Finite Group Databasebeta

← C2×#11738570 #14232256

Subgroups — C2×#11738570 #14232256

Order 1792.

1942 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90421C211yesmaximal, characteristic
2C2×#90270C211yesmaximal, characteristic
3C2×C7×#477C211yesmaximal, characteristic, complemented
4C2×#89850C211yesmaximal, characteristic, complemented
5C2×C4×#1144C211yesmaximal, characteristic, complemented
6#11738570C2116yesmaximal, direct product factor
7C2×#89656C212yesmaximal, complemented
8C2×D7×#107C212yesmaximal, complemented
9C2×#89622C211yesmaximal, characteristic, complemented
10C2×#89606C211yesmaximal, characteristic
11C2×#89581C212yesmaximal, complemented
12C2×#89585C212yesmaximal, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×#6509—22no—
16C2×#6509C2212yes—
17C22×#1144C2211yescharacteristic
18C22×C8×D7C2212yes—
19#90421—24no—
20#90421C2218yes—
21#90270—24no—
22#90270C2218yes—
23C2×#6460C2212yes—
24C2×#6459—22no—
25C2×#6456—21no—
26C2×D7×C4⋊C4C2212yes—
27C2×D7×C4⋊C4C2212yes—
28C2×#6453—21no—
29C2×C4×D28—21no—
30C2×C4×D28C2211yescharacteristic
31C2×#6433—21no—
32C2×#6432C2211yescharacteristic
33C2×C4×Dic14C2211yescharacteristic
34C7×#477C2218yescomplemented
35C2×C7×#107C2212yes—
36C2×C7×C4⋊C8C2211yescharacteristic
37C2×C7×#103C2212yes—
38C2×#6409C2211yescharacteristic
39C2×(C2×D7)⋊C8C2212yes—
40C2×#6392C2212yes—
41C2×#6390C2212yes—
42#89850C2218yescomplemented
43C4×#1144C2218yescomplemented
44C2×#6384C2211yescharacteristic
45C2×#6381C2211yescharacteristic
46C2×#6381C2212yes—
47C2×#6381C2212yes—
48C2×C4×C7⋊C8C2211yescharacteristic
49#89656C22116yescomplemented
50D7×#107C22116yescomplemented
51#89622C2218yescomplemented
52#89606C2218yes—
53#89585C22116yescomplemented
54#89581C22116yescomplemented
55C2×#3338—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8C2311yescharacteristic
58C22×D28D411yescharacteristic
59C22×C4×D7—22no—
60C22×C4×D7—22no—
61C22×C4×D7C2312yes—
62C22×Dic14—21no—
63C22×Dic14C2311yescharacteristic
64C22×C7×C8C2312yes—
65C7×C4⋊Q8—22no—
66C7×C4⋊Q8C2314yes—
67C4×C7×Q8—22no—
68C4×C7×Q8C2314yes—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2312yes—
73C2×C42×C7—21no—
74C2×C42×C7C2311yescharacteristic
75#6509—24no—
76#6509—216no—
77#6509C2318yes—
78C2×#1144—24no—
79C2×#1144C2314yes—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4D412yes—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7D411yescharacteristic
86C2×C4⋊Dic7C2312yes—
87C2×C4⋊Dic7C2311yescharacteristic
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4—22no—
92C2×C4×Dic7—21no—
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C2×C8×D7—28no—
96C2×C8×D7C2318yes—
97#6460—24no—
98#6460C2318yes—
99#6459—216no—
100#6456—28no—
101D7×C4⋊C4—24no—
102D7×C4⋊C4—24no—
103D7×C4⋊C4C2318yes—
104D7×C4⋊C4C2318yes—
105#6453—28no—
106C4×D28—28no—
107C4×D28D414yes—
108C4×D28C2314yes—
109#6433—28no—
110#6432—22no—
111#6432C2314yes—
112C4×Dic14—22no—
113C4×Dic14C2314yes—
114C7×#107C2318yes—
115C7×C4⋊C8C2314yes—
116C7×#103C2318yes—
117#6409C2314yes—
118(C2×D7)⋊C8C2318yes—
119#6392C2318yes—
120#6390C2318yes—
121#6384C2314yes—
122#6381C2314yes—
123#6381C2318yes—
124#6381C2318yes—
125C4×C7⋊C8C2314yes—
126C2×#554—71no—
127C2×#554—71no—
128#3338—716no—
129C2×#500—71no—
130C2×#484—72no—
131C2×#484—72no—
132C2×#477—71no—
133C2×#477D711yescharacteristic, complemented
134C2×#467—72no—
135C2×C4×Q16—71no—
136C2×C8×D4—71no—
137C22×#107—72no—
138C23×D7C2×D412yes—
139C2×C7×Q8—21no—
140C2×C7×Q8—24no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—82no—
144C2×C7×Q8C2412yes—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2411yescharacteristic
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7C2×D412yes—
155C2×D28Q1618yescomplemented
156C2×D28C2×D414yes—
157C2×C4×D7—24no—
158C2×C4×D7—24no—
159C2×C4×D7—28no—
160C2×C4×D7—28no—
161C2×C4×D7—84no—
162C2×C4×D7—84no—
163C2×C4×D7C2×D414yes—
164C2×C4×D7C2414yes—
165C2×Dic14—22no—
166C2×Dic14—22no—
167C2×Dic14—21no—
168C2×Dic14—24no—
169C2×Dic14—82no—
170C2×Dic14C2412yes—
171C2×C7×C8—24no—
172C2×C7×C8C2414yes—
173C7×C4⋊C4—24no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—22no—
176C7×C4⋊C4—24no—
177C7×C4⋊C4C2414yes—
178C7×C4⋊C4C2412yes—
179C42×C7—24no—
180C42×C7C2×D412yes—
181C42×C7C2412yes—
182#1144—28no—
183(C2×D7)⋊C4—28no—
184(C2×D7)⋊C4—28no—
185(C2×D7)⋊C4C2×D418yes—
186C4⋊Dic7—21no—
187C4⋊Dic7—22no—
188C4⋊Dic7—24no—
189C4⋊Dic7—28no—
190C4⋊Dic7C2×D414yes—
191C4⋊Dic7C2412yes—
192C4⋊Dic7C2414yes—
193Dic7⋊C4—24no—
194Dic7⋊C4—28no—
195Dic7⋊C4—28no—
196Dic7⋊C4—28no—
197C4×Dic7—24no—
198C2×C7⋊C8—22no—
199C2×C7⋊C8#4114yes—
200C2×C7⋊C8C2412yes—
201C2×C7⋊C8C2412yes—
202C8×D7—216no—
203C22×Q16—71no—
204C23×C8—72no—
205#554—78no—
206#554—78no—
207#554—144no—
208#554—144no—
209C2×C4⋊Q8—71no—
210C2×C4⋊Q8C2×D711yescharacteristic
211C2×#125—141no—
212C2×#125—141no—
213C2×C22⋊Q8—72no—
214C2×C22⋊Q8—72no—
215C2×C22⋊Q8—142no—
216C2×C22⋊Q8—142no—
217C2×C4×Q8—71no—
218C2×C4×Q8C2×D711yescharacteristic
219C2×C4×D4—71no—
220C2×C4×D4—141no—
221C2×C4×D4—141no—
222C22×C4⋊C4—72no—
223C22×C4⋊C4—72no—
224#500—78no—
225#484—716no—
226#484—716no—
227#477—78no—
228#477C2×D718yescomplemented
229#467—716no—
230C4×Q16—78no—
231C8×D4—78no—
232C2×#107—72no—
233C2×#107—72no—
234C2×#107—72no—
235C2×#107—71no—
236C2×#107—716no—
237C2×#107C2×D712yes—
238C2×C4⋊C8C2×D711yescharacteristic
239C2×#103—71no—
240C2×#103—72no—
241C2×#103—71no—
242C2×#103C2×D712yes—
243C2×C22⋊C8—72no—
244C2×C4×C8—71no—
245C23×C7C22×D411yescharacteristic
246C22×D7—24no—
247C22×D7—24no—
248C22×D7C2×Q1618yes—
249C22×D7C22×D414yes—
250C7×Q8—22no—
251C7×Q8—22no—
252C7×Q8—42no—
253C7×Q8—84no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—24no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—44no—
261C2×C4×C7C2×Q1614yes—
262C2×C4×C7C22×D412yes—
263C2×C4×C7C22×D411yescharacteristic
264C2×C4×C7C22×D412yes—
265C2×C4×C7C2×#4112yes—
266C2×C4×C72−1+412yes—
267C2×C4×C7C2511yescharacteristic
268C2×Dic7—24no—
269C2×Dic7—22no—
270C2×Dic7—22no—
271C2×Dic7—24no—
272C2×Dic7—42no—
273C2×Dic7—44no—
274C2×Dic7—42no—
275C2×Dic7C22×D414yes—
276D28C2×Q16116yescomplemented
277C4×D7—28no—
278C4×D7—24no—
279C4×D7—24no—
280C4×D7—88no—
281C4×D7—88no—
282Dic14—22no—
283Dic14—22no—
284Dic14—42no—
285Dic14—84no—
286C7×C8—24no—
287C7⋊C8—22no—
288C7⋊C8C2×#4114yes—
289C22×Q8—21no—
290C22×Q8—71no—
291C22×Q8—141no—
292C22×Q8C22×D711yescharacteristic
293C22×D4—71no—
294C23×C4—72no—
295C23×C4—142no—
296C23×C4—142no—
297C2×Q16—74no—
298C2×Q16—144no—
299C22×C8—71no—
300C22×C8—71no—
301C22×C8—78no—
302C22×C8—148no—
303C22×C8C22×D712yes—
304C4⋊Q8—22no—
305C4⋊Q8—74no—
306C4⋊Q8—142no—
307C4⋊Q8C22×D714yes—
308#125—148no—
309#125—148no—
310C22⋊Q8—78no—
311C22⋊Q8—78no—
312C22⋊Q8—1416no—
313C22⋊Q8—1416no—
314C22⋊Q8—144no—
315C22⋊Q8—144no—
316C4×Q8—22no—
317C4×Q8—74no—
318C4×Q8—142no—
319C4×Q8C22×D714yes—
320C4×D4—74no—
321C4×D4—74no—
322C4×D4—148no—
323C4×D4—148no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—71no—
327C2×C4⋊C4—71no—
328C2×C4⋊C4—72no—
329C2×C4⋊C4—78no—
330C2×C4⋊C4—78no—
331C2×C4⋊C4—144no—
332C2×C4⋊C4—144no—
333C2×C4⋊C4—142no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4—142no—
336C2×C4⋊C4—142no—
337C2×C4⋊C4—141no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4C22×D711yescharacteristic
340C2×C4⋊C4C22×D712yes—
341C2×C22⋊C4—72no—
342C2×C22⋊C4—142no—
343C2×C22⋊C4—142no—
344C2×C42—21no—
345C2×C42—141no—
346C2×C42C22×D711yescharacteristic
347#107—78no—
348#107—74no—
349#107—78no—
350#107—78no—
351#107C22×D718yes—
352C4⋊C8C22×D714yes—
353#103—74no—
354#103—78no—
355#103—74no—
356#103C22×D718yes—
357C22⋊C8—78no—
358C4×C8—74no—
359C22×C7#54712yes—
360C22×C7C22×Q1612yes—
361C22×C7#57612yes—
362C22×C7C23×D411yescharacteristic
363C2×D7—216no—
364C2×D7—24no—
365C2×D7—24no—
366C2×D7C22×Q1618yes—
367C4×C7—22no—
368C4×C7—42no—
369C4×C7—42no—
370C4×C7—44no—
371C4×C7#54712yes—
372C4×C7C22×Q1614yes—
373C4×C7C22×#4111yescharacteristic
374C4×C7C2×2−1+411yescharacteristic
375Dic7—24no—
376Dic7—42no—
377Dic7—44no—
378Dic7—42no—
379C24—72no—
380C2×Q8—21no—
381C2×Q8—24no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—72no—
385C2×Q8—82no—
386C2×Q8—141no—
387C2×Q8—144no—
388C2×Q8—142no—
389C2×Q8—142no—
390C2×Q8—562no—
391C2×Q8C23×D712yes—
392C2×D4—78no—
393C2×D4—74no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—72no—
398C22×C4—74no—
399C22×C4—74no—
400C22×C4—148no—
401C22×C4—148no—
402C22×C4—144no—
403C22×C4—144no—
404C22×C4—141no—
405C22×C4—141no—
406C22×C4—142no—
407C22×C4—564no—
408C22×C4—564no—
409C22×C4D4×D711yescharacteristic
410C22×C4D4×D711yescharacteristic
411C22×C4C23×D711yescharacteristic
412Q16—148no—
413C2×C8—24no—
414C2×C8—74no—
415C2×C8—72no—
416C2×C8—72no—
417C2×C8—1416no—
418C2×C8—142no—
419C2×C8C23×D714yes—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—74no—
425C4⋊C4—72no—
426C4⋊C4—74no—
427C4⋊C4—148no—
428C4⋊C4—148no—
429C4⋊C4—148no—
430C4⋊C4—148no—
431C4⋊C4—144no—
432C4⋊C4—141no—
433C4⋊C4—142no—
434C4⋊C4—144no—
435C4⋊C4C23×D712yes—
436C4⋊C4C23×D714yes—
437C22⋊C4—78no—
438C22⋊C4—148no—
439C22⋊C4—148no—
440C42—24no—
441C42—144no—
442C42D4×D712yes—
443C42C23×D712yes—
444C2×C7#333814yescomplemented
445C2×C7C2×#54711yescharacteristic
446C2×C7C23×Q1611yescharacteristic
447C2×C7C2×#57611yescharacteristic
448D7—28no—
449C23—78no—
450C23—74no—
451C23—144no—
452C23—144no—
453C23C2×D4×D711yescharacteristic
454Q8—22no—
455Q8—22no—
456Q8—42no—
457Q8—84no—
458Q8—142no—
459Q8—142no—
460Q8—282no—
461Q8—564no—
462D4—716no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—42no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—74no—
471C2×C4—144no—
472C2×C4—148no—
473C2×C4—144no—
474C2×C4—144no—
475C2×C4—142no—
476C2×C4—142no—
477C2×C4—144no—
478C2×C4—282no—
479C2×C4—284no—
480C2×C4—282no—
481C2×C4—568no—
482C2×C4—568no—
483C2×C4D7×Q1614yes—
484C2×C4C2×D4×D712yes—
485C2×C4C2×D4×D712yes—
486C2×C4C2×D4×D711yescharacteristic
487C2×C4#655112yes—
488C2×C4D7×#4112yes—
489C2×C4C24×D711yescharacteristic
490C8—24no—
491C8—74no—
492C8—142no—
493C7C2×#333811yescharacteristic, complemented, Sylow
494C22—78no—
495C22—144no—
496C22—144no—
497C22—1416no—
498C22#9032212yes—
499C22C2×D7×Q1612yes—
500C22#9046512yes—
501C22C22×D4×D711yescharacteristic
502C4—22no—
503C4—42no—
504C4—44no—
505C4—42no—
506C4—144no—
507C4—282no—
508C4—284no—
509C4—282no—
510C4#9032212yes—
511C4C2×D7×Q1614yes—
512C4C2×#655111yescharacteristic
513C4C2×D7×#4111yescharacteristic
514C2—148no—
515C2#1173857014yesdirect product factor
516C2C2×#9032211yescharacteristic
517C2C22×D7×Q1611yescharacteristic
518C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#477C2
socleC23×C7C22×D4
prime radicalC22×D28D4
hypercenterC2×#477D7
hypocenterC7C2×#3338
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. C2×C7×#477C2semidirect
4. C2×#89850C2semidirect
5. C2×C4×#1144C2semidirect
6. #11738570C2direct (N × H)
7. C2×#89656C2semidirect
8. C2×D7×#107C2semidirect
9. C2×#89622C2semidirect
11. C2×#89581C2semidirect
12. C2×#89585C2semidirect
34. C7×#477C22semidirect
42. #89850C22semidirect
43. C4×#1144C22semidirect
49. #89656C22semidirect
50. D7×#107C22semidirect
51. #89622C22semidirect
53. #89585C22semidirect
54. #89581C22semidirect
133. C2×#477D7semidirect
155. C2×D28Q16semidirect
228. #477C2×D7semidirect
276. D28C2×Q16semidirect
444. C2×C7#3338semidirect
493. C7C2×#3338semidirect
515. C2#11738570direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904212
C2×#902702
C2×C7×#4772
C2×#898502
C2×C4×#11442
#117385702
C2×#896562
C2×D7×#1072
C2×#896222
C2×#896062
C2×#895812
C2×#895852
C2×#33387