Finite Group Databasebeta

← C2×#11739421 #14223444

Subgroups — C2×#11739421 #14223444

Order 1792.

2118 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic
2C2×#90379C211yesmaximal, characteristic
3C2×C7×#501C211yesmaximal, characteristic, complemented
4C2×#89852C211yesmaximal, characteristic, complemented
5C2×#89837C211yesmaximal, characteristic, complemented
6#11739421C2116yesmaximal, direct product factor
7C2×#89653C212yesmaximal
8C2×#89646C212yesmaximal, complemented
9C2×#89633C212yesmaximal
10C2×#89627C212yesmaximal, complemented
11C2×#89479C211yesmaximal, characteristic
12C2×#89474C211yesmaximal, characteristic, complemented
13C22×Q8×D7—21no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C7×#125C2211yescharacteristic
16C2×#6507—21no—
17C22×#1131C2212yes—
18D7×C4⋊Q8—24no—
19D7×C4⋊Q8C2218yes—
20#90379—24no—
21#90379C2218yes—
22C2×#6459—21no—
23C2×#6459—21no—
24C2×#6455C2211yescharacteristic
25C2×#6455C2211yescharacteristic
26C2×D7×C4⋊C4—21no—
27C2×D7×C4⋊C4C2212yes—
28C2×#6451—21no—
29C2×#6451C2211yescharacteristic
30C2×#6451C2212yes—
31C2×#6451C2211yescharacteristic
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×C8×Dic7C2212yes—
44#89852C2218yescomplemented
45#89837C2218yescomplemented
46C2×#6382C2212yes—
47C2×#6382C2212yes—
48C2×#6381C2212yes—
49C2×#6381C2212yes—
50C2×#6377C2211yescharacteristic
51#89653C22116yes—
52#89646C22116yescomplemented
53#89633C22116yes—
54#89627C22116yescomplemented
55#89479C2218yes—
56#89474C2218yescomplemented
57C2×#3165—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C2×Q8×D7—28no—
60C2×Q8×D7—48no—
61C22×C4×D7—22no—
62C22×C4×D7D411yescharacteristic
63C22×C4×D7D411yescharacteristic
64C22×C4×D7C2311yescharacteristic
65C22×Dic14—21no—
66C22×Dic14—21no—
67C22×Dic14—21no—
68C22×Dic14—22no—
69C22×C7×C8C2312yes—
70C7×C4⋊Q8—22no—
71C7×C4⋊Q8C2314yes—
72C7×#125—22no—
73C7×#125C2314yes—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4C2312yes—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C42×C7C2311yescharacteristic
81#6507—28no—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84C2×C4⋊Dic7—21no—
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2312yes—
87C2×C4⋊Dic7C2311yescharacteristic
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7D411yescharacteristic
97C2×C4×Dic7D411yescharacteristic
98C2×C4×Dic7C2311yescharacteristic
99C22×C7⋊C8C2312yes—
100C2×#1131Q8116yescomplemented
101C2×#1131C2318yes—
102#6459—28no—
103#6459—28no—
104#6455—22no—
105#6455—22no—
106#6455C2314yes—
107#6455C2314yes—
108D7×C4⋊C4—24no—
109D7×C4⋊C4—28no—
110D7×C4⋊C4C2318yes—
111#6451—22no—
112#6451—22no—
113#6451—24no—
114#6451—28no—
115#6451C2314yes—
116#6451C2314yes—
117#6451C2318yes—
118#6450—28no—
119#6450—28no—
120C42×D7D414yes—
121C42×D7C2314yes—
122#6433—22no—
123#6433C2314yes—
124#6432—22no—
125#6432C2314yes—
126C7×#107C2318yes—
127C7×#106C2318yes—
128C7×#97C2314yes—
129#6392C2318yes—
130#6391C2318yes—
131C8×Dic7C2318yes—
132#6382C2318yes—
133#6382C2318yes—
134#6381C2318yes—
135#6381C2318yes—
136#6377C2314yes—
137C2×#533—71no—
138C22×C4⋊Q8—71no—
139#3165—716no—
140C2×#501—71no—
141C2×#501—71no—
142C2×#501—71no—
143C2×#501D711yescharacteristic, complemented
144C2×#500—72no—
145C2×#498—72no—
146C2×#428—72no—
147C2×#428—72no—
148C2×C4×M16—71no—
149C23×D7C2×D411yescharacteristic
150C2×C7×Q8—24no—
151C2×C7×Q8—44no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—22no—
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2411yescharacteristic
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—22no—
161C22×Dic7C2×D411yescharacteristic
162C22×Dic7C2×D411yescharacteristic
163C22×Dic7C2×D411yescharacteristic
164Q8×D7—432no—
165C2×C4×D7—24no—
166C2×C4×D7—24no—
167C2×C4×D7—28no—
168C2×C4×D7—48no—
169C2×C4×D7C2×D414yes—
170C2×C4×D7C2×D414yes—
171C2×C4×D7C2×D412yes—
172C2×C4×D7C2×Q818yes—
173C2×C4×D7C2412yes—
174C2×Dic14—24no—
175C2×Dic14—24no—
176C2×Dic14—24no—
177C2×Dic14—28no—
178C2×Dic14—44no—
179C2×Dic14—44no—
180C2×Dic14—48no—
181C2×Dic14—44no—
182C2×C7×C8C2×Q818yescomplemented
183C2×C7×C8C2414yes—
184C7×C4⋊C4—24no—
185C7×C4⋊C4—24no—
186C7×C4⋊C4—24no—
187C7×C4⋊C4—22no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—21no—
190C7×C4⋊C4C2412yes—
191C7×C4⋊C4C2414yes—
192C7×C4⋊C4C2412yes—
193C42×C7C2×D412yes—
194C42×C7C2412yes—
195(C2×D7)⋊C4—24no—
196(C2×D7)⋊C4—24no—
197C4⋊Dic7—22no—
198C4⋊Dic7—24no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7C2414yes—
202C4⋊Dic7C2412yes—
203C4⋊Dic7C2412yes—
204Dic7⋊C4—24no—
205Dic7⋊C4—24no—
206Dic7⋊C4—24no—
207Dic7⋊C4—24no—
208Dic7⋊C4—28no—
209Dic7⋊C4—28no—
210C4×Dic7—24no—
211C4×Dic7—24no—
212C4×Dic7C2×D412yes—
213C4×Dic7C2×D414yes—
214C4×Dic7C2×D414yes—
215C4×Dic7C2412yes—
216C2×C7⋊C8C2×Q818yescomplemented
217C2×C7⋊C8C2414yes—
218#1131C2×Q8132yescomplemented
219C23×Q8—141no—
220C22×M16—72no—
221#533—78no—
222#533—144no—
223C2×C4⋊Q8—78no—
224C2×C4⋊Q8—71no—
225C2×C4⋊Q8—72no—
226C2×C4⋊Q8—71no—
227C2×C4⋊Q8—71no—
228C2×C4⋊Q8—141no—
229C2×C4⋊Q8—144no—
230C2×C4⋊Q8—141no—
231C2×C4⋊Q8C2×D711yescharacteristic
232C2×#125—71no—
233C2×#125C2×D711yescharacteristic
234C2×C22⋊Q8—141no—
235C2×C22⋊Q8—141no—
236C2×C4×Q8—141no—
237C2×C4×Q8—141no—
238C2×#117—71no—
239C2×#117—71no—
240C22×C4⋊C4—72no—
241C22×C4⋊C4—141no—
242C22×C42—71no—
243#501—78no—
244#501—78no—
245#501—78no—
246#501C2×D718yescomplemented
247#500—716no—
248#498—716no—
249#428—716no—
250#428—716no—
251C2×#107—72no—
252C2×#107—72no—
253C2×#107—72no—
254C2×#107C2×D712yes—
255C2×#106—72no—
256C2×#106—72no—
257C2×#106—72no—
258C2×#106C2×D712yes—
259C4×M16—78no—
260C2×#97—71no—
261C2×#97C2×D711yescharacteristic
262C2×C4×C8—72no—
263C23×C7C22×D411yescharacteristic
264C22×D7—22no—
265C22×D7—22no—
266C22×D7C4⋊Q814yes—
267C22×D7C22×D412yes—
268C7×Q8—48no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—24no—
274C2×C4×C7—44no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7C22×D412yes—
278C2×C4×C7C22×D412yes—
279C2×C4×C7C22×D411yescharacteristic
280C2×C4×C7C22×Q814yes—
281C2×C4×C7C2511yescharacteristic
282C2×Dic7—22no—
283C2×Dic7—22no—
284C2×Dic7—24no—
285C2×Dic7—44no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7C4⋊Q814yes—
289C2×Dic7AGL(1,ℤ/8)14yes—
290C2×Dic7#13714yes—
291C2×Dic7C22×D412yes—
292C2×Dic7C22×D412yes—
293C2×Dic7C22×D412yes—
294C4×D7—28no—
295C4×D7—28no—
296C4×D7—416no—
297C4×D7C4⋊Q818yes—
298C4×D7C22×Q818yes—
299Dic14—48no—
300Dic14—48no—
301Dic14—416no—
302Dic14—48no—
303C7×C8C22×Q818yescomplemented
304C7⋊C8C22×Q818yescomplemented
305C22×Q8—21no—
306C22×Q8—141no—
307C22×Q8—141no—
308C22×Q8—142no—
309C22×Q8—148no—
310C22×Q8—141no—
311C22×Q8—288no—
312C23×C4—71no—
313C23×C4—71no—
314C23×C4—71no—
315C23×C4—142no—
316C2×M16—716no—
317C2×M16—78no—
318C22×C8—72no—
319C22×C8C22×D712yes—
320C4⋊Q8—22no—
321C4⋊Q8—78no—
322C4⋊Q8—74no—
323C4⋊Q8—74no—
324C4⋊Q8—74no—
325C4⋊Q8—148no—
326C4⋊Q8—144no—
327C4⋊Q8—142no—
328C4⋊Q8—142no—
329C4⋊Q8—148no—
330C4⋊Q8—142no—
331C4⋊Q8C22×D714yes—
332#125—22no—
333#125—74no—
334#125—142no—
335#125C22×D714yes—
336C22⋊Q8—148no—
337C22⋊Q8—148no—
338C4×Q8—148no—
339C4×Q8—148no—
340#117—74no—
341#117—74no—
342#117—142no—
343#117—142no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—72no—
348C2×C4⋊C4—71no—
349C2×C4⋊C4—71no—
350C2×C4⋊C4—78no—
351C2×C4⋊C4—144no—
352C2×C4⋊C4—148no—
353C2×C4⋊C4—142no—
354C2×C4⋊C4—142no—
355C2×C4⋊C4—141no—
356C2×C4⋊C4—141no—
357C2×C4⋊C4—141no—
358C2×C4⋊C4—141no—
359C2×C4⋊C4—141no—
360C2×C4⋊C4C22×D712yes—
361C2×C4⋊C4C22×D711yescharacteristic
362C2×C4⋊C4C22×D711yescharacteristic
363C2×C22⋊C4—141no—
364C2×C22⋊C4—141no—
365C2×C42—71no—
366C2×C42—71no—
367C2×C42—71no—
368C2×C42—74no—
369C2×C42—74no—
370C2×C42—141no—
371C2×C42—141no—
372C2×C42C22×D711yescharacteristic
373#107—78no—
374#107—78no—
375#107—78no—
376#107C22×D718yes—
377#106—78no—
378#106—78no—
379#106—78no—
380#106C22×D718yes—
381#97—74no—
382#97C22×D714yes—
383C4×C8—78no—
384C22×C7C2×C4⋊Q812yes—
385C22×C7C2×AGL(1,ℤ/8)12yes—
386C22×C7C2×#13712yes—
387C22×C7C23×D411yescharacteristic
388C2×D7—28no—
389C2×D7—22no—
390C2×D7—22no—
391C2×D7C2×C4⋊Q814yes—
392C4×C7—22no—
393C4×C7—22no—
394C4×C7—44no—
395C4×C7—42no—
396C4×C7—42no—
397C4×C7C2×C4⋊Q812yes—
398C4×C7C23×Q812yes—
399Dic7—44no—
400Dic7—42no—
401Dic7—42no—
402Dic7C2×C4⋊Q814yes—
403Dic7C2×AGL(1,ℤ/8)14yes—
404Dic7C2×#13714yes—
405C24—71no—
406C2×Q8—24no—
407C2×Q8—44no—
408C2×Q8—144no—
409C2×Q8—144no—
410C2×Q8—148no—
411C2×Q8—144no—
412C2×Q8—284no—
413C2×Q8—284no—
414C2×Q8—284no—
415C2×Q8—288no—
416C2×Q8—2832no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—71no—
421C22×C4—71no—
422C22×C4—71no—
423C22×C4—72no—
424C22×C4—78no—
425C22×C4—72no—
426C22×C4—74no—
427C22×C4—74no—
428C22×C4—144no—
429C22×C4—144no—
430C22×C4—148no—
431C22×C4—141no—
432C22×C4—141no—
433C22×C4—142no—
434C22×C4—288no—
435C22×C4D4×D711yescharacteristic
436C22×C4D4×D711yescharacteristic
437C22×C4C23×D711yescharacteristic
438M16—732no—
439C2×C8—78no—
440C2×C8—74no—
441C2×C8Q8×D718yescomplemented
442C2×C8C23×D714yes—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—72no—
450C4⋊C4—74no—
451C4⋊C4—72no—
452C4⋊C4—148no—
453C4⋊C4—148no—
454C4⋊C4—144no—
455C4⋊C4—144no—
456C4⋊C4—144no—
457C4⋊C4—144no—
458C4⋊C4—142no—
459C4⋊C4—141no—
460C4⋊C4—141no—
461C4⋊C4—144no—
462C4⋊C4C23×D712yes—
463C4⋊C4C23×D714yes—
464C4⋊C4C23×D712yes—
465C22⋊C4—144no—
466C22⋊C4—144no—
467C42—74no—
468C42—74no—
469C42—72no—
470C42—72no—
471C42—144no—
472C42—144no—
473C42D4×D712yes—
474C42C23×D712yes—
475C2×C7#316514yescomplemented
476C2×C7C22×C4⋊Q811yescharacteristic
477C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
478C2×C7C22×#13711yescharacteristic
479D7—24no—
480C23—74no—
481C23—72no—
482C23—142no—
483C23—142no—
484C23C2×D4×D711yescharacteristic
485Q8—48no—
486Q8—288no—
487Q8—288no—
488Q8—288no—
489Q8—2816no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—74no—
499C2×C4—74no—
500C2×C4—74no—
501C2×C4—72no—
502C2×C4—72no—
503C2×C4—72no—
504C2×C4—78no—
505C2×C4—78no—
506C2×C4—148no—
507C2×C4—148no—
508C2×C4—142no—
509C2×C4—142no—
510C2×C4—144no—
511C2×C4—2816no—
512C2×C4—284no—
513C2×C4—282no—
514C2×C4—282no—
515C2×C4C2×D4×D712yes—
516C2×C4C2×D4×D712yes—
517C2×C4C2×D4×D711yescharacteristic
518C2×C4C2×Q8×D714yes—
519C2×C4C24×D711yescharacteristic
520C8—78no—
521C8C2×Q8×D718yescomplemented
522C7C2×#316511yescharacteristic, complemented, Sylow
523C22—74no—
524C22—142no—
525C22—142no—
526C22—148no—
527C22D7×C4⋊Q812yes—
528C22D7×AGL(1,ℤ/8)12yes—
529C22D7×#13712yes—
530C22C22×D4×D711yescharacteristic
531C4—22no—
532C4—22no—
533C4—44no—
534C4—42no—
535C4—42no—
536C4—74no—
537C4—74no—
538C4—74no—
539C4—284no—
540C4—282no—
541C4—282no—
542C4D7×C4⋊Q812yes—
543C4C22×Q8×D712yes—
544C2—144no—
545C2#1173942114yesdirect product factor
546C2C2×D7×C4⋊Q811yescharacteristic
547C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
548C2C2×D7×#13711yescharacteristic
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×#3165
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. #11739421C2direct (N × H)
8. C2×#89646C2semidirect
10. C2×#89627C2semidirect
12. C2×#89474C2semidirect
37. C7×#501C22semidirect
44. #89852C22semidirect
45. #89837C22semidirect
52. #89646C22semidirect
54. #89627C22semidirect
56. #89474C22semidirect
100. C2×#1131Q8semidirect
143. C2×#501D7semidirect
182. C2×C7×C8C2×Q8semidirect
216. C2×C7⋊C8C2×Q8semidirect
218. #1131C2×Q8semidirect
246. #501C2×D7semidirect
303. C7×C8C22×Q8semidirect
304. C7⋊C8C22×Q8semidirect
441. C2×C8Q8×D7semidirect
475. C2×C7#3165semidirect
521. C8C2×Q8×D7semidirect
522. C7C2×#3165semidirect
545. C2#11739421direct (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×#903792
C2×C7×#5012
C2×#898522
C2×#898372
#117394212
C2×#896532
C2×#896462
C2×#896332
C2×#896272
C2×#894792
C2×#894742
C2×#31657