Finite Group Databasebeta

← C2×#11739384 #14223423

Subgroups — C2×#11739384 #14223423

Order 1792.

1854 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90420C212yesmaximal
2C2×C7×#500C211yesmaximal, characteristic, complemented
3C2×#89852C212yesmaximal, complemented
4#11739384C2116yesmaximal, direct product factor
5C2×#89653C212yesmaximal
6C2×#89652C211yesmaximal, characteristic
7C2×D7×#107C211yesmaximal, characteristic
8C2×#89650C211yesmaximal, characteristic, complemented
9C2×#89648C212yesmaximal, complemented
10C2×#89646C211yesmaximal, characteristic, complemented
11C2×#89461C211yesmaximal, characteristic
12C2×#89455C211yesmaximal, characteristic, complemented
13C2×C7×C4⋊Q8C2212yes—
14C2×#6509—22no—
15C2×#6507—22no—
16C22×#1131C2211yescharacteristic
17C22×C8×D7C2211yescharacteristic
18#90420—28no—
19#90420C22116yes—
20C2×#6459—22no—
21C2×#6455C2212yes—
22C2×D7×C4⋊C4C2212yes—
23C2×#6453C2212yes—
24C2×#6452—22no—
25C2×#6451C2212yes—
26C2×#6435C2211yescharacteristic
27C2×#6433C2212yes—
28C7×#500C2218yescomplemented
29C2×C7×#107C2211yescharacteristic
30C2×C7×#107C2212yes—
31C2×C7×#107C2211yescharacteristic
32C2×C4×C7×C8C2211yescharacteristic
33C2×#6392C2211yescharacteristic
34C2×#6392C2211yescharacteristic
35C2×#6391C2212yes—
36C2×#6389C2211yescharacteristic
37C2×C8×Dic7C2211yescharacteristic
38#89852C22116yescomplemented
39C2×#6382C2212yes—
40C2×#6382C2212yes—
41C2×#6381C2212yes—
42C2×#6381C2212yes—
43C2×#6377C2211yescharacteristic
44#89653C22116yes—
45#89652C2218yes—
46D7×#107C2218yes—
47#89650C2218yescomplemented
48#89648C22116yescomplemented
49#89646C2218yescomplemented
50#89461C2218yes—
51#89455C2218yescomplemented
52C2×#3164—71nomaximal, Sylow
53C22×C7×Q8—22no—
54C22×C4×D7—22no—
55C22×C4×D7C2311yescharacteristic
56C22×Dic14—22no—
57C22×C7×C8C2311yescharacteristic
58C22×C7×C8C2311yescharacteristic
59C7×C4⋊Q8—24no—
60C7×C4⋊Q8C2318yes—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4C2312yes—
63C2×C7×C4⋊C4C2312yes—
64C2×C42×C7C2311yescharacteristic
65#6509—216no—
66#6507—216no—
67C2×(C2×D7)⋊C4—22no—
68C2×(C2×D7)⋊C4D411yescharacteristic
69C2×(C2×D7)⋊C4D411yescharacteristic
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7C2312yes—
72C2×C4⋊Dic7C2312yes—
73C2×Dic7⋊C4—22no—
74C2×Dic7⋊C4—22no—
75C2×Dic7⋊C4—22no—
76C2×Dic7⋊C4—22no—
77C2×Dic7⋊C4—22no—
78C2×Dic7⋊C4D411yescharacteristic
79C2×Dic7⋊C4D411yescharacteristic
80C2×C4×Dic7—22no—
81C2×C4×Dic7C2311yescharacteristic
82C22×C7⋊C8C2311yescharacteristic
83C22×C7⋊C8C2311yescharacteristic
84C2×#1131Q818yescomplemented
85C2×#1131C2314yes—
86C2×C8×D7Q818yescomplemented
87C2×C8×D7C2314yes—
88#6459—216no—
89#6455—24no—
90#6455C2318yes—
91D7×C4⋊C4—24no—
92D7×C4⋊C4C2318yes—
93#6453—24no—
94#6453C2318yes—
95#6452—216no—
96#6451—24no—
97#6451C2318yes—
98#6435D414yes—
99#6435C2314yes—
100#6433—24no—
101#6433C2318yes—
102C7×#107C2314yes—
103C7×#107C2318yes—
104C7×#107C2314yes—
105C4×C7×C8C2314yes—
106#6392C2314yes—
107#6392C2314yes—
108#6391C2318yes—
109#6389C2314yes—
110C8×Dic7C2314yes—
111#6382C2318yes—
112#6382C2318yes—
113#6381C2318yes—
114#6381C2318yes—
115#6377C2314yes—
116C2×#544—72no—
117#3164—716no—
118C2×#501—72no—
119C2×#501—72no—
120C2×#500—71no—
121C2×#500D711yescharacteristic, complemented
122C2×#499—71no—
123C2×#499—71no—
124C2×#428—72no—
125C2×#427—71no—
126C22×#107—71no—
127C2×#405—71no—
128C23×D7C2×D411yescharacteristic
129C2×C7×Q8—28no—
130C2×C7×Q8—84no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7C2×D411yescharacteristic
134C22×C4×C7C2×D411yescharacteristic
135C22×C4×C7C2411yescharacteristic
136C22×Dic7—22no—
137C22×Dic7—22no—
138C22×Dic7C2×D411yescharacteristic
139C22×Dic7C2×D411yescharacteristic
140C22×Dic7C2×D411yescharacteristic
141C2×C4×D7—28no—
142C2×C4×D7—84no—
143C2×C4×D7C2×D412yes—
144C2×C4×D7C2×Q814yes—
145C2×C4×D7C2×Q814yes—
146C2×C4×D7C2412yes—
147C2×Dic14—28no—
148C2×Dic14—84no—
149C2×C7×C8C2×Q814yes—
150C2×C7×C8C2×Q814yes—
151C2×C7×C8C2412yes—
152C2×C7×C8C2412yes—
153C7×C4⋊C4—22no—
154C7×C4⋊C4—28no—
155C7×C4⋊C4—22no—
156C7×C4⋊C4C2414yes—
157C7×C4⋊C4C2414yes—
158C42×C7C2×D412yes—
159C42×C7C2412yes—
160(C2×D7)⋊C4—28no—
161(C2×D7)⋊C4C2×D414yes—
162(C2×D7)⋊C4C2×D414yes—
163C4⋊Dic7—22no—
164C4⋊Dic7—22no—
165C4⋊Dic7—28no—
166C4⋊Dic7C2414yes—
167C4⋊Dic7C2414yes—
168Dic7⋊C4—28no—
169Dic7⋊C4—28no—
170Dic7⋊C4—28no—
171Dic7⋊C4—28no—
172Dic7⋊C4—28no—
173Dic7⋊C4C2×D414yes—
174Dic7⋊C4C2×D414yes—
175C4×Dic7—28no—
176C4×Dic7C2×D412yes—
177C4×Dic7C2412yes—
178C2×C7⋊C8C2×Q814yes—
179C2×C7⋊C8C2×Q814yes—
180C2×C7⋊C8C2412yes—
181C2×C7⋊C8C2412yes—
182#1131C2×Q8116yescomplemented
183C8×D7C2×Q8116yescomplemented
184C22×M16—71no—
185C23×C8—71no—
186#544—716no—
187#544—148no—
188C2×C4⋊Q8—72no—
189C2×C4⋊Q8—142no—
190C2×C4⋊Q8C2×D712yes—
191C2×#125—72no—
192C2×#125—72no—
193C2×#125—142no—
194C2×C22⋊Q8—142no—
195C2×C22⋊Q8—142no—
196C2×#117—71no—
197C2×#117—72no—
198C22×C4⋊C4—72no—
199#501—716no—
200#501—716no—
201#500—78no—
202#500C2×D718yescomplemented
203#499—78no—
204#499—78no—
205#428—716no—
206#427—78no—
207C2×#107—71no—
208C2×#107—71no—
209C2×#107—72no—
210C2×#107—72no—
211C2×#107—78no—
212C2×#107C2×D711yescharacteristic
213C2×#107C2×D711yescharacteristic
214C2×#107C2×D712yes—
215C2×#106—72no—
216C2×#106—72no—
217C2×#106—72no—
218#405—78no—
219C2×#97—71no—
220C2×#97—71no—
221C2×C4×C8—71no—
222C2×C4×C8C2×D711yescharacteristic
223C23×C7C22×D411yescharacteristic
224C22×D7—22no—
225C22×D7—22no—
226C22×D7C4⋊Q814yes—
227C22×D7C22×D412yes—
228C7×Q8—88no—
229C2×C4×C7—22no—
230C2×C4×C7—22no—
231C2×C4×C7—24no—
232C2×C4×C7—24no—
233C2×C4×C7—44no—
234C2×C4×C7—44no—
235C2×C4×C7C22×D412yes—
236C2×C4×C7C22×D412yes—
237C2×C4×C7C22×D411yescharacteristic
238C2×C4×C7C22×Q812yes—
239C2×C4×C7C22×Q812yes—
240C2×C4×C7C2511yescharacteristic
241C2×Dic7—22no—
242C2×Dic7—22no—
243C2×Dic7—24no—
244C2×Dic7—24no—
245C2×Dic7—44no—
246C2×Dic7—44no—
247C2×Dic7C4⋊Q814yes—
248C2×Dic7C22×D412yes—
249C2×Dic7C22×D412yes—
250C2×Dic7C22×D412yes—
251C4×D7—88no—
252C4×D7C4⋊Q818yes—
253C4×D7C22×Q814yes—
254C4×D7C22×Q814yes—
255Dic14—88no—
256C7×C8C22×Q814yes—
257C7×C8C22×Q814yes—
258C7⋊C8C22×Q814yes—
259C7⋊C8C22×Q814yes—
260C22×Q8—22no—
261C22×Q8—142no—
262C23×C4—71no—
263C23×C4—142no—
264C2×M16—78no—
265C2×M16—74no—
266C22×C8—71no—
267C22×C8—71no—
268C22×C8—78no—
269C22×C8—74no—
270C22×C8C22×D711yescharacteristic
271C22×C8C22×D711yescharacteristic
272C4⋊Q8—24no—
273C4⋊Q8—78no—
274C4⋊Q8—144no—
275C4⋊Q8—1416no—
276C4⋊Q8C22×D718yes—
277#125—78no—
278#125—78no—
279#125—144no—
280#125—1416no—
281#125—144no—
282C22⋊Q8—1416no—
283C22⋊Q8—1416no—
284#117—74no—
285#117—74no—
286#117—78no—
287#117—144no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—71no—
290C2×C4⋊C4—71no—
291C2×C4⋊C4—72no—
292C2×C4⋊C4—72no—
293C2×C4⋊C4—78no—
294C2×C4⋊C4—144no—
295C2×C4⋊C4—142no—
296C2×C4⋊C4—142no—
297C2×C4⋊C4—142no—
298C2×C4⋊C4—142no—
299C2×C4⋊C4—142no—
300C2×C4⋊C4—142no—
301C2×C4⋊C4C22×D712yes—
302C2×C4⋊C4C22×D712yes—
303C2×C22⋊C4—71no—
304C2×C22⋊C4—71no—
305C2×C22⋊C4—142no—
306C2×C42—71no—
307C2×C42—142no—
308C2×C42C22×D711yescharacteristic
309#107—74no—
310#107—74no—
311#107—78no—
312#107—78no—
313#107C22×D714yes—
314#107C22×D714yes—
315#107C22×D718yes—
316#106—78no—
317#106—78no—
318#106—78no—
319#97—74no—
320#97—74no—
321C4×C8—74no—
322C4×C8C22×D714yes—
323C22×C7C2×C4⋊Q812yes—
324C22×C7#57612yes—
325C22×C7#57812yes—
326C22×C7C23×D411yescharacteristic
327C2×D7—28no—
328C2×D7—22no—
329C2×D7—22no—
330C2×D7C2×C4⋊Q814yes—
331C4×C7—22no—
332C4×C7—22no—
333C4×C7—44no—
334C4×C7—44no—
335C4×C7C2×C4⋊Q812yes—
336C4×C7C23×Q811yescharacteristic
337C4×C7C23×Q811yescharacteristic
338Dic7—22no—
339Dic7—22no—
340Dic7—44no—
341Dic7—44no—
342Dic7C2×C4⋊Q814yes—
343C24—71no—
344C2×Q8—28no—
345C2×Q8—84no—
346C2×Q8—148no—
347C2×Q8—564no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—71no—
351C22×C4—72no—
352C22×C4—74no—
353C22×C4—74no—
354C22×C4—72no—
355C22×C4—71no—
356C22×C4—71no—
357C22×C4—148no—
358C22×C4—142no—
359C22×C4—142no—
360C22×C4—564no—
361C22×C4D4×D711yescharacteristic
362C22×C4D4×D711yescharacteristic
363C22×C4C23×D711yescharacteristic
364M16—716no—
365C2×C8—74no—
366C2×C8—74no—
367C2×C8—72no—
368C2×C8—72no—
369C2×C8—716no—
370C2×C8Q8×D714yes—
371C2×C8Q8×D714yes—
372C2×C8C23×D712yes—
373C2×C8C23×D712yes—
374C4⋊C4—28no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—74no—
378C4⋊C4—74no—
379C4⋊C4—74no—
380C4⋊C4—74no—
381C4⋊C4—148no—
382C4⋊C4—148no—
383C4⋊C4—148no—
384C4⋊C4—148no—
385C4⋊C4—148no—
386C4⋊C4—148no—
387C4⋊C4—142no—
388C4⋊C4—142no—
389C4⋊C4C23×D714yes—
390C4⋊C4C23×D714yes—
391C22⋊C4—74no—
392C22⋊C4—74no—
393C22⋊C4—148no—
394C42—72no—
395C42—72no—
396C42—148no—
397C42D4×D712yes—
398C42C23×D712yes—
399C2×C7#316414yescomplemented
400C2×C7C22×C4⋊Q811yescharacteristic
401C2×C7C2×#57611yescharacteristic
402C2×C7C2×#57811yescharacteristic
403D7—24no—
404C23—74no—
405C23—72no—
406C23—142no—
407C23—142no—
408C23C2×D4×D711yescharacteristic
409Q8—88no—
410Q8—568no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—74no—
418C2×C4—72no—
419C2×C4—78no—
420C2×C4—74no—
421C2×C4—74no—
422C2×C4—72no—
423C2×C4—72no—
424C2×C4—142no—
425C2×C4—142no—
426C2×C4—144no—
427C2×C4—144no—
428C2×C4—284no—
429C2×C4—284no—
430C2×C4—568no—
431C2×C4C2×D4×D712yes—
432C2×C4C2×D4×D712yes—
433C2×C4C2×D4×D711yescharacteristic
434C2×C4C2×Q8×D712yes—
435C2×C4C2×Q8×D712yes—
436C2×C4C24×D711yescharacteristic
437C8—74no—
438C8—74no—
439C8C2×Q8×D714yes—
440C8C2×Q8×D714yes—
441C7C2×#316411yescharacteristic, complemented, Sylow
442C22—74no—
443C22—142no—
444C22—148no—
445C22—142no—
446C22D7×C4⋊Q812yes—
447C22#9044812yes—
448C22#9045712yes—
449C22C22×D4×D711yescharacteristic
450C4—22no—
451C4—22no—
452C4—44no—
453C4—44no—
454C4—74no—
455C4—142no—
456C4—142no—
457C4—284no—
458C4—284no—
459C4D7×C4⋊Q812yes—
460C4C22×Q8×D711yescharacteristic
461C4C22×Q8×D711yescharacteristic
462C2—144no—
463C2#1173938414yesdirect product factor
464C2C2×D7×C4⋊Q811yescharacteristic
465C2C2×#9044811yescharacteristic
466C2C2×#9045711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#500C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#500D7
hypocenterC7C2×#3164
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. C2×C7×#500C2semidirect
3. C2×#89852C2semidirect
4. #11739384C2direct (N × H)
8. C2×#89650C2semidirect
9. C2×#89648C2semidirect
10. C2×#89646C2semidirect
12. C2×#89455C2semidirect
28. C7×#500C22semidirect
38. #89852C22semidirect
47. #89650C22semidirect
48. #89648C22semidirect
49. #89646C22semidirect
51. #89455C22semidirect
84. C2×#1131Q8semidirect
86. C2×C8×D7Q8semidirect
121. C2×#500D7semidirect
182. #1131C2×Q8semidirect
183. C8×D7C2×Q8semidirect
202. #500C2×D7semidirect
399. C2×C7#3164semidirect
441. C7C2×#3164semidirect
463. C2#11739384direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904202
C2×C7×#5002
C2×#898522
#117393842
C2×#896532
C2×#896522
C2×D7×#1072
C2×#896502
C2×#896482
C2×#896462
C2×#894612
C2×#894552
C2×#31647