Finite Group Databasebeta

← C2×#11737620 #14221945

Subgroups — C2×#11737620 #14221945

Order 1792.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic7C211yesmaximal, characteristic, complemented
2C2×#90315C211yesmaximal, characteristic
3C2×C7×#451C211yesmaximal, characteristic, complemented
4C2×#89999C211yesmaximal, characteristic
5C2×#89957C212yesmaximal, complemented
6C2×#89956C212yesmaximal, complemented
7C2×#89816C211yesmaximal, characteristic, complemented
8#11737620C2116yesmaximal, direct product factor
9C2×#89571C212yesmaximal, complemented
10C2×#89589C212yesmaximal, complemented
11C2×#89507C211yesmaximal, characteristic
12C2×#89491C211yesmaximal, characteristic, complemented
13C23×C7×Q8C2211yescharacteristic
14C22×C7×Q16C2212yes—
15C2×C7×C22⋊Q8C2211yescharacteristic
16C2×#6510C2211yescharacteristic
17C2×Q8×Dic7—21no—
18C2×Q8×Dic7—21no—
19C2×Q8×Dic7—24no—
20C2×Q8×Dic7C2211yescharacteristic
21C2×Q8×Dic7C2212yes—
22C2×Q8×Dic7C2212yes—
23C2×Q8×Dic7C2218yescomplemented
24C22×#1143C2212yes—
25C2×#6493C2211yescharacteristic
26C22×C4⋊Dic7—21no—
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4×Dic7—21no—
29C22×C4×Dic7C2211yescharacteristic
30#90315—24no—
31#90315C2218yes—
32C2×#6461—21no—
33C2×#6456C2211yescharacteristic
34C2×#6455—21no—
35C2×#6453C2211yescharacteristic
36C2×#6449—21no—
37C2×(C22⋊D7)⋊C4—21no—
38C7×#451C2218yescomplemented
39C2×C7×#103C2212yes—
40C2×C7×C22⋊C8C2211yescharacteristic
41#89999C2218yes—
42C2×#6409C2212yes—
43C2×#6409C2212yes—
44C2×C22⋊(C7⋊C8)C2211yescharacteristic
45#89957C22116yescomplemented
46#89956C22116yescomplemented
47C2×#6395C2212yes—
48C2×#6391C2212yes—
49C2×#6389C2212yes—
50C2×Dic7⋊C8C2212yes—
51#89816C2218yescomplemented
52C2×#6381C2212yes—
53#89589C22116yescomplemented
54#89571C22116yescomplemented
55#89507C2218yes—
56#89491C2218yescomplemented
57C2×#3117—71nomaximal, Sylow
58C22×C7×Q8—28no—
59C22×C7×Q8—21no—
60C22×C7×Q8—22no—
61C22×C7×Q8C2314yes—
62C22×C7×Q8C2311yescharacteristic
63C22×C7×Q8C2312yes—
64C23×C4×C7—21no—
65C23×C4×C7C2311yescharacteristic
66C22×C22⋊D7—21no—
67C23×Dic7—21no—
68C23×Dic7D411yescharacteristic
69C23×Dic7D411yescharacteristic
70C22×D28C2311yescharacteristic
71C22×C4×D7—21no—
72C2×C7×Q16—28no—
73C2×C7×Q16C2318yes—
74C22×C7×C8C2312yes—
75C7×C22⋊Q8—22no—
76C7×C22⋊Q8C2314yes—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C22⋊C4—21no—
80#6510—22no—
81#6510C2314yes—
82Q8×Dic7—24no—
83Q8×Dic7—24no—
84Q8×Dic7—28no—
85Q8×Dic7—28no—
86Q8×Dic7—22no—
87Q8×Dic7C2314yes—
88Q8×Dic7C2318yes—
89Q8×Dic7C2318yes—
90C2×#1143—28no—
91C2×#1143C2318yes—
92#6493—22no—
93#6493C2314yes—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×(C2×D7)⋊C4—21no—
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7—21no—
101C2×C4⋊Dic7—21no—
102C2×C4⋊Dic7—22no—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—28no—
105C2×C4⋊Dic7C2311yescharacteristic
106C2×C4⋊Dic7C2312yes—
107C2×C4⋊Dic7C2314yes—
108C2×Dic7⋊C4—21no—
109C2×C4×Dic7—21no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—28no—
113C2×C4×Dic7D411yescharacteristic
114C2×C4×Dic7D411yescharacteristic
115C2×C4×Dic7D414yes—
116C2×C4×Dic7C2311yescharacteristic
117C2×C4×Dic7C2311yescharacteristic
118C2×C4×Dic7C2314yes—
119C22×C7⋊C8C2312yes—
120#6461—28no—
121#6456—22no—
122#6456C2314yes—
123#6455—28no—
124#6453—22no—
125#6453C2314yes—
126#6449—28no—
127(C22⋊D7)⋊C4—28no—
128C7×#103C2318yes—
129C7×C22⋊C8C2314yes—
130#6409C2318yes—
131#6409C2318yes—
132C22⋊(C7⋊C8)C2314yes—
133#6395C2318yes—
134#6391C2318yes—
135#6389C2318yes—
136Dic7⋊C8C2318yes—
137#6381C2318yes—
138C2×#529—71no—
139C22×C4×Q8—71no—
140#3117—716no—
141C2×#484—71no—
142C2×#481—71no—
143C2×#479—72no—
144C2×#464—72no—
145C2×#451D711yescharacteristic, complemented
146C2×#448—71no—
147C2×#441—72no—
148C2×#440—72no—
149C2×#432—71no—
150C24×C7C2×D411yescharacteristic
151C23×D7—21no—
152C2×C7×Q8—216no—
153C2×C7×Q8—28no—
154C2×C7×Q8—216no—
155C2×C7×Q8—24no—
156C2×C7×Q8—22no—
157C2×C7×Q8—21no—
158C2×C7×Q8—24no—
159C2×C7×Q8—24no—
160C2×C7×Q8#4118yes—
161C2×C7×Q8C2412yes—
162C2×C7×Q8C2414yes—
163C22×C4×C7—28no—
164C22×C4×C7—24no—
165C22×C4×C7—22no—
166C22×C4×C7—24no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2412yes—
172C22×C4×C7C2411yescharacteristic
173C2×C22⋊D7—24no—
174C2×C22⋊D7—44no—
175C22×Dic7—24no—
176C22×Dic7—24no—
177C22×Dic7—22no—
178C22×Dic7—21no—
179C22×Dic7—42no—
180C22×Dic7—44no—
181C22×Dic7C2×D414yes—
182C22×Dic7C2×D411yescharacteristic
183C22×Dic7C2×D411yescharacteristic
184C22×Dic7C2×D411yescharacteristic
185C22×Dic7C2×D411yescharacteristic
186C22×Dic7C2×D414yes—
187C2×D28—24no—
188C2×D28—21no—
189C2×D28C2412yes—
190C2×C4×D7—24no—
191C2×C4×D7—44no—
192C7×Q16—216no—
193C2×C7×C8—24no—
194C2×C7×C8C2414yes—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—24no—
197C7×C4⋊C4C2412yes—
198C7×C22⋊C4—24no—
199#1143—216no—
200(C2×D7)⋊C4—24no—
201(C2×D7)⋊C4—24no—
202(C2×D7)⋊C4—24no—
203(C2×D7)⋊C4—24no—
204C4⋊Dic7—21no—
205C4⋊Dic7—24no—
206C4⋊Dic7—22no—
207C4⋊Dic7—24no—
208C4⋊Dic7—24no—
209C4⋊Dic7—28no—
210C4⋊Dic7—28no—
211C4⋊Dic7C2412yes—
212C4⋊Dic7C2414yes—
213Dic7⋊C4—24no—
214C4×Dic7—24no—
215C4×Dic7—28no—
216C4×Dic7—28no—
217C4×Dic7C2×D412yes—
218C4×Dic7C2×D414yes—
219C4×Dic7C2×D412yes—
220C4×Dic7C2×D414yes—
221C4×Dic7C2412yes—
222C4×Dic7C2412yes—
223C2×C7⋊C8—24no—
224C2×C7⋊C8C2414yes—
225C23×Q8C2×D711yescharacteristic
226C22×Q16C2×D712yes—
227C22×SD16—72no—
228#529—78no—
229#529—144no—
230C2×#126—141no—
231C2×#125—71no—
232C2×#124—71no—
233C2×#123—141no—
234C2×C22⋊Q8C2×D711yescharacteristic
235C2×#121—71no—
236C2×C4×Q8—72no—
237C2×C4×Q8—78no—
238C2×C4×Q8—72no—
239C2×C4×Q8—71no—
240C2×C4×Q8—141no—
241C2×C4×Q8—141no—
242C2×C4×Q8—144no—
243C2×C4×D4—71no—
244C2×C4×D4—141no—
245C2×#117—141no—
246C22×C4⋊C4—71no—
247C22×C4⋊C4—141no—
248C22×C42—71no—
249C22×C42—141no—
250#484—78no—
251#481—78no—
252#479—716no—
253#464—716no—
254#451C2×D718yescomplemented
255#448—78no—
256#441—716no—
257#440—716no—
258#432—78no—
259C2×#107—72no—
260C2×#106—72no—
261C2×C4⋊C8—72no—
262C2×#103—72no—
263C2×#103—72no—
264C2×#103C2×D712yes—
265C2×#102—72no—
266C2×C22⋊C8—71no—
267C2×C22⋊C8C2×D711yescharacteristic
268C2×#97—72no—
269C23×C7—22no—
270C23×C7—22no—
271C23×C7#13714yes—
272C23×C7C22×D412yes—
273C23×C7C22×D411yescharacteristic
274C22×D7—22no—
275C22×D7—42no—
276C22×D7—42no—
277C22×D7—42no—
278C7×Q8—216no—
279C7×Q8—28no—
280C7×Q8—24no—
281C7×Q8—24no—
282C7×Q8—42no—
283C7×Q8C2×#4118yes—
284C2×C4×C7—216no—
285C2×C4×C7—28no—
286C2×C4×C7—22no—
287C2×C4×C7—24no—
288C2×C4×C7—24no—
289C2×C4×C7—24no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—42no—
293C2×C4×C7—42no—
294C2×C4×C7C22×D412yes—
295C2×C4×C7C22×D411yescharacteristic
296C2×C4×C7C2×#4114yes—
297C2×C4×C7C2511yescharacteristic
298C22⋊D7—48no—
299C2×Dic7—28no—
300C2×Dic7—22no—
301C2×Dic7—22no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—24no—
305C2×Dic7—22no—
306C2×Dic7—44no—
307C2×Dic7—48no—
308C2×Dic7—42no—
309C2×Dic7—44no—
310C2×Dic7C22×D412yes—
311C2×Dic7C22×D412yes—
312C2×Dic7C22×D412yes—
313C2×Dic7C22×D412yes—
314D28—24no—
315D28—42no—
316C4×D7—48no—
317C7×C8—24no—
318C7⋊C8—24no—
319C22×Q8—28no—
320C22×Q8—22no—
321C22×Q8—21no—
322C22×Q8C22×D714yes—
323C22×Q8C22×D711yescharacteristic
324C22×Q8C22×D712yes—
325C22×D4—71no—
326C22×D4—141no—
327C23×C4—21no—
328C23×C4—71no—
329C23×C4—71no—
330C23×C4—141no—
331C23×C4—141no—
332C23×C4C22×D711yescharacteristic
333C2×Q16—28no—
334C2×Q16C22×D718yes—
335C2×SD16—78no—
336C2×SD16—148no—
337C22×C8—72no—
338C22×C8C22×D712yes—
339#126—148no—
340#125—74no—
341#125—142no—
342#124—74no—
343#124—142no—
344#123—148no—
345C22⋊Q8—22no—
346C22⋊Q8C22×D714yes—
347#121—74no—
348#121—142no—
349C4×Q8—78no—
350C4×Q8—78no—
351C4×Q8—74no—
352C4×Q8—148no—
353C4×Q8—144no—
354C4×Q8—144no—
355C4×Q8—148no—
356C4×Q8—142no—
357C4×D4—74no—
358C4×D4—142no—
359C4×D4—148no—
360#117—148no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—72no—
363C2×C4⋊C4—74no—
364C2×C4⋊C4—71no—
365C2×C4⋊C4—148no—
366C2×C4⋊C4—142no—
367C2×C4⋊C4—142no—
368C2×C4⋊C4—141no—
369C2×C4⋊C4—141no—
370C2×C4⋊C4—141no—
371C2×C4⋊C4—142no—
372C2×C4⋊C4—141no—
373C2×C4⋊C4C22×D711yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—141no—
376C2×C22⋊C4—141no—
377C2×C22⋊C4—141no—
378C2×C22⋊C4—141no—
379C2×C42—71no—
380C2×C42—71no—
381C2×C42—74no—
382C2×C42—71no—
383C2×C42—71no—
384C2×C42—74no—
385C2×C42—141no—
386C2×C42—148no—
387C2×C42—142no—
388C2×C42—142no—
389#107—78no—
390#106—78no—
391C4⋊C8—78no—
392#103—78no—
393#103—78no—
394#103C22×D718yes—
395#102—78no—
396C22⋊C8—74no—
397C22⋊C8C22×D714yes—
398#97—78no—
399C22×C7—28no—
400C22×C7—22no—
401C22×C7—22no—
402C22×C7#52512yes—
403C22×C7C2×#13714yes—
404C22×C7C2×#13712yes—
405C22×C7#57512yes—
406C22×C7C23×D411yescharacteristic
407C2×D7—42no—
408C2×D7—42no—
409C2×D7—42no—
410C2×D7—84no—
411C4×C7—28no—
412C4×C7—22no—
413C4×C7—42no—
414C4×C7—42no—
415C4×C7#52512yes—
416C4×C7C22×#4112yes—
417Dic7—22no—
418Dic7—22no—
419Dic7—22no—
420Dic7—22no—
421Dic7—42no—
422Dic7—44no—
423C24—141no—
424C24D4×D711yescharacteristic
425C2×Q8—216no—
426C2×Q8—28no—
427C2×Q8—216no—
428C2×Q8—24no—
429C2×Q8—22no—
430C2×Q8—21no—
431C2×Q8—24no—
432C2×Q8—24no—
433C2×Q8#115918yes—
434C2×Q8C23×D712yes—
435C2×Q8C23×D714yes—
436C2×D4—72no—
437C2×D4—144no—
438C2×D4—141no—
439C2×D4—144no—
440C2×D4—284no—
441C22×C4—28no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—74no—
448C22×C4—71no—
449C22×C4—71no—
450C22×C4—71no—
451C22×C4—71no—
452C22×C4—74no—
453C22×C4—144no—
454C22×C4—144no—
455C22×C4—144no—
456C22×C4—142no—
457C22×C4—141no—
458C22×C4—284no—
459C22×C4—282no—
460C22×C4—284no—
461C22×C4D4×D712yes—
462C22×C4D4×D711yescharacteristic
463C22×C4C23×D712yes—
464C22×C4C23×D711yescharacteristic
465Q16—216no—
466SD16—1416no—
467C2×C8—24no—
468C2×C8—74no—
469C2×C8—144no—
470C2×C8C23×D714yes—
471C4⋊C4—24no—
472C4⋊C4—21no—
473C4⋊C4—74no—
474C4⋊C4—72no—
475C4⋊C4—144no—
476C4⋊C4—148no—
477C4⋊C4—148no—
478C4⋊C4—144no—
479C4⋊C4—144no—
480C4⋊C4—144no—
481C4⋊C4—142no—
482C4⋊C4—141no—
483C4⋊C4C23×D712yes—
484C22⋊C4—24no—
485C22⋊C4—144no—
486C22⋊C4—144no—
487C22⋊C4—144no—
488C22⋊C4—144no—
489C42—74no—
490C42—72no—
491C42—72no—
492C42—74no—
493C42—72no—
494C42—72no—
495C42—148no—
496C42—148no—
497C42—144no—
498C2×C7—24no—
499C2×C7#311714yescomplemented
500C2×C7C2×#52511yescharacteristic
501C2×C7C22×#13711yescharacteristic
502C2×C7C2×#57511yescharacteristic
503D7—82no—
504C23—22no—
505C23—22no—
506C23—142no—
507C23—282no—
508C23—282no—
509C23—282no—
510C23#648114yes—
511C23C2×D4×D712yes—
512C23C2×D4×D711yescharacteristic
513Q8—216no—
514Q8—28no—
515Q8—24no—
516Q8—24no—
517Q8—42no—
518Q8C2×#115918yes—
519D4—144no—
520D4—288no—
521D4—282no—
522C2×C4—216no—
523C2×C4—28no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—72no—
533C2×C4—72no—
534C2×C4—72no—
535C2×C4—72no—
536C2×C4—148no—
537C2×C4—142no—
538C2×C4—142no—
539C2×C4—142no—
540C2×C4—142no—
541C2×C4—144no—
542C2×C4—142no—
543C2×C4—288no—
544C2×C4—284no—
545C2×C4—288no—
546C2×C4—282no—
547C2×C4—284no—
548C2×C4C2×D4×D712yes—
549C2×C4C2×D4×D711yescharacteristic
550C2×C4C2×#115914yes—
551C2×C4C24×D711yescharacteristic
552C8—24no—
553C8—144no—
554C7C2×#311711yescharacteristic, complemented, Sylow
555C22—22no—
556C22—22no—
557C22—28no—
558C22—282no—
559C22—282no—
560C22—282no—
561C22—564no—
562C22#9027712yes—
563C22C2×#648114yes—
564C22C2×#648112yes—
565C22#9046812yes—
566C22C22×D4×D711yescharacteristic
567C4—28no—
568C4—22no—
569C4—42no—
570C4—42no—
571C4—142no—
572C4—142no—
573C4—142no—
574C4—142no—
575C4—284no—
576C4—282no—
577C4#9027712yes—
578C4C22×#115912yes—
579C2—24no—
580C2—562no—
581C2#1173762014yesdirect product factor
582C2C2×#9027711yescharacteristic
583C2C22×#648111yescharacteristic
584C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#451C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenterC2×#451D7
hypocenterC7C2×#3117
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic7C2semidirect
3. C2×C7×#451C2semidirect
5. C2×#89957C2semidirect
6. C2×#89956C2semidirect
7. C2×#89816C2semidirect
8. #11737620C2direct (N × H)
9. C2×#89571C2semidirect
10. C2×#89589C2semidirect
12. C2×#89491C2semidirect
23. C2×Q8×Dic7C22semidirect
38. C7×#451C22semidirect
45. #89957C22semidirect
46. #89956C22semidirect
51. #89816C22semidirect
53. #89589C22semidirect
54. #89571C22semidirect
56. #89491C22semidirect
145. C2×#451D7semidirect
254. #451C2×D7semidirect
499. C2×C7#3117semidirect
554. C7C2×#3117semidirect
581. C2#11737620direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×Dic72
C2×#903152
C2×C7×#4512
C2×#899992
C2×#899572
C2×#899562
C2×#898162
#117376202
C2×#895712
C2×#895892
C2×#895072
C2×#894912
C2×#31177