Finite Group Databasebeta

← C2×#11738511 #14225937

Subgroups — C2×#11738511 #14225937

Order 1792.

2038 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90419C211yesmaximal, characteristic, complemented
2C2×#90239C211yesmaximal, characteristic
3C2×C7×#476C211yesmaximal, characteristic, complemented
4C2×#89856C211yesmaximal, characteristic, complemented
5C2×#89779C211yesmaximal, characteristic, complemented
6#11738511C2116yesmaximal, direct product factor
7C2×#89638C212yesmaximal, complemented
8C2×#89628C212yesmaximal, complemented
9C2×#89618C211yesmaximal, characteristic, complemented
10C2×#89607C211yesmaximal, characteristic, complemented
11C2×#89556C212yesmaximal, complemented
12C2×#89536C212yesmaximal, complemented
13C22×#1157—21no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C4×C7×D4C2211yescharacteristic
16C2×#6509—21no—
17C2×Q8×Dic7—21no—
18C2×#6503C2211yescharacteristic
19C2×#6501C2211yescharacteristic
20C2×C4×C22⋊D7—21no—
21#90419—24no—
22#90419C2218yescomplemented
23#90239—24no—
24#90239C2218yes—
25C2×#6460—21no—
26C2×#6458C2211yescharacteristic
27C2×#6455C2212yes—
28C2×#6453C2212yes—
29C2×#6451C2211yescharacteristic
30C2×#6450—21no—
31C2×#6448—21no—
32C2×#6447—21no—
33C2×C4×D28C2211yescharacteristic
34C2×C42×D7C2211yescharacteristic
35C2×#6432C2211yescharacteristic
36C7×#476C2218yescomplemented
37C2×C7×#106C2212yes—
38C2×C7×C4⋊C8C2211yescharacteristic
39C2×C7×#102C2212yes—
40C2×#6406C2212yes—
41C2×#6395C2212yes—
42C2×(C2×D7)⋊C8C2212yes—
43C2×#6392C2212yes—
44C2×#6389C2212yes—
45#89856C2218yescomplemented
46#89779C2218yescomplemented
47C2×#6383C2212yes—
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51#89638C22116yescomplemented
52#89628C22116yescomplemented
53#89618C2218yescomplemented
54#89607C2218yescomplemented
55#89556C22116yescomplemented
56#89536C22116yescomplemented
57C2×#3235—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×D4C2311yescharacteristic
60C23×C4×C7—21no—
61C22×C22⋊D7—21no—
62C22×C22⋊D7—21no—
63C22×C22⋊D7—21no—
64C2×#1157—28no—
65C2×#1157—48no—
66C22×D28—21no—
67C22×D28C2311yescharacteristic
68C22×C4×D7—21no—
69C22×C4×D7D411yescharacteristic
70C22×C4×D7D411yescharacteristic
71C22×C4×D7C2311yescharacteristic
72C22×Dic14—21no—
73C22×Dic14—21no—
74C22×C7×C8C2312yes—
75C7×C4⋊Q8—22no—
76C7×C4⋊Q8C2314yes—
77C4×C7×D4—22no—
78C4×C7×D4C2314yes—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2312yes—
82C2×C7×C22⋊C4—21no—
83C2×C42×C7C2311yescharacteristic
84C2×C22⋊Dic7—21no—
85#6509—28no—
86Q8×Dic7—28no—
87#6503—22no—
88#6503C2314yes—
89#6501—22no—
90#6501C2314yes—
91C4×C22⋊D7—28no—
92C2×(C2×D7)⋊C4—22no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2312yes—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7D411yescharacteristic
103C2×C4×Dic7D411yescharacteristic
104C2×C4×Dic7C2311yescharacteristic
105C22×C7⋊C8C2312yes—
106#6460—28no—
107#6458—22no—
108#6458C2314yes—
109#6455—24no—
110#6455C2318yes—
111#6453—24no—
112#6453C2318yes—
113#6451—22no—
114#6451C2314yes—
115#6450—28no—
116#6448—28no—
117#6447—28no—
118C4×D28—22no—
119C4×D28C2314yes—
120C42×D7D414yes—
121C42×D7C2314yes—
122#6432—22no—
123#6432C2314yes—
124C7×#106C2318yes—
125C7×C4⋊C8C2314yes—
126C7×#102C2318yes—
127#6406C2318yes—
128#6395C2318yes—
129(C2×D7)⋊C8C2318yes—
130#6392C2318yes—
131#6389C2318yes—
132#6383C2318yes—
133#6382C2318yes—
134#6381C2318yes—
135C4⋊(C7⋊C8)C2314yes—
136C2×#533—71no—
137C2×#532—71no—
138#3235—716no—
139C2×#501—72no—
140C2×#490—72no—
141C2×#482—72no—
142C2×#482—72no—
143C2×#476—71no—
144C2×#476D711yescharacteristic, complemented
145C2×#474—71no—
146C2×#474—71no—
147C2×#432—71no—
148C24×C7—21no—
149C23×D7—21no—
150C23×D7C2×D411yescharacteristic
151C2×C7×Q8—24no—
152C2×C7×Q8—44no—
153C2×C7×D4—21no—
154C2×C7×D4—22no—
155C2×C7×D4—22no—
156C2×C7×D4C2412yes—
157C22×C4×C7—22no—
158C22×C4×C7—21no—
159C22×C4×C7—24no—
160C22×C4×C7—44no—
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2411yescharacteristic
164C2×C22⋊D7—24no—
165C2×C22⋊D7—24no—
166C2×C22⋊D7—24no—
167C2×C22⋊D7—44no—
168C2×C22⋊D7—44no—
169C2×C22⋊D7—44no—
170C22×Dic7—22no—
171C22×Dic7—21no—
172C22×Dic7C2×D411yescharacteristic
173C22×Dic7C2×D411yescharacteristic
174C22×Dic7C2×D411yescharacteristic
175#1157—432no—
176C2×D28—22no—
177C2×D28—22no—
178C2×D28—24no—
179C2×D28—21no—
180C2×D28—44no—
181C2×D28C2412yes—
182C2×C4×D7—24no—
183C2×C4×D7—22no—
184C2×C4×D7—22no—
185C2×C4×D7—24no—
186C2×C4×D7—42no—
187C2×C4×D7—44no—
188C2×C4×D7C2×D412yes—
189C2×C4×D7C2×D414yes—
190C2×C4×D7C2×D414yes—
191C2×C4×D7C2412yes—
192C2×Dic14—24no—
193C2×Dic14—24no—
194C2×Dic14—44no—
195C2×Dic14—44no—
196C2×C7×C8—24no—
197C2×C7×C8C2414yes—
198C7×C4⋊C4—24no—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—22no—
201C7×C4⋊C4C2414yes—
202C7×C4⋊C4C2412yes—
203C7×C22⋊C4—24no—
204C42×C7C2×D412yes—
205C42×C7C2412yes—
206C22⋊Dic7—24no—
207(C2×D7)⋊C4—28no—
208(C2×D7)⋊C4—24no—
209(C2×D7)⋊C4—24no—
210C4⋊Dic7—22no—
211C4⋊Dic7—24no—
212C4⋊Dic7—21no—
213C4⋊Dic7—28no—
214C4⋊Dic7C2414yes—
215C4⋊Dic7C2412yes—
216Dic7⋊C4—24no—
217Dic7⋊C4—28no—
218C4×Dic7—28no—
219C4×Dic7C2×D412yes—
220C4×Dic7C2×D414yes—
221C4×Dic7C2×D414yes—
222C4×Dic7C2412yes—
223C2×C7⋊C8—24no—
224C2×C7⋊C8C2414yes—
225C22×#41—141no—
226#533—78no—
227#533—144no—
228#532—78no—
229#532—144no—
230C2×C4⋊Q8—71no—
231C2×C4⋊Q8—71no—
232C2×C4⋊Q8C2×D711yescharacteristic
233C2×#127—71no—
234C2×#125—72no—
235C2×#124—141no—
236C2×C22⋊Q8—141no—
237C2×C22⋊Q8—141no—
238C2×#121—71no—
239C2×#121—71no—
240C2×#121—141no—
241C2×C4×Q8—141no—
242C2×C4×Q8—141no—
243C2×C4×D4—71no—
244C2×C4×D4—141no—
245C2×C4×D4C2×D711yescharacteristic
246C2×#117—72no—
247C22×C42—71no—
248#501—716no—
249#490—716no—
250#482—716no—
251#482—716no—
252#476—78no—
253#476C2×D718yescomplemented
254#474—78no—
255#474—78no—
256#432—78no—
257C2×#107—72no—
258C2×#107—72no—
259C2×#106—72no—
260C2×#106C2×D712yes—
261C2×C4⋊C8—71no—
262C2×C4⋊C8C2×D711yescharacteristic
263C2×#102—72no—
264C2×#102—72no—
265C2×#102—72no—
266C2×#102C2×D712yes—
267C2×C22⋊C8—72no—
268C2×#97—72no—
269C23×C7—22no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7C22×D411yescharacteristic
274C22×D7—22no—
275C22×D7—22no—
276C22×D7—22no—
277C22×D7—22no—
278C22×D7—42no—
279C22×D7—42no—
280C22×D7—42no—
281C22×D7C22×D412yes—
282C7×Q8—48no—
283C7×D4—22no—
284C7×D4—22no—
285C7×D4—42no—
286C2×C4×C7—22no—
287C2×C4×C7—24no—
288C2×C4×C7—22no—
289C2×C4×C7—42no—
290C2×C4×C7—44no—
291C2×C4×C7—48no—
292C2×C4×C7AGL(1,ℤ/8)14yes—
293C2×C4×C7C22×D412yes—
294C2×C4×C7C22×D411yescharacteristic
295C2×C4×C7C22×D412yes—
296C2×C4×C72−1+412yes—
297C2×C4×C72−1+412yes—
298C2×C4×C7C2511yescharacteristic
299C22⋊D7—48no—
300C22⋊D7—48no—
301C22⋊D7—48no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—22no—
305C2×Dic7—24no—
306C2×Dic7—22no—
307C2×Dic7—42no—
308C2×Dic7—44no—
309C2×Dic7C22×D412yes—
310C2×Dic7C22×D412yes—
311C2×Dic7C22×D412yes—
312D28—22no—
313D28—22no—
314D28—48no—
315D28—42no—
316C4×D7—24no—
317C4×D7—28no—
318C4×D7—22no—
319C4×D7—22no—
320C4×D7—44no—
321C4×D7—48no—
322Dic14—48no—
323Dic14—48no—
324C7×C8—24no—
325C7⋊C8—24no—
326C2×#41—148no—
327C2×#41—288no—
328C22×Q8—21no—
329C22×Q8—141no—
330C22×Q8—141no—
331C22×D4—71no—
332C22×D4—141no—
333C22×D4—141no—
334C22×D4—141no—
335C22×D4—141no—
336C22×D4C22×D711yescharacteristic
337C23×C4—21no—
338C23×C4—71no—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—141no—
342C22×C8—72no—
343C22×C8C22×D712yes—
344C4⋊Q8—22no—
345C4⋊Q8—74no—
346C4⋊Q8—74no—
347C4⋊Q8—142no—
348C4⋊Q8—142no—
349C4⋊Q8C22×D714yes—
350#127—74no—
351#127—142no—
352#125—78no—
353#125—144no—
354#124—148no—
355C22⋊Q8—148no—
356C22⋊Q8—148no—
357#121—74no—
358#121—74no—
359#121—148no—
360#121—142no—
361#121—142no—
362C4×Q8—148no—
363C4×Q8—148no—
364C4×D4—22no—
365C4×D4—74no—
366C4×D4—148no—
367C4×D4—142no—
368C4×D4C22×D714yes—
369#117—78no—
370#117—144no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—72no—
373C2×C4⋊C4—71no—
374C2×C4⋊C4—141no—
375C2×C4⋊C4—142no—
376C2×C4⋊C4—142no—
377C2×C4⋊C4—141no—
378C2×C4⋊C4C22×D712yes—
379C2×C4⋊C4C22×D711yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—141no—
382C2×C22⋊C4—142no—
383C2×C22⋊C4—141no—
384C2×C22⋊C4—141no—
385C2×C42—71no—
386C2×C42—71no—
387C2×C42—71no—
388C2×C42—74no—
389C2×C42—74no—
390C2×C42—142no—
391C2×C42C22×D711yescharacteristic
392#107—78no—
393#107—78no—
394#106—78no—
395#106C22×D718yes—
396C4⋊C8—74no—
397C4⋊C8C22×D714yes—
398#102—78no—
399#102—78no—
400#102—78no—
401#102C22×D718yes—
402C22⋊C8—78no—
403#97—78no—
404C22×C7—42no—
405C22×C7—42no—
406C22×C7—42no—
407C22×C7—84no—
408C22×C7#53612yes—
409C22×C7C2×AGL(1,ℤ/8)12yes—
410C22×C7#57512yes—
411C22×C7C23×D411yescharacteristic
412C2×D7—22no—
413C2×D7—22no—
414C2×D7—22no—
415C2×D7—44no—
416C2×D7—42no—
417C2×D7—42no—
418C2×D7—42no—
419C2×D7—84no—
420C4×C7—22no—
421C4×C7—42no—
422C4×C7—44no—
423C4×C7#53612yes—
424C4×C7C2×AGL(1,ℤ/8)14yes—
425C4×C7C2×2−1+411yescharacteristic
426C4×C7C2×2−1+411yescharacteristic
427Dic7—22no—
428Dic7—22no—
429Dic7—22no—
430Dic7—42no—
431Dic7—44no—
432C24—21no—
433C24—71no—
434C24—141no—
435#41—2832no—
436C2×Q8—24no—
437C2×Q8—44no—
438C2×Q8—144no—
439C2×Q8—144no—
440C2×Q8—284no—
441C2×Q8—284no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—72no—
446C2×D4—144no—
447C2×D4—144no—
448C2×D4—144no—
449C2×D4—144no—
450C2×D4—141no—
451C2×D4—142no—
452C2×D4—142no—
453C2×D4—284no—
454C2×D4—284no—
455C2×D4—284no—
456C2×D4—284no—
457C2×D4C23×D712yes—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—44no—
462C22×C4—71no—
463C22×C4—71no—
464C22×C4—71no—
465C22×C4—72no—
466C22×C4—74no—
467C22×C4—72no—
468C22×C4—74no—
469C22×C4—144no—
470C22×C4—142no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—141no—
474C22×C4—144no—
475C22×C4—282no—
476C22×C4—284no—
477C22×C4D4×D711yescharacteristic
478C22×C4D4×D711yescharacteristic
479C22×C4C23×D711yescharacteristic
480C2×C8—24no—
481C2×C8—74no—
482C2×C8—144no—
483C2×C8C23×D714yes—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—74no—
488C4⋊C4—72no—
489C4⋊C4—144no—
490C4⋊C4—148no—
491C4⋊C4—148no—
492C4⋊C4—142no—
493C4⋊C4—141no—
494C4⋊C4—144no—
495C4⋊C4C23×D714yes—
496C4⋊C4C23×D712yes—
497C22⋊C4—24no—
498C22⋊C4—144no—
499C22⋊C4—148no—
500C22⋊C4—144no—
501C22⋊C4—144no—
502C42—74no—
503C42—74no—
504C42—72no—
505C42—72no—
506C42—148no—
507C42D4×D712yes—
508C42C23×D712yes—
509C2×C7—82no—
510C2×C7#323514yescomplemented
511C2×C7C2×#53611yescharacteristic
512C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
513C2×C7C2×#57511yescharacteristic
514D7—42no—
515D7—82no—
516C23—22no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—72no—
521C23—142no—
522C23—142no—
523C23—142no—
524C23—142no—
525C23—282no—
526C23—282no—
527C23—282no—
528C23C2×D4×D711yescharacteristic
529Q8—48no—
530Q8—288no—
531Q8—288no—
532D4—22no—
533D4—22no—
534D4—42no—
535D4—142no—
536D4—142no—
537D4—288no—
538D4—288no—
539D4—288no—
540D4—288no—
541D4—282no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—48no—
548C2×C4—72no—
549C2×C4—72no—
550C2×C4—72no—
551C2×C4—142no—
552C2×C4—142no—
553C2×C4—142no—
554C2×C4—148no—
555C2×C4—144no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—144no—
559C2×C4—142no—
560C2×C4—284no—
561C2×C4—282no—
562C2×C4—284no—
563C2×C4—288no—
564C2×C4#647714yes—
565C2×C4C2×D4×D712yes—
566C2×C4C2×D4×D712yes—
567C2×C4C2×D4×D711yescharacteristic
568C2×C4#655112yes—
569C2×C4#655412yes—
570C2×C4C24×D711yescharacteristic
571C8—24no—
572C8—144no—
573C7C2×#323511yescharacteristic, complemented, Sylow
574C22—42no—
575C22—42no—
576C22—42no—
577C22—84no—
578C22—142no—
579C22—142no—
580C22—142no—
581C22—284no—
582C22—282no—
583C22—282no—
584C22—282no—
585C22—564no—
586C22#9031912yes—
587C22C2×#647712yes—
588C22#9046412yes—
589C22C22×D4×D711yescharacteristic
590C4—22no—
591C4—44no—
592C4—42no—
593C4—142no—
594C4—142no—
595C4—142no—
596C4—282no—
597C4—284no—
598C4#9031912yes—
599C4C2×#647714yes—
600C4C2×#655111yescharacteristic
601C4C2×#655411yescharacteristic
602C2—82no—
603C2—282no—
604C2—562no—
605C2#1173851114yesdirect product factor
606C2C2×#9031911yescharacteristic
607C2C22×#647711yescharacteristic
608C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#476C2
socleC23×C7C22×D4
prime radicalC2×#90239C2
hypercenterC2×#476D7
hypocenterC7C2×#3235
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×#89856C2semidirect
5. C2×#89779C2semidirect
6. #11738511C2direct (N × H)
7. C2×#89638C2semidirect
8. C2×#89628C2semidirect
9. C2×#89618C2semidirect
10. C2×#89607C2semidirect
11. C2×#89556C2semidirect
12. C2×#89536C2semidirect
22. #90419C22semidirect
36. C7×#476C22semidirect
45. #89856C22semidirect
46. #89779C22semidirect
51. #89638C22semidirect
52. #89628C22semidirect
53. #89618C22semidirect
54. #89607C22semidirect
55. #89556C22semidirect
56. #89536C22semidirect
144. C2×#476D7semidirect
253. #476C2×D7semidirect
510. C2×C7#3235semidirect
573. C7C2×#3235semidirect
605. C2#11738511direct (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×#902392
C2×C7×#4762
C2×#898562
C2×#897792
#117385112
C2×#896382
C2×#896282
C2×#896182
C2×#896072
C2×#895562
C2×#895362
C2×#32357