Finite Group Databasebeta

← C2×#11739186 #14225071

Subgroups — C2×#11739186 #14225071

Order 1792.

2146 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#90382C211yesmaximal, characteristic
3C2×C7×#491C211yesmaximal, characteristic, complemented
4C2×#89858C211yesmaximal, characteristic, complemented
5C2×#89841C211yesmaximal, characteristic, complemented
6#11739186C2116yesmaximal, direct product factor
7C2×#89565C212yesmaximal, complemented
8C2×#89590C212yesmaximal, complemented
9C2×#89580C212yesmaximal, complemented
10C2×#89578C212yesmaximal
11C2×#89487C211yesmaximal, characteristic, complemented
12C2×#89477C211yesmaximal, characteristic, complemented
13C22×Q8×D7C2212yes—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C7×#125C2211yescharacteristic
16C2×#6507C2212yes—
17C22×#1144C2212yes—
18C22×#1143C2212yes—
19C22×Dic28C2212yes—
20C22×#1132C2212yes—
21D7×C4⋊Q8—24no—
22D7×C4⋊Q8C2218yescomplemented
23#90382—24no—
24#90382C2218yes—
25C2×#6461—21no—
26C2×#6460C2211yescharacteristic
27C2×#6458C2211yescharacteristic
28C2×#6457—21no—
29C2×#6456—21no—
30C2×#6456C2211yescharacteristic
31C2×#6455—21no—
32C2×D7×C4⋊C4—21no—
33C2×D7×C4⋊C4—21no—
34C2×#6451—21no—
35C2×#6451—21no—
36C2×#6450C2211yescharacteristic
37C2×#6438C2211yescharacteristic
38C2×C42×D7C2211yescharacteristic
39C2×#6432C2211yescharacteristic
40C7×#491C2218yescomplemented
41C2×C7×#103C2212yes—
42C2×C7×#103C2212yes—
43C2×C7×#97C2211yescharacteristic
44C2×(C2×D7)⋊C8C2212yes—
45C2×Dic7⋊C8C2212yes—
46#89858C2218yescomplemented
47#89841C2218yescomplemented
48C2×#6384C2212yes—
49C2×#6384C2212yes—
50C2×#6377C2211yescharacteristic
51#89590C22116yescomplemented
52#89580C22116yescomplemented
53#89578C22116yes—
54#89565C22116yescomplemented
55#89487C2218yescomplemented
56#89477C2218yescomplemented
57C2×#3218—71nomaximal, Sylow
58C22×C7×Q8C2312yes—
59C2×Q8×D7—24no—
60C2×Q8×D7—44no—
61C2×Q8×D7—44no—
62C2×Q8×D7C2318yes—
63C22×D28—21no—
64C22×D28C2311yescharacteristic
65C22×C4×D7—22no—
66C22×C4×D7—21no—
67C22×C4×D7D411yescharacteristic
68C22×C4×D7D411yescharacteristic
69C22×C4×D7C2311yescharacteristic
70C22×Dic14—22no—
71C22×Dic14C2312yes—
72C22×Dic14C2311yescharacteristic
73C22×C7×C8C2312yes—
74C7×C4⋊Q8—22no—
75C7×C4⋊Q8C2314yes—
76C7×#125—22no—
77C7×#125C2314yes—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4—21no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C42×C7C2311yescharacteristic
85#6507—24no—
86#6507C2318yes—
87C2×#1144—44no—
88C2×#1144C2318yes—
89C2×#1143—44no—
90C2×#1143C2318yes—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4—21no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7D411yescharacteristic
104C2×C4×Dic7D411yescharacteristic
105C2×C4×Dic7C2311yescharacteristic
106C22×C7⋊C8C2312yes—
107C2×Dic28—44no—
108C2×Dic28C2318yes—
109C2×#1132—44no—
110C2×#1132C2318yes—
111#6461—28no—
112#6460—22no—
113#6460C2314yes—
114#6458—22no—
115#6458C2314yes—
116#6457—28no—
117#6456—28no—
118#6456—22no—
119#6456C2314yes—
120#6455—28no—
121D7×C4⋊C4—28no—
122D7×C4⋊C4—28no—
123#6451—28no—
124#6451—28no—
125#6450—22no—
126#6450C2314yes—
127#6438—22no—
128#6438C2314yes—
129C42×D7D414yes—
130C42×D7C2314yes—
131#6432—22no—
132#6432C2314yes—
133C7×#103C2318yes—
134C7×#103C2318yes—
135C7×#97C2314yes—
136(C2×D7)⋊C8C2318yes—
137Dic7⋊C8C2318yes—
138#6384C2318yes—
139#6384C2318yes—
140#6377C2314yes—
141C22×C4⋊Q8—71no—
142C2×#529—71no—
143#3218—716no—
144C2×#497—71no—
145C2×#497—71no—
146C2×#491—71no—
147C2×#491D711yescharacteristic, complemented
148C2×#462—72no—
149C2×#461—72no—
150C2×#451—72no—
151C2×#448—72no—
152C2×#432—71no—
153C23×D7—21no—
154C23×D7C2×D411yescharacteristic
155C2×C7×Q8—22no—
156C2×C7×Q8—24no—
157C2×C7×Q8—24no—
158C2×C7×Q8C2414yes—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—21no—
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2411yescharacteristic
165C22×Dic7—21no—
166C22×Dic7—22no—
167C22×Dic7C2×D411yescharacteristic
168C22×Dic7C2×D411yescharacteristic
169C22×Dic7C2×D411yescharacteristic
170Q8×D7—48no—
171Q8×D7—48no—
172Q8×D7—416no—
173C2×D28—24no—
174C2×D28—24no—
175C2×D28—21no—
176C2×D28—44no—
177C2×D28C2412yes—
178C2×C4×D7—24no—
179C2×C4×D7—24no—
180C2×C4×D7—24no—
181C2×C4×D7—28no—
182C2×C4×D7—24no—
183C2×C4×D7—48no—
184C2×C4×D7—44no—
185C2×C4×D7C2×D412yes—
186C2×C4×D7C2×D414yes—
187C2×C4×D7C2×D414yes—
188C2×C4×D7C2412yes—
189C2×Dic14—24no—
190C2×Dic14—24no—
191C2×Dic14—24no—
192C2×Dic14—22no—
193C2×Dic14—21no—
194C2×Dic14—28no—
195C2×Dic14—48no—
196C2×Dic14C2414yes—
197C2×Dic14C2412yes—
198C2×C7×C8—24no—
199C2×C7×C8C2414yes—
200C7×C4⋊C4—21no—
201C7×C4⋊C4—24no—
202C7×C4⋊C4—24no—
203C7×C4⋊C4—24no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4—24no—
206C7×C4⋊C4C2412yes—
207C7×C4⋊C4C2412yes—
208C42×C7C2×D412yes—
209C42×C7C2412yes—
210#1144—48no—
211#1143—48no—
212(C2×D7)⋊C4—24no—
213(C2×D7)⋊C4—24no—
214(C2×D7)⋊C4—24no—
215(C2×D7)⋊C4—24no—
216(C2×D7)⋊C4—24no—
217C4⋊Dic7—24no—
218C4⋊Dic7—24no—
219C4⋊Dic7—24no—
220Dic7⋊C4—24no—
221Dic7⋊C4—28no—
222Dic7⋊C4—28no—
223C4×Dic7—24no—
224C4×Dic7C2×D412yes—
225C4×Dic7C2×D414yes—
226C4×Dic7C2×D414yes—
227C4×Dic7C2412yes—
228C2×C7⋊C8—24no—
229C2×C7⋊C8C2414yes—
230Dic28—48no—
231#1132—48no—
232C23×Q8—72no—
233C22×Q16—72no—
234C22×Q16—72no—
235C22×SD16—72no—
236C22×SD16—72no—
237C2×C4⋊Q8—72no—
238C2×C4⋊Q8—78no—
239C2×C4⋊Q8—71no—
240C2×C4⋊Q8—141no—
241C2×C4⋊Q8—141no—
242C2×C4⋊Q8—144no—
243C2×C4⋊Q8C2×D711yescharacteristic
244#529—78no—
245#529—144no—
246C2×#126—141no—
247C2×#125C2×D711yescharacteristic
248C2×#124—71no—
249C2×#123—141no—
250C2×C22⋊Q8—71no—
251C2×#121—71no—
252C2×C4×Q8—71no—
253C2×C4×D4—71no—
254C2×C4×D4—141no—
255C2×#117—141no—
256C22×C4⋊C4—141no—
257C22×C4⋊C4—141no—
258C22×C42—71no—
259#497—78no—
260#497—78no—
261#491—78no—
262#491C2×D718yescomplemented
263#462—716no—
264#461—716no—
265#451—716no—
266#448—716no—
267#432—78no—
268C2×C4⋊C8—72no—
269C2×#103—72no—
270C2×#103—72no—
271C2×#103C2×D712yes—
272C2×#103C2×D712yes—
273C2×C22⋊C8—72no—
274C2×#97—71no—
275C2×#97C2×D711yescharacteristic
276C23×C7C22×D411yescharacteristic
277C22×D7—22no—
278C22×D7—22no—
279C22×D7—22no—
280C22×D7—42no—
281C22×D7—42no—
282C22×D7—42no—
283C22×D7#13714yes—
284C22×D7C22×D412yes—
285C7×Q8—24no—
286C7×Q8—24no—
287C7×Q8—44no—
288C2×C4×C7—22no—
289C2×C4×C7—22no—
290C2×C4×C7—22no—
291C2×C4×C7—24no—
292C2×C4×C7—22no—
293C2×C4×C7—44no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7C22×D412yes—
297C2×C4×C7C22×D412yes—
298C2×C4×C7C22×D411yescharacteristic
299C2×C4×C7H(5,𝔽2)14yes—
300C2×C4×C7C2511yescharacteristic
301C2×Dic7—22no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—24no—
305C2×Dic7—44no—
306C2×Dic7—42no—
307C2×Dic7#13714yes—
308C2×Dic7C22×D412yes—
309C2×Dic7C22×D412yes—
310C2×Dic7C22×D412yes—
311D28—24no—
312D28—48no—
313D28—42no—
314C4×D7—28no—
315C4×D7—24no—
316C4×D7—24no—
317C4×D7—28no—
318C4×D7—416no—
319C4×D7—48no—
320Dic14—24no—
321Dic14—24no—
322Dic14—24no—
323Dic14—416no—
324Dic14—42no—
325Dic14—44no—
326C7×C8—24no—
327C7⋊C8—24no—
328C22×Q8—78no—
329C22×Q8—71no—
330C22×Q8—72no—
331C22×Q8—142no—
332C22×Q8—144no—
333C22×Q8—284no—
334C22×Q8—284no—
335C22×Q8C22×D712yes—
336C22×D4—71no—
337C22×D4—141no—
338C23×C4—71no—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—141no—
342C23×C4—142no—
343C2×Q16—78no—
344C2×Q16—78no—
345C2×Q16—284no—
346C2×Q16—284no—
347C2×SD16—78no—
348C2×SD16—78no—
349C2×SD16—284no—
350C2×SD16—284no—
351C22×C8—72no—
352C22×C8C22×D712yes—
353C4⋊Q8—22no—
354C4⋊Q8—78no—
355C4⋊Q8—74no—
356C4⋊Q8—148no—
357C4⋊Q8—148no—
358C4⋊Q8—144no—
359C4⋊Q8—142no—
360C4⋊Q8C22×D714yes—
361#126—148no—
362#125—22no—
363#125C22×D714yes—
364#124—74no—
365#124—142no—
366#123—148no—
367C22⋊Q8—74no—
368C22⋊Q8—142no—
369#121—74no—
370#121—142no—
371C4×Q8—74no—
372C4×Q8—142no—
373C4×D4—74no—
374C4×D4—142no—
375C4×D4—148no—
376#117—148no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—148no—
382C2×C4⋊C4—148no—
383C2×C4⋊C4—142no—
384C2×C4⋊C4—142no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4—141no—
388C2×C4⋊C4—141no—
389C2×C4⋊C4C22×D711yescharacteristic
390C2×C4⋊C4C22×D711yescharacteristic
391C2×C22⋊C4—141no—
392C2×C22⋊C4—141no—
393C2×C22⋊C4—141no—
394C2×C22⋊C4—141no—
395C2×C22⋊C4—141no—
396C2×C42—71no—
397C2×C42—71no—
398C2×C42—71no—
399C2×C42—74no—
400C2×C42—74no—
401C2×C42—141no—
402C2×C42C22×D711yescharacteristic
403C4⋊C8—78no—
404#103—78no—
405#103—78no—
406#103C22×D718yes—
407#103C22×D718yes—
408C22⋊C8—78no—
409#97—74no—
410#97C22×D714yes—
411C22×C7#53512yes—
412C22×C7C2×#13712yes—
413C22×C7C2×#13712yes—
414C22×C7C23×D411yescharacteristic
415C2×D7—22no—
416C2×D7—28no—
417C2×D7—22no—
418C2×D7—42no—
419C2×D7—42no—
420C2×D7—42no—
421C2×D7—84no—
422C2×D7C2×#13714yes—
423C4×C7—22no—
424C4×C7—22no—
425C4×C7—44no—
426C4×C7—42no—
427C4×C7—42no—
428C4×C7#53512yes—
429C4×C7C2×H(5,𝔽2)12yes—
430Dic7—22no—
431Dic7—22no—
432Dic7—44no—
433Dic7—42no—
434Dic7C2×#13714yes—
435C24—71no—
436C24—141no—
437C2×Q8—22no—
438C2×Q8—24no—
439C2×Q8—24no—
440C2×Q8—74no—
441C2×Q8—72no—
442C2×Q8—148no—
443C2×Q8—141no—
444C2×Q8—142no—
445C2×Q8—144no—
446C2×Q8—144no—
447C2×Q8—144no—
448C2×Q8—288no—
449C2×Q8—288no—
450C2×Q8—288no—
451C2×Q8—2816no—
452C2×Q8C23×D714yes—
453C2×D4—72no—
454C2×D4—144no—
455C2×D4—141no—
456C2×D4—144no—
457C2×D4—284no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—71no—
462C22×C4—71no—
463C22×C4—71no—
464C22×C4—74no—
465C22×C4—74no—
466C22×C4—72no—
467C22×C4—72no—
468C22×C4—144no—
469C22×C4—144no—
470C22×C4—144no—
471C22×C4—148no—
472C22×C4—144no—
473C22×C4—141no—
474C22×C4—142no—
475C22×C4—284no—
476C22×C4—288no—
477C22×C4D4×D711yescharacteristic
478C22×C4D4×D711yescharacteristic
479C22×C4C23×D711yescharacteristic
480Q16—288no—
481Q16—288no—
482SD16—288no—
483SD16—288no—
484C2×C8—24no—
485C2×C8—74no—
486C2×C8—144no—
487C2×C8C23×D714yes—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—24no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—148no—
495C4⋊C4—148no—
496C4⋊C4—144no—
497C4⋊C4—144no—
498C4⋊C4—144no—
499C4⋊C4—144no—
500C4⋊C4C23×D712yes—
501C4⋊C4C23×D712yes—
502C22⋊C4—144no—
503C22⋊C4—144no—
504C22⋊C4—144no—
505C22⋊C4—144no—
506C22⋊C4—144no—
507C42—74no—
508C42—72no—
509C42—74no—
510C42—72no—
511C42—144no—
512C42D4×D712yes—
513C42C23×D712yes—
514C2×C7#321814yescomplemented
515C2×C7C2×#53511yescharacteristic
516C2×C7C22×#13711yescharacteristic
517C2×C7C22×#13711yescharacteristic
518D7—24no—
519D7—82no—
520C23—74no—
521C23—72no—
522C23—142no—
523C23—142no—
524C23—142no—
525C23—282no—
526C23—282no—
527C23—282no—
528C23C2×D4×D711yescharacteristic
529Q8—24no—
530Q8—24no—
531Q8—44no—
532Q8—144no—
533Q8—144no—
534Q8—144no—
535Q8—2816no—
536Q8—282no—
537Q8—284no—
538D4—144no—
539D4—288no—
540D4—282no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—74no—
550C2×C4—72no—
551C2×C4—72no—
552C2×C4—72no—
553C2×C4—148no—
554C2×C4—148no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—144no—
558C2×C4—144no—
559C2×C4—142no—
560C2×C4—144no—
561C2×C4—288no—
562C2×C4—2816no—
563C2×C4—284no—
564C2×C4—282no—
565C2×C4C2×D4×D712yes—
566C2×C4C2×D4×D712yes—
567C2×C4C2×D4×D711yescharacteristic
568C2×C4#655314yes—
569C2×C4C24×D711yescharacteristic
570C8—24no—
571C8—144no—
572C7C2×#321811yescharacteristic, complemented, Sylow
573C22—74no—
574C22—142no—
575C22—148no—
576C22—142no—
577C22—282no—
578C22—282no—
579C22—282no—
580C22—564no—
581C22#9036512yes—
582C22D7×#13712yes—
583C22D7×#13712yes—
584C22C22×D4×D711yescharacteristic
585C4—22no—
586C4—22no—
587C4—42no—
588C4—42no—
589C4—44no—
590C4—74no—
591C4—142no—
592C4—142no—
593C4—284no—
594C4—282no—
595C4#9036512yes—
596C4C2×#655312yes—
597C2—144no—
598C2—562no—
599C2#1173918614yesdirect product factor
600C2C2×#9036511yescharacteristic
601C2C2×D7×#13711yescharacteristic
602C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#491C2
socleC23×C7C22×D4
prime radicalC2×#6458C22
hypercenterC2×#491D7
hypocenterC7C2×#3218
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×D7×C4⋊Q8C2semidirect
3. C2×C7×#491C2semidirect
4. C2×#89858C2semidirect
5. C2×#89841C2semidirect
6. #11739186C2direct (N × H)
7. C2×#89565C2semidirect
8. C2×#89590C2semidirect
9. C2×#89580C2semidirect
11. C2×#89487C2semidirect
12. C2×#89477C2semidirect
22. D7×C4⋊Q8C22semidirect
40. C7×#491C22semidirect
46. #89858C22semidirect
47. #89841C22semidirect
51. #89590C22semidirect
52. #89580C22semidirect
54. #89565C22semidirect
55. #89487C22semidirect
56. #89477C22semidirect
147. C2×#491D7semidirect
262. #491C2×D7semidirect
514. C2×C7#3218semidirect
572. C7C2×#3218semidirect
599. C2#11739186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C4⋊Q82
C2×#903822
C2×C7×#4912
C2×#898582
C2×#898412
#117391862
C2×#895652
C2×#895902
C2×#895802
C2×#895782
C2×#894872
C2×#894772
C2×#32187