Finite Group Databasebeta

← C2×#11739418 #14223409

Subgroups — C2×#11739418 #14223409

Order 1792.

1902 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90419C211yesmaximal, characteristic
2C2×#90379C211yesmaximal, characteristic
3C2×C7×#501C211yesmaximal, characteristic, complemented
4C2×#89852C211yesmaximal, characteristic, complemented
5C2×#89837C211yesmaximal, characteristic, complemented
6#11739418C2116yesmaximal, direct product factor
7C2×#89652C212yesmaximal
8C2×#89648C212yesmaximal, complemented
9C2×#89632C212yesmaximal
10C2×#89628C212yesmaximal, complemented
11C2×D7×#97C211yesmaximal, characteristic
12C2×#89474C211yesmaximal, characteristic, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C7×#125C2211yescharacteristic
15C2×#6509—21no—
16C2×Q8×Dic7—21no—
17C22×C8×D7C2212yes—
18#90419—24no—
19#90419C2218yes—
20#90379—24no—
21#90379C2218yes—
22C2×#6460—21no—
23C2×#6459—21no—
24C2×#6459—21no—
25C2×#6455C2211yescharacteristic
26C2×#6455C2212yes—
27C2×#6455C2211yescharacteristic
28C2×#6453C2212yes—
29C2×#6451C2211yescharacteristic
30C2×#6451C2211yescharacteristic
31C2×#6450—21no—
32C2×#6450—21no—
33C2×#6450—21no—
34C2×C42×D7C2211yescharacteristic
35C2×#6433C2211yescharacteristic
36C2×#6432C2211yescharacteristic
37C7×#501C2218yescomplemented
38C2×C7×#107C2212yes—
39C2×C7×#106C2212yes—
40C2×C7×#97C2211yescharacteristic
41C2×#6392C2212yes—
42C2×#6391C2212yes—
43C2×#6389C2212yes—
44#89852C2218yescomplemented
45#89837C2218yescomplemented
46C2×#6382C2212yes—
47C2×#6382C2212yes—
48C2×#6381C2212yes—
49C2×#6381C2212yes—
50C2×#6377C2211yescharacteristic
51#89652C22116yes—
52#89648C22116yescomplemented
53#89632C22116yes—
54#89628C22116yescomplemented
55D7×#97C2218yes—
56#89474C2218yescomplemented
57C2×#3162—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C4×D7D411yescharacteristic
60C22×C4×D7D411yescharacteristic
61C22×C4×D7C2311yescharacteristic
62C22×Dic14—21no—
63C22×Dic14—21no—
64C22×Dic14—21no—
65C22×C7×C8C2312yes—
66C7×C4⋊Q8—22no—
67C7×C4⋊Q8C2314yes—
68C7×#125—22no—
69C7×#125C2314yes—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2312yes—
76C2×C42×C7C2311yescharacteristic
77#6509—28no—
78Q8×Dic7—28no—
79C2×(C2×D7)⋊C4—21no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—22no—
82C2×C4⋊Dic7—21no—
83C2×C4⋊Dic7—22no—
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2312yes—
86C2×C4⋊Dic7C2311yescharacteristic
87C2×Dic7⋊C4—21no—
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—22no—
92C2×C4×Dic7—21no—
93C2×C4×Dic7—21no—
94C2×C4×Dic7—22no—
95C2×C4×Dic7D411yescharacteristic
96C2×C4×Dic7D411yescharacteristic
97C2×C4×Dic7C2311yescharacteristic
98C22×C7⋊C8C2312yes—
99C2×C8×D7Q8116yescomplemented
100C2×C8×D7C2318yes—
101#6460—28no—
102#6459—28no—
103#6459—28no—
104#6455—22no—
105#6455—22no—
106#6455—24no—
107#6455C2314yes—
108#6455C2314yes—
109#6455C2318yes—
110#6453—24no—
111#6453C2318yes—
112#6451—22no—
113#6451—22no—
114#6451C2314yes—
115#6451C2314yes—
116#6450—28no—
117#6450—28no—
118#6450—28no—
119C42×D7D414yes—
120C42×D7C2314yes—
121#6433—22no—
122#6433C2314yes—
123#6432—22no—
124#6432C2314yes—
125C7×#107C2318yes—
126C7×#106C2318yes—
127C7×#97C2314yes—
128#6392C2318yes—
129#6391C2318yes—
130#6389C2318yes—
131#6382C2318yes—
132#6382C2318yes—
133#6381C2318yes—
134#6381C2318yes—
135#6377C2314yes—
136C2×#533—71no—
137C2×#533—71no—
138#3162—716no—
139C2×#501—72no—
140C2×#501—72no—
141C2×#501—71no—
142C2×#501—71no—
143C2×#501—71no—
144C2×#501D711yescharacteristic, complemented
145C2×#427—72no—
146C2×#427—72no—
147C22×#97—71no—
148C23×D7C2×D411yescharacteristic
149C2×C7×Q8—24no—
150C2×C7×Q8—44no—
151C22×C4×C7—22no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2411yescharacteristic
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—22no—
160C22×Dic7C2×D411yescharacteristic
161C22×Dic7C2×D411yescharacteristic
162C22×Dic7C2×D411yescharacteristic
163C2×C4×D7—42no—
164C2×C4×D7—42no—
165C2×C4×D7C2×D414yes—
166C2×C4×D7C2×D414yes—
167C2×C4×D7C2×D412yes—
168C2×C4×D7C2×Q818yes—
169C2×C4×D7C2412yes—
170C2×Dic14—24no—
171C2×Dic14—24no—
172C2×Dic14—24no—
173C2×Dic14—44no—
174C2×Dic14—44no—
175C2×Dic14—44no—
176C2×C7×C8C2×Q818yes—
177C2×C7×C8C2414yes—
178C7×C4⋊C4—24no—
179C7×C4⋊C4—24no—
180C7×C4⋊C4—24no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—22no—
184C7×C4⋊C4C2412yes—
185C7×C4⋊C4C2414yes—
186C7×C4⋊C4C2412yes—
187C42×C7C2×D412yes—
188C42×C7C2412yes—
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—24no—
191(C2×D7)⋊C4—28no—
192C4⋊Dic7—22no—
193C4⋊Dic7—24no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—28no—
197C4⋊Dic7C2414yes—
198C4⋊Dic7C2412yes—
199C4⋊Dic7C2412yes—
200Dic7⋊C4—24no—
201Dic7⋊C4—24no—
202Dic7⋊C4—24no—
203Dic7⋊C4—24no—
204Dic7⋊C4—28no—
205C4×Dic7—24no—
206C4×Dic7—24no—
207C4×Dic7—28no—
208C4×Dic7C2×D412yes—
209C4×Dic7C2×D414yes—
210C4×Dic7C2×D414yes—
211C4×Dic7C2412yes—
212C2×C7⋊C8C2×Q818yes—
213C2×C7⋊C8C2414yes—
214C8×D7C2×Q8132yescomplemented
215C23×C8—72no—
216#533—78no—
217#533—78no—
218#533—144no—
219#533—144no—
220C2×C4⋊Q8—71no—
221C2×C4⋊Q8—71no—
222C2×C4⋊Q8—71no—
223C2×C4⋊Q8C2×D711yescharacteristic
224C2×#125—72no—
225C2×#125—71no—
226C2×#125C2×D711yescharacteristic
227C2×C22⋊Q8—141no—
228C2×C22⋊Q8—141no—
229C2×C22⋊Q8—141no—
230C2×C22⋊Q8—141no—
231C2×C4×Q8—141no—
232C2×C4×Q8—141no—
233C2×C4×Q8—141no—
234C2×C4×Q8—141no—
235C2×#117—72no—
236C2×#117—71no—
237C2×#117—71no—
238C22×C42—71no—
239#501—78no—
240#501—78no—
241#501—716no—
242#501—716no—
243#501—78no—
244#501C2×D718yescomplemented
245#427—716no—
246#427—716no—
247C2×#107—72no—
248C2×#107—72no—
249C2×#107—72no—
250C2×#107C2×D712yes—
251C2×#106—72no—
252C2×#106—72no—
253C2×#106—72no—
254C2×#106C2×D712yes—
255C2×#97—72no—
256C2×#97—71no—
257C2×#97—78no—
258C2×#97C2×D711yescharacteristic
259C23×C7C22×D411yescharacteristic
260C22×D7—22no—
261C22×D7—22no—
262C22×D7C4⋊Q814yes—
263C22×D7C22×D412yes—
264C7×Q8—48no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—24no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—42no—
271C2×C4×C7—42no—
272C2×C4×C7—44no—
273C2×C4×C7C22×D412yes—
274C2×C4×C7C22×D412yes—
275C2×C4×C7C22×D411yescharacteristic
276C2×C4×C7C22×Q814yes—
277C2×C4×C7C2511yescharacteristic
278C2×Dic7—22no—
279C2×Dic7—22no—
280C2×Dic7—22no—
281C2×Dic7—22no—
282C2×Dic7—24no—
283C2×Dic7—42no—
284C2×Dic7—42no—
285C2×Dic7—44no—
286C2×Dic7C4⋊Q814yes—
287C2×Dic7C22×D412yes—
288C2×Dic7C22×D412yes—
289C2×Dic7C22×D412yes—
290C4×D7—44no—
291C4×D7—44no—
292C4×D7C4⋊Q818yes—
293C4×D7C22×Q818yes—
294Dic14—48no—
295Dic14—48no—
296Dic14—48no—
297C7×C8C22×Q818yes—
298C7⋊C8C22×Q818yes—
299C22×Q8—21no—
300C22×Q8—141no—
301C22×Q8—141no—
302C22×Q8—141no—
303C23×C4—71no—
304C23×C4—71no—
305C23×C4—71no—
306C22×C8—72no—
307C22×C8—716no—
308C22×C8—78no—
309C22×C8C22×D712yes—
310C4⋊Q8—22no—
311C4⋊Q8—74no—
312C4⋊Q8—74no—
313C4⋊Q8—74no—
314C4⋊Q8—142no—
315C4⋊Q8—142no—
316C4⋊Q8—142no—
317C4⋊Q8C22×D714yes—
318#125—22no—
319#125—78no—
320#125—74no—
321#125—144no—
322#125—142no—
323#125C22×D714yes—
324C22⋊Q8—148no—
325C22⋊Q8—148no—
326C22⋊Q8—148no—
327C22⋊Q8—148no—
328C4×Q8—148no—
329C4×Q8—148no—
330C4×Q8—148no—
331C4×Q8—148no—
332#117—74no—
333#117—78no—
334#117—74no—
335#117—142no—
336#117—142no—
337#117—144no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—72no—
342C2×C4⋊C4—71no—
343C2×C4⋊C4—71no—
344C2×C4⋊C4—142no—
345C2×C4⋊C4—142no—
346C2×C4⋊C4—141no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4—141no—
349C2×C4⋊C4—141no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4C22×D712yes—
352C2×C4⋊C4C22×D711yescharacteristic
353C2×C4⋊C4C22×D711yescharacteristic
354C2×C22⋊C4—141no—
355C2×C22⋊C4—141no—
356C2×C22⋊C4—142no—
357C2×C42—71no—
358C2×C42—71no—
359C2×C42—71no—
360C2×C42—74no—
361C2×C42—74no—
362C2×C42—141no—
363C2×C42—141no—
364C2×C42—142no—
365C2×C42C22×D711yescharacteristic
366#107—78no—
367#107—78no—
368#107—78no—
369#107C22×D718yes—
370#106—78no—
371#106—78no—
372#106—78no—
373#106C22×D718yes—
374#97—78no—
375#97—74no—
376#97C22×D714yes—
377C22×C7C2×C4⋊Q812yes—
378C22×C7#57512yes—
379C22×C7#57512yes—
380C22×C7C23×D411yescharacteristic
381C2×D7—28no—
382C2×D7—22no—
383C2×D7—22no—
384C2×D7C2×C4⋊Q814yes—
385C4×C7—22no—
386C4×C7—22no—
387C4×C7—42no—
388C4×C7—42no—
389C4×C7—44no—
390C4×C7C2×C4⋊Q812yes—
391C4×C7C23×Q812yes—
392Dic7—22no—
393Dic7—22no—
394Dic7—42no—
395Dic7—42no—
396Dic7—44no—
397Dic7C2×C4⋊Q814yes—
398C24—71no—
399C2×Q8—24no—
400C2×Q8—44no—
401C2×Q8—144no—
402C2×Q8—144no—
403C2×Q8—144no—
404C2×Q8—284no—
405C2×Q8—284no—
406C2×Q8—284no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—71no—
411C22×C4—72no—
412C22×C4—78no—
413C22×C4—72no—
414C22×C4—71no—
415C22×C4—71no—
416C22×C4—74no—
417C22×C4—74no—
418C22×C4—141no—
419C22×C4—142no—
420C22×C4—141no—
421C22×C4—282no—
422C22×C4—282no—
423C22×C4D4×D711yescharacteristic
424C22×C4D4×D711yescharacteristic
425C22×C4C23×D711yescharacteristic
426C2×C8—78no—
427C2×C8—74no—
428C2×C8—732no—
429C2×C8Q8×D718yes—
430C2×C8C23×D714yes—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—72no—
438C4⋊C4—74no—
439C4⋊C4—72no—
440C4⋊C4—148no—
441C4⋊C4—144no—
442C4⋊C4—144no—
443C4⋊C4—148no—
444C4⋊C4—144no—
445C4⋊C4—144no—
446C4⋊C4—142no—
447C4⋊C4—141no—
448C4⋊C4—141no—
449C4⋊C4—144no—
450C4⋊C4C23×D712yes—
451C4⋊C4C23×D714yes—
452C4⋊C4C23×D712yes—
453C22⋊C4—144no—
454C22⋊C4—144no—
455C22⋊C4—148no—
456C42—74no—
457C42—74no—
458C42—72no—
459C42—72no—
460C42—144no—
461C42—144no—
462C42—148no—
463C42D4×D712yes—
464C42C23×D712yes—
465C2×C7#316214yescomplemented
466C2×C7C22×C4⋊Q811yescharacteristic
467C2×C7C2×#57511yescharacteristic
468C2×C7C2×#57511yescharacteristic
469D7—24no—
470C23—74no—
471C23—72no—
472C23—142no—
473C23—142no—
474C23C2×D4×D711yescharacteristic
475Q8—48no—
476Q8—288no—
477Q8—288no—
478Q8—288no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—74no—
488C2×C4—72no—
489C2×C4—78no—
490C2×C4—78no—
491C2×C4—72no—
492C2×C4—72no—
493C2×C4—142no—
494C2×C4—142no—
495C2×C4—142no—
496C2×C4—142no—
497C2×C4—144no—
498C2×C4—284no—
499C2×C4—284no—
500C2×C4—282no—
501C2×C4—284no—
502C2×C4—282no—
503C2×C4C2×D4×D712yes—
504C2×C4C2×D4×D712yes—
505C2×C4C2×D4×D711yescharacteristic
506C2×C4C2×Q8×D714yes—
507C2×C4C24×D711yescharacteristic
508C8—78no—
509C8C2×Q8×D718yes—
510C7C2×#316211yescharacteristic, complemented, Sylow
511C22—74no—
512C22—142no—
513C22—142no—
514C22—148no—
515C22D7×C4⋊Q812yes—
516C22#9046412yes—
517C22#9046812yes—
518C22C22×D4×D711yescharacteristic
519C4—22no—
520C4—22no—
521C4—44no—
522C4—42no—
523C4—42no—
524C4—74no—
525C4—142no—
526C4—142no—
527C4—282no—
528C4—284no—
529C4—282no—
530C4D7×C4⋊Q812yes—
531C4C22×Q8×D712yes—
532C2—144no—
533C2#1173941814yesdirect product factor
534C2C2×D7×C4⋊Q811yescharacteristic
535C2C2×#9046411yescharacteristic
536C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#501C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#501D7
hypocenterC7C2×#3162
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. C2×C7×#501C2semidirect
4. C2×#89852C2semidirect
5. C2×#89837C2semidirect
6. #11739418C2direct (N × H)
8. C2×#89648C2semidirect
10. C2×#89628C2semidirect
12. C2×#89474C2semidirect
37. C7×#501C22semidirect
44. #89852C22semidirect
45. #89837C22semidirect
52. #89648C22semidirect
54. #89628C22semidirect
56. #89474C22semidirect
99. C2×C8×D7Q8semidirect
144. C2×#501D7semidirect
214. C8×D7C2×Q8semidirect
244. #501C2×D7semidirect
465. C2×C7#3162semidirect
510. C7C2×#3162semidirect
533. C2#11739418direct (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×#903792
C2×C7×#5012
C2×#898522
C2×#898372
#117394182
C2×#896522
C2×#896482
C2×#896322
C2×#896282
C2×D7×#972
C2×#894742
C2×#31627