C4⋊C4—22no—
124D7×C4⋊C4C2314yes—
125D7×C22⋊C4—28no—
126#6441—28no—
127C7×#107C2318yescomplemented
128C7×#103C2318yescomplemented
129C7×C22⋊C8C2314yes—
130#6409C2318yescomplemented
131C22⋊(C7⋊C8)C2314yes—
132(C2×D7)⋊C8C2318yes—
133#6391C2318yescomplemented
134#6390C2318yescomplemented
135#6384C2318yescomplemented
136#6382C2318yescomplemented
137#6381C2318yescomplemented
138C22×C22⋊Q8—71no—
139C22×#117—71no—
140#3095—716no—
141C2×#484—71no—
142C2×#484D711yescharacteristic, complemented
143C2×#485—72no—
144C2×#485—72no—
145C2×#483—71no—
146C2×#483—71no—
147C2×#428—72no—
148C2×#419—72no—
149C2×#407—71no—
150C24×C7C2×D411yescharacteristic
151C23×D7—24no—
152C23×D7—24no—
153C23×D7—42no—
154C23×D7C2×D411yescharacteristic
155C23×D7C2×D414yes—
156C23×D7C2×D411yescharacteristic
157C2×C7×Q8—21no—
158C2×C7×Q8—24no—
159C2×C7×Q8C2412yes—
160C22×C4×C7—24no—
161C22×C4×C7—24no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—44no—
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2412yes—
169C22×C4×C7C2411yescharacteristic
170C22×Dic7—24no—
171C22×Dic7—24no—
172C22×Dic7—22no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—44no—
176C22×Dic7C2×D414yes—
177C22×Dic7C2×D411yescharacteristic
178C22×Dic7C2×D411yescharacteristic
179Q8×D7—216no—
180Q8×D7—48no—
181C2×C4×D7—24no—
182C2×C4×D7—24no—
183C2×C4×D7—24no—
184C2×C4×D7—216no—
185C2×C4×D7—216no—
186C2×C4×D7—24no—
187C2×C4×D7—24no—
188C2×C4×D7—44no—
189C2×C4×D7—44no—
190C2×C4×D7C2×D414yes—
191C2×C4×D7C2×D414yes—
192C2×C4×D7C2×D412yes—
193C2×C4×D7C2×D412yes—
194C2×C4×D7#4118yes—
195C2×C4×D7C2412yes—
196C2×C4×D7C2412yes—
197C2×Dic14—24no—
198C2×Dic14—21no—
199C2×Dic14—24no—
200C2×Dic14—44no—
201C2×Dic14C2412yes—
202C2×C7×C8—24no—
203C2×C7×C8C2414yes—
204C7×C4⋊C4—24no—
205C7×C4⋊C4—21no—
206C7×C4⋊C4—24no—
207C7×C4⋊C4—22no—
208C7×C4⋊C4C2414yes—
209C7×C4⋊C4C2412yes—
210C7×C22⋊C4—24no—
211C22⋊Dic7—24no—
212(C2×D7)⋊C4—24no—
213(C2×D7)⋊C4—24no—
214(C2×D7)⋊C4—28no—
215(C2×D7)⋊C4—28no—
216C4⋊Dic7—21no—
217C4⋊Dic7—24no—
218C4⋊Dic7—22no—
219C4⋊Dic7—24no—
220C4⋊Dic7C2414yes—
221C4⋊Dic7C2412yes—
222Dic7⋊C4—24no—
223Dic7⋊C4—24no—
224Dic7⋊C4—24no—
225C4×Dic7—28no—
226C4×Dic7—28no—
227C2×C7⋊C8—24no—
228C2×C7⋊C8C2414yes—
229#1131—216no—
230C23×Q8—71no—
231C24×C4—71no—
232C22×M16—72no—
233C2×C22⋊Q8—71no—
234C2×C22⋊Q8—71no—
235C2×C22⋊Q8—78no—
236C2×C22⋊Q8—71no—
237C2×C22⋊Q8—141no—
238C2×C22⋊Q8—141no—
239C2×C22⋊Q8—144no—
240C2×C22⋊Q8C2×D711yescharacteristic
241C2×#117—72no—
242C2×#117—78no—
243C2×#117—72no—
244C2×#117—141no—
245C2×#117—144no—
246C2×#117—141no—
247C22×C4⋊C4—71no—
248C22×C4⋊C4—71no—
249C22×C4⋊C4—141no—
250C22×C4⋊C4C2×D711yescharacteristic
251C22×C22⋊C4—141no—
252C22×C22⋊C4—141no—
253C22×C42—141no—
254#485—716no—
255#485—716no—
256#484—78no—
257#484C2×D718yescomplemented
258#483—78no—
259#483—78no—
260#428—716no—
261C2×#107—72no—
262C2×#107C2×D712yescomplemented
263C2×#106—72no—
264C2×#106—72no—
265#419—716no—
266C2×#103—72no—
267C2×#103—72no—
268C2×#103—72no—
269C2×#103C2×D712yescomplemented
270#407—78no—
271C2×C22⋊C8—71no—
272C2×C22⋊C8—72no—
273C2×C22⋊C8C2×D711yescharacteristic
274C23×C7—22no—
275C23×C7—22no—
276C23×C7#13714yes—
277C23×C7C22×D412yes—
278C23×C7C22×D411yescharacteristic
279C22×D7—22no—
280C22×D7—22no—
281C22×D7—22no—
282C22×D7—28no—
283C22×D7—22no—
284C22×D7—22no—
285C22×D7—28no—
286C22×D7—44no—
287C22×D7—416no—
288C22×D7#12314yes—
289C22×D7C22×D412yes—
290C22×D7C22×D412yes—
291C7×Q8—24no—
292C7×Q8—42no—
293C2×C4×C7—22no—
294C2×C4×C7—24no—
295C2×C4×C7—24no—
296C2×C4×C7—24no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—48no—
300C2×C4×C7—42no—
301C2×C4×C7—42no—
302C2×C4×C7—44no—
303C2×C4×C7C22×D412yes—
304C2×C4×C7C22×D411yescharacteristic
305C2×C4×C7C2×#4114yes—
306C2×C4×C7C2511yescharacteristic
307C2×Dic7—22no—
308C2×Dic7—28no—
309C2×Dic7—24no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—42no—
313C2×Dic7—48no—
314C2×Dic7—44no—
315C2×Dic7—42no—
316C2×Dic7#12314yes—
317C2×Dic7C22×D412yes—
318C2×Dic7C22×D412yes—
319C4×D7—28no—
320C4×D7—24no—
321C4×D7—24no—
322C4×D7—28no—
323C4×D7—48no—
324C4×D7—48no—
325C4×D7#12318yes—
326C4×D7C2×#4118yes—
327Dic14—24no—
328Dic14—42no—
329Dic14—48no—
330C7×C8—24no—
331C7⋊C8—24no—
332C25—71no—
333C22×Q8—74no—
334C22×Q8—71no—
335C22×Q8—141no—
336C22×Q8—142no—
337C22×Q8—148no—
338C22×Q8C22×D711yescharacteristic
339C23×C4—21no—
340C23×C4—71no—
341C23×C4—71no—
342C23×C4—71no—
343C23×C4—71no—
344C23×C4—74no—
345C23×C4—71no—
346C23×C4—74no—
347C23×C4—148no—
348C23×C4—141no—
349C23×C4—141no—
350C23×C4—141no—
351C23×C4C22×D711yescharacteristic
352C2×M16—78no—
353C2×M16—148no—
354C22×C8—72no—
355C22×C8C22×D712yes—
356C22⋊Q8—22no—
357C22⋊Q8—74no—
358C22⋊Q8—74no—
359C22⋊Q8—74no—
360C22⋊Q8—148no—
361C22⋊Q8—148no—
362C22⋊Q8—142no—
363C22⋊Q8—142no—
364C22⋊Q8—142no—
365C22⋊Q8C22×D714yes—
366#117—78no—
367#117—78no—
368#117—144no—
369#117—148no—
370#117—144no—
371#117—148no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—72no—
376C2×C4⋊C4—74no—
377C2×C4⋊C4—71no—
378C2×C4⋊C4—74no—
379C2×C4⋊C4—142no—
380C2×C4⋊C4—148no—
381C2×C4⋊C4—141no—
382C2×C4⋊C4—141no—
383C2×C4⋊C4—141no—
384C2×C4⋊C4—142no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4C22×D711yescharacteristic
388C2×C4⋊C4C22×D712yes—
389C2×C4⋊C4C22×D714yes—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—148no—
392C2×C22⋊C4—148no—
393C2×C22⋊C4—142no—
394C2×C22⋊C4—142no—
395C2×C22⋊C4—141no—
396C2×C22⋊C4—141no—
397C2×C22⋊C4—141no—
398C2×C42—148no—
399C2×C42—142no—
400C2×C42—142no—
401#107—78no—
402#107C22×D718yescomplemented
403#106—78no—
404#106—78no—
405#103—78no—
406#103—78no—
407#103—78no—
408#103C22×D718yescomplemented
409C22⋊C8—74no—
410C22⋊C8—78no—
411C22⋊C8C22×D714yes—
412C22×C7—28no—
413C22×C7—22no—
414C22×C7—22no—
415C22×C7C2×#12312yes—
416C22×C7C2×#13714yes—
417C22×C7C2×#13712yes—
418C22×C7#57512yes—
419C22×C7C23×D411yescharacteristic
420C2×D7—28no—
421C2×D7—22no—
422C2×D7—22no—
423C2×D7—22no—
424C2×D7—22no—
425C2×D7—22no—
426C2×D7—416no—
427C2×D7—44no—
428C2×D7C2×#12314yes—
429C4×C7—22no—
430C4×C7—42no—
431C4×C7—42no—
432C4×C7—44no—
433C4×C7C2×#12312yes—
434C4×C7C22×#4112yes—
435Dic7—22no—
436Dic7—42no—
437Dic7—44no—
438Dic7—42no—
439Dic7C2×#12314yes—
440C24—71no—
441C24—71no—
442C24—74no—
443C24—144no—
444C24—144no—
445C24—282no—
446C24D4×D711yescharacteristic
447C2×Q8—21no—
448C2×Q8—24no—
449C2×Q8—72no—
450C2×Q8—144no—
451C2×Q8—1416no—
452C2×Q8—141no—
453C2×Q8—144no—
454C2×Q8—284no—
455C2×Q8—288no—
456C2×Q8C23×D712yes—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—44no—
463C22×C4—71no—
464C22×C4—72no—
465C22×C4—78no—
466C22×C4—72no—
467C22×C4—74no—
468C22×C4—71no—
469C22×C4—74no—
470C22×C4—74no—
471C22×C4—72no—
472C22×C4—72no—
473C22×C4—144no—
474C22×C4—1416no—
475C22×C4—1416no—
476C22×C4—144no—
477C22×C4—144no—
478C22×C4—144no—
479C22×C4—144no—
480C22×C4—144no—
481C22×C4—144no—
482C22×C4—142no—
483C22×C4—141no—
484C22×C4—141no—
485C22×C4—284no—
486C22×C4—284no—
487C22×C4—284no—
488C22×C4D4×D712yes—
489C22×C4D4×D711yescharacteristic
490C22×C4C23×D712yes—
491C22×C4C23×D711yescharacteristic
492M16—1416no—
493C2×C8—24no—
494C2×C8—74no—
495C2×C8—144no—
496C2×C8C23×D714yes—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—24no—
500C4⋊C4—21no—
501C4⋊C4—74no—
502C4⋊C4—72no—
503C4⋊C4—144no—
504C4⋊C4—144no—
505C4⋊C4—144no—
506C4⋊C4—144no—
507C4⋊C4—144no—
508C4⋊C4—142no—
509C4⋊C4—141no—
510C4⋊C4C23×D714yes—
511C4⋊C4C23×D712yes—
512C22⋊C4—24no—
513C22⋊C4—148no—
514C22⋊C4—148no—
515C22⋊C4—144no—
516C22⋊C4—144no—
517C22⋊C4—144no—
518C42—148no—
519C42—148no—
520C2×C7—24no—
521C2×C7#309514yescomplemented
522C2×C7C22×#12311yescharacteristic
523C2×C7C22×#13711yescharacteristic
524C2×C7C2×#57511yescharacteristic
525D7—24no—
526D7—42no—
527C23—22no—
528C23—22no—
529C23—74no—
530C23—72no—
531C23—72no—
532C23—148no—
533C23—142no—
534C23—142no—
535C23—148no—
536C23—142no—
537C23—142no—
538C23—142no—
539C23—284no—
540C23—2816no—
541C23#648114yes—
542C23C2×D4×D712yes—
543C23C2×D4×D711yescharacteristic
544Q8—24no—
545Q8—42no—
546Q8—144no—
547Q8—288no—
548Q8—282no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—48no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—74no—
560C2×C4—72no—
561C2×C4—78no—
562C2×C4—78no—
563C2×C4—72no—
564C2×C4—148no—
565C2×C4—148no—
566C2×C4—148no—
567C2×C4—142no—
568C2×C4—144no—
569C2×C4—144no—
570C2×C4—144no—
571C2×C4—142no—
572C2×C4—142no—
573C2×C4—288no—
574C2×C4—288no—
575C2×C4—288no—
576C2×C4—284no—
577C2×C4—282no—
578C2×C4—282no—
579C2×C4C2×D4×D712yes—
580C2×C4C2×D4×D711yescharacteristic
581C2×C4D7×#4114yes—
582C2×C4C24×D711yescharacteristic
583C8—24no—
584C8—144no—
585C7C2×#309511yescharacteristic, complemented, Sylow
586C22—22no—
587C22—28no—
588C22—22no—
589C22—74no—
590C22—142no—
591C22—148no—
592C22—142no—
593C22—142no—
594C22—142no—
595C22—142no—
596C22—2816no—
597C22—284no—
598C22D7×#12312yes—
599C22C2×#648114yes—
600C22C2×#648112yes—
601C22#9046412yes—
602C22C22×D4×D711yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—42no—
607C4—74no—
608C4—142no—
609C4—282no—
610C4—282no—
611C4—284no—
612C4D7×#12312yes—
613C4C2×D7×#4112yes—
614C2—24no—
615C2—144no—
616C2—282no—
617C2#1173891414yesdirect product factor
618C2C2×D7×#12311yescharacteristic
619C2C22×#648111yescharacteristic
620C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#484C2
socleC23×C7C22×D4
prime radicalC24×D7D4
hypercenterC2×#484D7
hypocenterC7C2×#3095
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. C2×C7×#484C2semidirect
4. C2×#89815C2semidirect
5. C2×#89742C2semidirect
6. #11738914C2direct (N × H)
7. C2×#89660C2semidirect
8. C2×#89653C2semidirect
9. C2×#89587C2semidirect
10. C2×#89574C2semidirect
12. C2×#89493C2semidirect
37. C7×#484C22semidirect
38. C2×C7×#107C22semidirect
39. C2×C7×#103C22semidirect
41. C2×#6409C22semidirect
44. C2×#6391C22semidirect
45. C2×#6390C22semidirect
46. #89815C22semidirect
47. #89742C22semidirect
48. C2×#6384C22semidirect
49. C2×#6382C22semidirect
50. C2×#6381C22semidirect
51. #89660C22semidirect
52. #89653C22semidirect
53. #89587C22semidirect
54. #89574C22semidirect
56. #89493C22semidirect
127. C7×#107C23semidirect
128. C7×#103C23semidirect
130. #6409C23semidirect
133. #6391C23semidirect
134. #6390C23semidirect
135. #6384C23semidirect
136. #6382C23semidirect
137. #6381C23semidirect
142. C2×#484D7semidirect
257. #484C2×D7semidirect
262. C2×#107C2×D7semidirect
269. C2×#103C2×D7semidirect
402. #107C22×D7semidirect
408. #103C22×D7semidirect
521. C2×C7#3095semidirect
585. C7C2×#3095semidirect
617. C2#11738914direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C22⋊Q82
C22×#64552
C2×C7×#4842
C2×#898152
C2×#897422
#117389142
C2×#896602
C2×#896532
C2×#895872
C2×#895742
C2×#894982
C2×#894932
C2×#30957