Finite Group Databasebeta

← C2×#11738492 #14221936

Subgroups — C2×#11738492 #14221936

Order 1792.

2150 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90419C211yesmaximal, characteristic, complemented
2C2×C4×#1159C211yesmaximal, characteristic
3C2×C7×#476C211yesmaximal, characteristic, complemented
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89791C211yesmaximal, characteristic, complemented
6#11738492C2116yesmaximal, direct product factor
7C2×#89639C212yesmaximal, complemented
8C2×#89625C212yesmaximal, complemented
9C2×#89621C211yesmaximal, characteristic, complemented
10C2×#89607C211yesmaximal, characteristic, complemented
11C2×#89555C212yesmaximal
12C2×#89529C212yesmaximal, complemented
13C22×#1159C2211yescharacteristic
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C4×C7×D4C2211yescharacteristic
16C2×#6509—21no—
17C2×Q8×Dic7—21no—
18C2×D4×Dic7C2211yescharacteristic
19C22×#1142C2212yes—
20C2×C4×C22⋊D7—21no—
21C22×C4×Dic7—21no—
22C22×Dic28C2212yes—
23#90419—24no—
24#90419C2218yescomplemented
25C4×#1159—24no—
26C4×#1159C2218yes—
27C2×#6460C2212yes—
28C2×#6455—21no—
29C2×#6455C2211yescharacteristic
30C2×#6453—21no—
31C2×#6450C2212yes—
32C2×#6450C2211yescharacteristic
33C2×(C22⋊D7)⋊C4—21no—
34C2×#6440—21no—
35C2×C42×D7C2211yescharacteristic
36C2×#6432C2211yescharacteristic
37C2×C4×Dic14C2211yescharacteristic
38C7×#476C2218yescomplemented
39C2×C7×#106C2212yes—
40C2×C7×C4⋊C8C2211yescharacteristic
41C2×C7×#102C2212yes—
42C2×(C2×D7)⋊C8C2212yes—
43C2×#6390C2212yes—
44C2×#6389C2212yes—
45#89863C2218yescomplemented
46#89791C2218yescomplemented
47C2×#6384C2212yes—
48C2×#6384C2212yes—
49C2×#6381C2212yes—
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51#89639C22116yescomplemented
52#89625C22116yescomplemented
53#89621C2218yescomplemented
54#89607C2218yescomplemented
55#89555C22116yes—
56#89529C22116yescomplemented
57C2×#3116—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×D4C2311yescharacteristic
60C23×C4×C7—21no—
61C22×C22⋊D7—21no—
62C23×Dic7—21no—
63C23×Dic7—21no—
64C2×#1159—24no—
65C2×#1159—22no—
66C2×#1159—24no—
67C2×#1159C2314yes—
68C22×C4×D7D411yescharacteristic
69C22×C4×D7D411yescharacteristic
70C22×C4×D7C2311yescharacteristic
71C22×Dic14C2312yes—
72C22×Dic14C2311yescharacteristic
73C22×C7×C8C2312yes—
74C7×C4⋊Q8—22no—
75C7×C4⋊Q8C2314yes—
76C4×C7×D4—22no—
77C4×C7×D4C2314yes—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2312yes—
81C2×C7×C22⋊C4—21no—
82C2×C42×C7C2311yescharacteristic
83C2×C22⋊Dic7—21no—
84#6509—28no—
85Q8×Dic7—28no—
86D4×Dic7—22no—
87D4×Dic7C2314yes—
88C2×#1142—28no—
89C2×#1142C2318yes—
90C4×C22⋊D7—28no—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—22no—
93C2×C4⋊Dic7—21no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7—22no—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—22no—
100C2×C4×Dic7—21no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—28no—
105C2×C4×Dic7D411yescharacteristic
106C2×C4×Dic7D411yescharacteristic
107C2×C4×Dic7C2311yescharacteristic
108C22×C7⋊C8C2312yes—
109C2×Dic28—28no—
110C2×Dic28C2318yes—
111#6460—24no—
112#6460C2318yes—
113#6455—28no—
114#6455—22no—
115#6455C2314yes—
116#6453—28no—
117#6450—24no—
118#6450—22no—
119#6450C2314yes—
120#6450C2318yes—
121(C22⋊D7)⋊C4—28no—
122#6440—28no—
123C42×D7D414yes—
124C42×D7C2314yes—
125#6432—22no—
126#6432C2314yes—
127C4×Dic14—22no—
128C4×Dic14C2314yes—
129C7×#106C2318yes—
130C7×C4⋊C8C2314yes—
131C7×#102C2318yes—
132(C2×D7)⋊C8C2318yes—
133#6390C2318yes—
134#6389C2318yes—
135#6384C2318yes—
136#6384C2318yes—
137#6381C2318yes—
138C4⋊(C7⋊C8)C2314yes—
139C2×#533—71no—
140C2×C4×#41—71no—
141#3116—716no—
142C2×#485—72no—
143C2×#477—71no—
144C2×#476D711yescharacteristic, complemented
145C2×#462—71no—
146C2×#461—71no—
147C2×#452—72no—
148C2×#441—72no—
149C2×#440—72no—
150C2×#432—71no—
151C24×C7—21no—
152C23×D7C2×D411yescharacteristic
153C2×C7×Q8—24no—
154C2×C7×Q8—44no—
155C2×C7×D4—21no—
156C2×C7×D4—22no—
157C2×C7×D4#4114yes—
158C2×C7×D4C2412yes—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—24no—
162C22×C4×C7—44no—
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2411yescharacteristic
166C2×C22⋊D7—28no—
167C2×C22⋊D7—24no—
168C22×Dic7—28no—
169C22×Dic7—21no—
170C22×Dic7—24no—
171C22×Dic7—21no—
172C22×Dic7—22no—
173C22×Dic7—24no—
174C22×Dic7—44no—
175C22×Dic7C2×D411yescharacteristic
176C22×Dic7C2×D411yescharacteristic
177C22×Dic7C2×D411yescharacteristic
178#1159—216no—
179#1159—28no—
180#1159—28no—
181C2×C4×D7—24no—
182C2×C4×D7—22no—
183C2×C4×D7—22no—
184C2×C4×D7—42no—
185C2×C4×D7C2×D412yes—
186C2×C4×D7C2×D414yes—
187C2×C4×D7C2×D414yes—
188C2×C4×D7C2412yes—
189C2×Dic14—21no—
190C2×Dic14—22no—
191C2×Dic14—24no—
192C2×Dic14—24no—
193C2×Dic14—22no—
194C2×Dic14#4114yes—
195C2×Dic14C2414yes—
196C2×Dic14C2412yes—
197C2×C7×C8—24no—
198C2×C7×C8C2414yes—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—22no—
201C7×C4⋊C4—24no—
202C7×C4⋊C4C2414yes—
203C7×C4⋊C4C2412yes—
204C7×C22⋊C4—24no—
205C42×C7C2×D412yes—
206C42×C7C2412yes—
207C22⋊Dic7—24no—
208#1142—216no—
209(C2×D7)⋊C4—24no—
210(C2×D7)⋊C4—28no—
211C4⋊Dic7—21no—
212C4⋊Dic7—24no—
213C4⋊Dic7—24no—
214C4⋊Dic7—28no—
215C4⋊Dic7C2412yes—
216Dic7⋊C4—24no—
217Dic7⋊C4—24no—
218Dic7⋊C4—28no—
219C4×Dic7—24no—
220C4×Dic7—24no—
221C4×Dic7—24no—
222C4×Dic7—28no—
223C4×Dic7C2×D412yes—
224C4×Dic7C2×D414yes—
225C4×Dic7C2×D414yes—
226C4×Dic7C2412yes—
227C2×C7⋊C8—24no—
228C2×C7⋊C8C2414yes—
229Dic28—216no—
230C22×#41—71no—
231C22×Q16—72no—
232C22×SD16—72no—
233#533—78no—
234#533—144no—
235C2×C4⋊Q8—71no—
236C2×C4⋊Q8C2×D711yescharacteristic
237C2×#125—141no—
238C2×C22⋊Q8—72no—
239C2×C22⋊Q8—141no—
240C4×#41—78no—
241C4×#41—144no—
242C2×C4×Q8—71no—
243C2×C4×Q8—72no—
244C2×C4×Q8—71no—
245C2×C4×Q8—141no—
246C2×C4×D4—71no—
247C2×C4×D4—141no—
248C2×C4×D4—141no—
249C2×C4×D4C2×D711yescharacteristic
250C2×#117—71no—
251C2×#117—141no—
252C2×#117—141no—
253C22×C42—71no—
254C22×C42—141no—
255#485—716no—
256#477—78no—
257#476C2×D718yescomplemented
258#462—78no—
259#461—78no—
260#452—716no—
261#441—716no—
262#440—716no—
263#432—78no—
264C2×#107—72no—
265C2×#106C2×D712yes—
266C2×C4⋊C8—71no—
267C2×C4⋊C8C2×D711yescharacteristic
268C2×#103—72no—
269C2×#103—72no—
270C2×#103—72no—
271C2×#102C2×D712yes—
272C2×C22⋊C8—72no—
273C2×#97—72no—
274C23×C7—24no—
275C23×C7—22no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7C22×D411yescharacteristic
279C22×D7—22no—
280C22×D7—22no—
281C22×D7—22no—
282C22×D7C22×D412yes—
283C7×Q8—48no—
284C7×D4—24no—
285C7×D4—22no—
286C7×D4C2×#4114yes—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—24no—
290C2×C4×C7—42no—
291C2×C4×C7—44no—
292C2×C4×C7—48no—
293C2×C4×C7#13714yes—
294C2×C4×C7C22×D412yes—
295C2×C4×C7C22×D411yescharacteristic
296C2×C4×C7C22×D412yes—
297C2×C4×C7C2×#4112yes—
298C2×C4×C7C2×#4112yes—
299C2×C4×C7C2511yescharacteristic
300C22⋊D7—216no—
301C2×Dic7—216no—
302C2×Dic7—24no—
303C2×Dic7—22no—
304C2×Dic7—22no—
305C2×Dic7—22no—
306C2×Dic7—22no—
307C2×Dic7—22no—
308C2×Dic7—24no—
309C2×Dic7—48no—
310C2×Dic7—44no—
311C2×Dic7—42no—
312C2×Dic7C22×D412yes—
313C2×Dic7C22×D412yes—
314C2×Dic7C22×D412yes—
315C4×D7—24no—
316C4×D7—28no—
317C4×D7—22no—
318C4×D7—22no—
319C4×D7—44no—
320Dic14—24no—
321Dic14—22no—
322Dic14—24no—
323Dic14—24no—
324Dic14—44no—
325Dic14C2×#4114yes—
326C7×C8—24no—
327C7⋊C8—24no—
328C2×#41—74no—
329C2×#41—142no—
330C2×#41—144no—
331C2×#41—144no—
332C22×Q8—21no—
333C22×Q8—71no—
334C22×Q8—72no—
335C22×D4—141no—
336C22×D4C22×D711yescharacteristic
337C23×C4—21no—
338C23×C4—71no—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—141no—
342C23×C4—141no—
343C2×Q16—78no—
344C2×Q16—148no—
345C2×SD16—78no—
346C2×SD16—148no—
347C22×C8—72no—
348C22×C8C22×D712yes—
349C4⋊Q8—22no—
350C4⋊Q8—74no—
351C4⋊Q8—142no—
352C4⋊Q8C22×D714yes—
353#125—148no—
354C22⋊Q8—78no—
355C22⋊Q8—144no—
356C22⋊Q8—148no—
357C4×Q8—74no—
358C4×Q8—78no—
359C4×Q8—74no—
360C4×Q8—142no—
361C4×Q8—144no—
362C4×Q8—148no—
363C4×Q8—142no—
364C4×D4—22no—
365C4×D4—74no—
366C4×D4—142no—
367C4×D4—148no—
368C4×D4—148no—
369C4×D4C22×D714yes—
370#117—74no—
371#117—148no—
372#117—142no—
373#117—148no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—71no—
376C2×C4⋊C4—141no—
377C2×C4⋊C4—142no—
378C2×C4⋊C4—142no—
379C2×C4⋊C4—141no—
380C2×C4⋊C4—141no—
381C2×C4⋊C4—141no—
382C2×C4⋊C4C22×D711yescharacteristic
383C2×C4⋊C4C22×D712yes—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—141no—
386C2×C22⋊C4—142no—
387C2×C22⋊C4—141no—
388C2×C42—71no—
389C2×C42—71no—
390C2×C42—71no—
391C2×C42—74no—
392C2×C42—74no—
393C2×C42—148no—
394C2×C42—141no—
395C2×C42—142no—
396C2×C42—141no—
397C2×C42—141no—
398C2×C42C22×D711yescharacteristic
399#107—78no—
400#106C22×D718yes—
401C4⋊C8—74no—
402C4⋊C8C22×D714yes—
403#103—78no—
404#103—78no—
405#103—78no—
406#102C22×D718yes—
407C22⋊C8—78no—
408#97—78no—
409C22×C7—24no—
410C22×C7—48no—
411C22×C7—42no—
412C22×C7—42no—
413C22×C7#52512yes—
414C22×C7C2×#13712yes—
415C22×C7#57512yes—
416C22×C7C23×D411yescharacteristic
417C2×D7—22no—
418C2×D7—22no—
419C2×D7—22no—
420C2×D7—44no—
421C4×C7—22no—
422C4×C7—42no—
423C4×C7—44no—
424C4×C7#52512yes—
425C4×C7C2×#13714yes—
426C4×C7C22×#4111yescharacteristic
427C4×C7C22×#4111yescharacteristic
428Dic7—24no—
429Dic7—22no—
430Dic7—22no—
431Dic7—22no—
432Dic7—44no—
433Dic7—42no—
434C24—21no—
435C24—71no—
436#41—148no—
437#41—1416no—
438#41—148no—
439C2×Q8—24no—
440C2×Q8—44no—
441C2×Q8—74no—
442C2×Q8—72no—
443C2×Q8—74no—
444C2×Q8—141no—
445C2×Q8—142no—
446C2×Q8—142no—
447C2×Q8—144no—
448C2×Q8—144no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—144no—
452C2×D4—148no—
453C2×D4#116114yes—
454C2×D4C23×D712yes—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—44no—
459C22×C4—71no—
460C22×C4—71no—
461C22×C4—71no—
462C22×C4—74no—
463C22×C4—72no—
464C22×C4—72no—
465C22×C4—74no—
466C22×C4—144no—
467C22×C4—144no—
468C22×C4—148no—
469C22×C4—141no—
470C22×C4—144no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—141no—
474C22×C4—142no—
475C22×C4—282no—
476C22×C4—284no—
477C22×C4D4×D711yescharacteristic
478C22×C4D4×D711yescharacteristic
479C22×C4C23×D711yescharacteristic
480Q16—1416no—
481SD16—1416no—
482C2×C8—24no—
483C2×C8—74no—
484C2×C8—144no—
485C2×C8C23×D714yes—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—72no—
490C4⋊C4—144no—
491C4⋊C4—148no—
492C4⋊C4—148no—
493C4⋊C4—144no—
494C4⋊C4—141no—
495C4⋊C4—144no—
496C4⋊C4—144no—
497C4⋊C4C23×D714yes—
498C4⋊C4C23×D712yes—
499C22⋊C4—24no—
500C22⋊C4—144no—
501C22⋊C4—148no—
502C22⋊C4—144no—
503C42—74no—
504C42—74no—
505C42—72no—
506C42—72no—
507C42—144no—
508C42—144no—
509C42—148no—
510C42—144no—
511C42D4×D712yes—
512C42C23×D712yes—
513C2×C7—44no—
514C2×C7#311614yescomplemented
515C2×C7C2×#52511yescharacteristic
516C2×C7C22×#13711yescharacteristic
517C2×C7C2×#57511yescharacteristic
518D7—42no—
519C23—24no—
520C23—22no—
521C23—42no—
522C23—42no—
523C23—72no—
524C23—142no—
525C23—142no—
526C23—142no—
527C23C2×D4×D711yescharacteristic
528Q8—48no—
529Q8—74no—
530Q8—144no—
531Q8—142no—
532Q8—144no—
533Q8—144no—
534Q8—284no—
535D4—24no—
536D4—22no—
537D4—1416no—
538D4C2×#116114yes—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—48no—
545C2×C4—72no—
546C2×C4—72no—
547C2×C4—72no—
548C2×C4—1416no—
549C2×C4—142no—
550C2×C4—142no—
551C2×C4—142no—
552C2×C4—144no—
553C2×C4—142no—
554C2×C4—148no—
555C2×C4—144no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—144no—
560C2×C4—284no—
561C2×C4—288no—
562C2×C4—282no—
563C2×C4—284no—
564C2×C4#647814yes—
565C2×C4C2×D4×D712yes—
566C2×C4C2×D4×D712yes—
567C2×C4C2×D4×D711yescharacteristic
568C2×C4C2×#116112yes—
569C2×C4D7×#4112yes—
570C2×C4C24×D711yescharacteristic
571C8—24no—
572C8—144no—
573C7C2×#311611yescharacteristic, complemented, Sylow
574C22—24no—
575C22—42no—
576C22—48no—
577C22—42no—
578C22—142no—
579C22—142no—
580C22—142no—
581C22—284no—
582C22#9031812yes—
583C22C2×#647812yes—
584C22#9046412yes—
585C22C22×D4×D711yescharacteristic
586C4—22no—
587C4—44no—
588C4—42no—
589C4—142no—
590C4—142no—
591C4—144no—
592C4—142no—
593C4—282no—
594C4—284no—
595C4#9031812yes—
596C4C2×#647814yes—
597C4C22×#116111yescharacteristic
598C4C2×D7×#4111yescharacteristic
599C2—44no—
600C2—282no—
601C2#1173849214yesdirect product factor
602C2C2×#9031811yescharacteristic
603C2C22×#647811yescharacteristic
604C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#476C2
socleC23×C7C22×D4
prime radicalC22×#1159C22
hypercenterC2×#476D7
hypocenterC7C2×#3116
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#90419C2semidirect
3. C2×C7×#476C2semidirect
4. C2×#89863C2semidirect
5. C2×#89791C2semidirect
6. #11738492C2direct (N × H)
7. C2×#89639C2semidirect
8. C2×#89625C2semidirect
9. C2×#89621C2semidirect
10. C2×#89607C2semidirect
12. C2×#89529C2semidirect
24. #90419C22semidirect
38. C7×#476C22semidirect
45. #89863C22semidirect
46. #89791C22semidirect
51. #89639C22semidirect
52. #89625C22semidirect
53. #89621C22semidirect
54. #89607C22semidirect
56. #89529C22semidirect
144. C2×#476D7semidirect
257. #476C2×D7semidirect
514. C2×C7#3116semidirect
573. C7C2×#3116semidirect
601. C2#11738492direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904192
C2×C4×#11592
C2×C7×#4762
C2×#898632
C2×#897912
#117384922
C2×#896392
C2×#896252
C2×#896212
C2×#896072
C2×#895552
C2×#895292
C2×#31167