Finite Group Databasebeta

← C2×#11737811 #14226576

Subgroups — C2×#11737811 #14226576

Order 1792.

2178 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90407C211yesmaximal, characteristic
2C2×#90269C211yesmaximal, characteristic, complemented
3C2×C7×#460C211yesmaximal, characteristic, complemented
4C2×#89943C212yesmaximal, complemented
5C2×#89934C212yesmaximal, complemented
6C2×#89847C211yesmaximal, characteristic, complemented
7C2×#89792C211yesmaximal, characteristic, complemented
8#11737811C2116yesmaximal, direct product factor
9C2×#89623C211yesmaximal, characteristic, complemented
10C2×D7×C4⋊C8C211yesmaximal, characteristic, complemented
11C2×#89550C212yesmaximal, complemented
12C2×#89533C212yesmaximal, complemented
13C22×#1159—21no—
14C22×C7×SD16C2212yes—
15C2×C7×#127C2211yescharacteristic
16C2×C4×C7×Q8C2211yescharacteristic
17C2×#6509C2211yescharacteristic
18C2×#6507C2211yescharacteristic
19C2×#6501—21no—
20C2×#6501C2212yes—
21C2×#6499—21no—
22C2×D4×Dic7—21no—
23C2×D4×Dic7C2212yes—
24C22×#1142C2212yes—
25C22×C8×D7C2212yes—
26#90407—24no—
27#90407C2218yes—
28#90269—24no—
29#90269C2218yescomplemented
30C2×#6460C2211yescharacteristic
31C2×#6459—21no—
32C2×#6452—21no—
33C2×#6451C2211yescharacteristic
34C2×#6435—21no—
35C2×C42×D7C2211yescharacteristic
36C2×#6432C2211yescharacteristic
37C2×C4×Dic14—21no—
38C2×C4×Dic14C2211yescharacteristic
39C7×#460C2218yescomplemented
40C2×C7×C4⋊C8C2211yescharacteristic
41C2×C7×#102C2212yes—
42C2×#6409C2212yes—
43C2×#6406C2212yes—
44#89943C22116yescomplemented
45#89934C22116yescomplemented
46C2×#6391C2212yes—
47C2×#6390C2212yes—
48C2×Dic7⋊C8C2212yes—
49#89847C2218yescomplemented
50#89792C2218yescomplemented
51C2×#6382C2212yes—
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53#89623C2218yescomplemented
54D7×C4⋊C8C2218yescomplemented
55#89550C22116yescomplemented
56#89533C22116yescomplemented
57C2×#3246—71nomaximal, Sylow
58C22×C7×Q8C2311yescharacteristic
59C22×C7×D4—21no—
60C22×C7×D4—21no—
61C22×C7×D4C2312yes—
62C22×C22⋊D7—22no—
63C23×Dic7—22no—
64C2×#1159—28no—
65C2×#1159—48no—
66C22×C4×D7D411yescharacteristic
67C22×C4×D7D411yescharacteristic
68C22×C4×D7C2311yescharacteristic
69C22×Dic14—21no—
70C22×Dic14—21no—
71C22×Dic14C2311yescharacteristic
72C2×C7×SD16—44no—
73C2×C7×SD16C2318yes—
74C22×C7×C8C2312yes—
75C7×#127—22no—
76C7×#127C2314yes—
77C4×C7×Q8—22no—
78C4×C7×Q8C2314yes—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C42×C7—21no—
82C2×C42×C7C2311yescharacteristic
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85#6509—22no—
86#6509C2314yes—
87#6507—22no—
88#6507C2314yes—
89#6501—24no—
90#6501—28no—
91#6501C2318yes—
92#6499—28no—
93D4×Dic7—24no—
94D4×Dic7—28no—
95D4×Dic7C2318yes—
96C2×#1142—44no—
97C2×#1142C2318yes—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×C4⋊Dic7—21no—
101C2×C4⋊Dic7—21no—
102C2×C4⋊Dic7C2312yes—
103C2×C4⋊Dic7C2311yescharacteristic
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×C4×Dic7—21no—
110C2×C4×Dic7D411yescharacteristic
111C2×C4×Dic7D411yescharacteristic
112C2×C4×Dic7C2311yescharacteristic
113C22×C7⋊C8C2312yes—
114C2×C8×D7—44no—
115C2×C8×D7C2318yes—
116#6460—22no—
117#6460C2314yes—
118#6459—28no—
119#6452—28no—
120#6451—22no—
121#6451C2314yes—
122#6435—28no—
123C42×D7D414yes—
124C42×D7C2314yes—
125#6432—22no—
126#6432C2314yes—
127C4×Dic14—22no—
128C4×Dic14—28no—
129C4×Dic14C2314yes—
130C7×C4⋊C8C2314yes—
131C7×#102C2318yes—
132#6409C2318yes—
133#6406C2318yes—
134#6391C2318yes—
135#6390C2318yes—
136Dic7⋊C8C2318yes—
137#6382C2318yes—
138C4⋊(C7⋊C8)C2314yes—
139C2×#533—71no—
140C2×#532—71no—
141#3246—716no—
142C2×#475—71no—
143C2×#475—71no—
144C2×#476—72no—
145C2×#465—72no—
146C2×#465—72no—
147C2×#460—71no—
148C2×#460D711yescharacteristic, complemented
149C2×#461—72no—
150C22×C4⋊C8—71no—
151C24×C7—22no—
152C23×D7C2×D411yescharacteristic
153C2×C7×Q8—21no—
154C2×C7×Q8—22no—
155C2×C7×Q8—22no—
156C2×C7×Q8C2412yes—
157C2×C7×D4—22no—
158C2×C7×D4—24no—
159C2×C7×D4—24no—
160C2×C7×D4—24no—
161C2×C7×D4—24no—
162C2×C7×D4—44no—
163C2×C7×D4—44no—
164C2×C7×D4C2414yes—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7C2×D411yescharacteristic
168C22×C4×C7C2×D411yescharacteristic
169C22×C4×C7C2411yescharacteristic
170C2×C22⋊D7—28no—
171C2×C22⋊D7—48no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—22no—
175C22×Dic7—28no—
176C22×Dic7—48no—
177C22×Dic7C2×D411yescharacteristic
178C22×Dic7C2×D411yescharacteristic
179C22×Dic7C2×D411yescharacteristic
180#1159—432no—
181C2×C4×D7—22no—
182C2×C4×D7—22no—
183C2×C4×D7—42no—
184C2×C4×D7SD1618yescomplemented
185C2×C4×D7C2×D412yes—
186C2×C4×D7C2×D414yes—
187C2×C4×D7C2×D414yes—
188C2×C4×D7C2412yes—
189C2×Dic14—22no—
190C2×Dic14—22no—
191C2×Dic14—21no—
192C2×Dic14—24no—
193C2×Dic14—24no—
194C2×Dic14—44no—
195C2×Dic14—44no—
196C2×Dic14C2412yes—
197C7×SD16—48no—
198C2×C7×C8—24no—
199C2×C7×C8C2414yes—
200C7×C4⋊C4—21no—
201C7×C4⋊C4—24no—
202C7×C4⋊C4C2412yes—
203C42×C7—24no—
204C42×C7C2×D412yes—
205C42×C7C2412yes—
206C22⋊Dic7—28no—
207C22⋊Dic7—28no—
208#1142—48no—
209(C2×D7)⋊C4—24no—
210(C2×D7)⋊C4—24no—
211C4⋊Dic7—21no—
212C4⋊Dic7—22no—
213C4⋊Dic7—24no—
214C4⋊Dic7—24no—
215C4⋊Dic7C2412yes—
216C4⋊Dic7C2414yes—
217Dic7⋊C4—24no—
218Dic7⋊C4—24no—
219Dic7⋊C4—24no—
220Dic7⋊C4—24no—
221Dic7⋊C4—24no—
222C4×Dic7—24no—
223C4×Dic7C2×D414yes—
224C4×Dic7C2×D412yes—
225C4×Dic7C2×D414yes—
226C4×Dic7C2412yes—
227C2×C7⋊C8—24no—
228C2×C7⋊C8C2414yes—
229C8×D7—48no—
230C22×#41—141no—
231C22×SD16—72no—
232C22×SD16C2×D712yes—
233C23×C8—72no—
234#533—78no—
235#533—144no—
236#532—78no—
237#532—144no—
238C2×C4⋊Q8—71no—
239C2×C4⋊Q8—71no—
240C2×C4⋊Q8—71no—
241C2×#127C2×D711yescharacteristic
242C2×#125—141no—
243C2×#124—141no—
244C2×C22⋊Q8—71no—
245C2×C22⋊Q8—71no—
246C2×C22⋊Q8—141no—
247C2×#121—72no—
248C2×#121—141no—
249C2×C4×Q8—71no—
250C2×C4×Q8—141no—
251C2×C4×Q8C2×D711yescharacteristic
252C2×C4×D4—72no—
253C2×C4×D4—141no—
254C2×#117—141no—
255C22×C42—71no—
256#476—716no—
257#475—78no—
258#475—78no—
259#465—716no—
260#465—716no—
261#461—716no—
262#460—78no—
263#460C2×D718yescomplemented
264C2×#106—72no—
265C2×#106—72no—
266C2×C4⋊C8—72no—
267C2×C4⋊C8—71no—
268C2×C4⋊C8—78no—
269C2×C4⋊C8C2×D711yescharacteristic
270C2×#103—72no—
271C2×#103—72no—
272C2×#102—72no—
273C2×#102C2×D712yes—
274C23×C7—24no—
275C23×C7—44no—
276C23×C7—44no—
277C23×C7—44no—
278C23×C7C22×D411yescharacteristic
279C22×D7—22no—
280C22×D7—22no—
281C22×D7C2×SD1614yes—
282C22×D7C22×D412yes—
283C7×Q8—22no—
284C7×Q8—22no—
285C7×Q8—42no—
286C7×D4—24no—
287C7×D4—24no—
288C7×D4—48no—
289C7×D4—44no—
290C7×D4—48no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7C2×SD1614yes—
297C2×C4×C7C22×D412yes—
298C2×C4×C7C22×D411yescharacteristic
299C2×C4×C7C22×D412yes—
300C2×C4×C7H(5,𝔽2)12yes—
301C2×C4×C72−1+412yes—
302C2×C4×C7C2511yescharacteristic
303C22⋊D7—416no—
304C2×Dic7—22no—
305C2×Dic7—22no—
306C2×Dic7—22no—
307C2×Dic7—22no—
308C2×Dic7—24no—
309C2×Dic7—42no—
310C2×Dic7—44no—
311C2×Dic7—42no—
312C2×Dic7—416no—
313C2×Dic7C2×SD1614yes—
314C2×Dic7C22×D412yes—
315C2×Dic7C22×D412yes—
316C2×Dic7C22×D412yes—
317C4×D7—24no—
318C4×D7—22no—
319C4×D7—22no—
320C4×D7—44no—
321C4×D7C2×SD16116yescomplemented
322Dic14—22no—
323Dic14—22no—
324Dic14—48no—
325Dic14—42no—
326Dic14—48no—
327C7×C8—24no—
328C7⋊C8—24no—
329C2×#41—148no—
330C2×#41—288no—
331C22×Q8—71no—
332C22×Q8—141no—
333C22×Q8—141no—
334C22×Q8C22×D711yescharacteristic
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—142no—
338C22×D4C22×D712yes—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—71no—
342C23×C4—142no—
343C2×SD16—44no—
344C2×SD16—78no—
345C2×SD16—284no—
346C2×SD16C22×D718yes—
347C22×C8—72no—
348C22×C8—78no—
349C22×C8—284no—
350C22×C8C22×D712yes—
351C4⋊Q8—74no—
352C4⋊Q8—74no—
353C4⋊Q8—74no—
354C4⋊Q8—142no—
355C4⋊Q8—142no—
356C4⋊Q8—142no—
357#127—22no—
358#127C22×D714yes—
359#125—148no—
360#124—148no—
361C22⋊Q8—74no—
362C22⋊Q8—74no—
363C22⋊Q8—142no—
364C22⋊Q8—148no—
365C22⋊Q8—142no—
366#121—78no—
367#121—144no—
368#121—148no—
369C4×Q8—22no—
370C4×Q8—74no—
371C4×Q8—148no—
372C4×Q8—142no—
373C4×Q8C22×D714yes—
374C4×D4—78no—
375C4×D4—144no—
376C4×D4—148no—
377#117—148no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—72no—
380C2×C4⋊C4—71no—
381C2×C4⋊C4—141no—
382C2×C4⋊C4—141no—
383C2×C4⋊C4—141no—
384C2×C4⋊C4—141no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4—141no—
388C2×C4⋊C4C22×D711yescharacteristic
389C2×C22⋊C4—141no—
390C2×C22⋊C4—141no—
391C2×C22⋊C4—142no—
392C2×C22⋊C4—142no—
393C2×C42—21no—
394C2×C42—71no—
395C2×C42—71no—
396C2×C42—71no—
397C2×C42—74no—
398C2×C42—74no—
399C2×C42—141no—
400C2×C42C22×D711yescharacteristic
401#106—78no—
402#106—78no—
403C4⋊C8—78no—
404C4⋊C8—74no—
405C4⋊C8C22×D714yes—
406#103—78no—
407#103—78no—
408#102—78no—
409#102C22×D718yes—
410C22×C7—44no—
411C22×C7—44no—
412C22×C7—44no—
413C22×C7—88no—
414C22×C7#53712yes—
415C22×C7C22×SD1612yes—
416C22×C7#57512yes—
417C22×C7C23×D411yescharacteristic
418C2×D7—22no—
419C2×D7—28no—
420C2×D7—22no—
421C2×D7C22×SD1614yes—
422C4×C7—22no—
423C4×C7—42no—
424C4×C7—42no—
425C4×C7#53712yes—
426C4×C7C22×SD1614yes—
427C4×C7C2×H(5,𝔽2)11yescharacteristic
428C4×C7C2×2−1+411yescharacteristic
429Dic7—22no—
430Dic7—22no—
431Dic7—42no—
432Dic7—44no—
433Dic7—42no—
434Dic7C22×SD1614yes—
435C24—22no—
436C24—71no—
437#41—2832no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—72no—
442C2×Q8—144no—
443C2×Q8—141no—
444C2×Q8—144no—
445C2×Q8—142no—
446C2×Q8—142no—
447C2×Q8—284no—
448C2×Q8—284no—
449C2×Q8C23×D712yes—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—148no—
458C2×D4—288no—
459C2×D4C23×D714yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—71no—
463C22×C4—78no—
464C22×C4—74no—
465C22×C4—71no—
466C22×C4—71no—
467C22×C4—72no—
468C22×C4—72no—
469C22×C4—74no—
470C22×C4—148no—
471C22×C4—142no—
472C22×C4—142no—
473C22×C4—141no—
474C22×C4—141no—
475C22×C4—142no—
476C22×C4—282no—
477C22×C4—288no—
478C22×C4D4×D711yescharacteristic
479C22×C4D4×D711yescharacteristic
480C22×C4C23×D711yescharacteristic
481SD16—48no—
482SD16—288no—
483C2×C8—24no—
484C2×C8—74no—
485C2×C8—144no—
486C2×C8—288no—
487C2×C8C23×D714yes—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—72no—
491C4⋊C4—74no—
492C4⋊C4—144no—
493C4⋊C4—144no—
494C4⋊C4—144no—
495C4⋊C4—144no—
496C4⋊C4—144no—
497C4⋊C4—144no—
498C4⋊C4—142no—
499C4⋊C4—141no—
500C4⋊C4—144no—
501C4⋊C4C23×D712yes—
502C22⋊C4—144no—
503C22⋊C4—144no—
504C22⋊C4—148no—
505C22⋊C4—148no—
506C42—24no—
507C42—74no—
508C42—72no—
509C42—74no—
510C42—72no—
511C42—144no—
512C42D4×D712yes—
513C42C23×D712yes—
514C2×C7—84no—
515C2×C7#324614yescomplemented
516C2×C7C2×#53711yescharacteristic
517C2×C7C23×SD1611yescharacteristic
518C2×C7C2×#57511yescharacteristic
519D7—24no—
520C23—24no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—74no—
525C23—72no—
526C23—142no—
527C23—142no—
528C23C2×D4×D711yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—42no—
532Q8—142no—
533Q8—142no—
534Q8—288no—
535Q8—288no—
536Q8—282no—
537D4—24no—
538D4—24no—
539D4—48no—
540D4—48no—
541D4—44no—
542D4—2816no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—74no—
549C2×C4—72no—
550C2×C4—716no—
551C2×C4—72no—
552C2×C4—72no—
553C2×C4—142no—
554C2×C4—142no—
555C2×C4—144no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—144no—
561C2×C4—284no—
562C2×C4—2816no—
563C2×C4—284no—
564C2×C4—282no—
565C2×C4—282no—
566C2×C4D7×SD1614yes—
567C2×C4C2×D4×D712yes—
568C2×C4C2×D4×D712yes—
569C2×C4C2×D4×D711yescharacteristic
570C2×C4#654812yes—
571C2×C4#655412yes—
572C2×C4C24×D711yescharacteristic
573C8—24no—
574C8—144no—
575C7C2×#324611yescharacteristic, complemented, Sylow
576C22—44no—
577C22—44no—
578C22—44no—
579C22—74no—
580C22—88no—
581C22—142no—
582C22—142no—
583C22—148no—
584C22#9029912yes—
585C22C2×D7×SD1612yes—
586C22#9046412yes—
587C22C22×D4×D711yescharacteristic
588C4—22no—
589C4—42no—
590C4—42no—
591C4—74no—
592C4—142no—
593C4—142no—
594C4—282no—
595C4—282no—
596C4—284no—
597C4#9029912yes—
598C4C2×D7×SD1614yes—
599C4C2×#654811yescharacteristic
600C4C2×#655411yescharacteristic
601C2—84no—
602C2—144no—
603C2#1173781114yesdirect product factor
604C2C2×#9029911yescharacteristic
605C2C22×D7×SD1611yescharacteristic
606C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#460C2
socleC23×C7C22×D4
prime radicalC2×#90407C2
hypercenterC2×#460D7
hypocenterC7C2×#3246
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. C2×#90269C2semidirect
3. C2×C7×#460C2semidirect
4. C2×#89943C2semidirect
5. C2×#89934C2semidirect
6. C2×#89847C2semidirect
7. C2×#89792C2semidirect
8. #11737811C2direct (N × H)
9. C2×#89623C2semidirect
10. C2×D7×C4⋊C8C2semidirect
11. C2×#89550C2semidirect
12. C2×#89533C2semidirect
29. #90269C22semidirect
39. C7×#460C22semidirect
44. #89943C22semidirect
45. #89934C22semidirect
49. #89847C22semidirect
50. #89792C22semidirect
53. #89623C22semidirect
54. D7×C4⋊C8C22semidirect
55. #89550C22semidirect
56. #89533C22semidirect
148. C2×#460D7semidirect
184. C2×C4×D7SD16semidirect
263. #460C2×D7semidirect
321. C4×D7C2×SD16semidirect
515. C2×C7#3246semidirect
575. C7C2×#3246semidirect
603. C2#11737811direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904072
C2×#902692
C2×C7×#4602
C2×#899432
C2×#899342
C2×#898472
C2×#897922
#117378112
C2×#896232
C2×D7×C4⋊C82
C2×#895502
C2×#895332
C2×#32467