Finite Group Databasebeta

← C2×#11739363 #14223427

Subgroups — C2×#11739363 #14223427

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×#90380C212yesmaximal
2C2×C7×#499C211yesmaximal, characteristic, complemented
3C2×#89837C212yesmaximal, complemented
4#11739363C2116yesmaximal, direct product factor
5C2×#89652C211yesmaximal, characteristic
6C2×D7×#107C211yesmaximal, characteristic
7C2×#89650C211yesmaximal, characteristic, complemented
8C2×#89646C211yesmaximal, characteristic, complemented
9C2×#89633C212yesmaximal
10C2×#89628C212yesmaximal, complemented
11C2×#89461C211yesmaximal, characteristic
12C2×#89454C211yesmaximal, characteristic, complemented
13C2×C7×#125C2212yes—
14C22×#1131C2211yescharacteristic
15C22×C8×D7C2211yescharacteristic
16#90380—28no—
17#90380C22116yes—
18C2×#6460—22no—
19C2×#6459—22no—
20C2×#6455C2212yes—
21C2×D7×C4⋊C4C2212yes—
22C2×#6453C2212yes—
23C2×#6452—22no—
24C2×#6451—22no—
25C2×#6451C2212yes—
26C2×#6435C2211yescharacteristic
27C2×#6432C2212yes—
28C7×#499C2218yescomplemented
29C2×C7×#107C2211yescharacteristic
30C2×C7×#107C2211yescharacteristic
31C2×C7×#106C2212yes—
32C2×C4×C7×C8C2211yescharacteristic
33C2×#6392C2211yescharacteristic
34C2×#6392C2211yescharacteristic
35C2×#6392C2212yes—
36C2×#6389C2211yescharacteristic
37C2×C8×Dic7C2211yescharacteristic
38#89837C22116yescomplemented
39C2×#6382C2212yes—
40C2×#6382C2212yes—
41C2×#6381C2212yes—
42C2×#6381C2212yes—
43C2×#6377C2211yescharacteristic
44#89652C2218yes—
45D7×#107C2218yes—
46#89650C2218yescomplemented
47#89646C2218yescomplemented
48#89633C22116yes—
49#89628C22116yescomplemented
50#89461C2218yes—
51#89454C2218yescomplemented
52C2×#3164—71nomaximal, Sylow
53C22×C4×D7—22no—
54C22×C4×D7C2311yescharacteristic
55C22×Dic14—22no—
56C22×Dic14—22no—
57C22×C7×C8C2311yescharacteristic
58C22×C7×C8C2311yescharacteristic
59C7×#125—24no—
60C7×#125C2318yes—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4C2312yes—
64C2×C7×C4⋊C4C2312yes—
65C2×C42×C7C2311yescharacteristic
66C2×(C2×D7)⋊C4—22no—
67C2×(C2×D7)⋊C4D411yescharacteristic
68C2×(C2×D7)⋊C4D411yescharacteristic
69C2×C4⋊Dic7—22no—
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7C2312yes—
72C2×C4⋊Dic7C2312yes—
73C2×Dic7⋊C4—22no—
74C2×Dic7⋊C4—22no—
75C2×Dic7⋊C4—22no—
76C2×Dic7⋊C4D411yescharacteristic
77C2×Dic7⋊C4D411yescharacteristic
78C2×C4×Dic7—22no—
79C2×C4×Dic7C2311yescharacteristic
80C22×C7⋊C8C2311yescharacteristic
81C22×C7⋊C8C2311yescharacteristic
82C2×#1131Q818yescomplemented
83C2×#1131C2314yes—
84C2×C8×D7Q818yescomplemented
85C2×C8×D7C2314yes—
86#6460—216no—
87#6459—216no—
88#6455—24no—
89#6455C2318yes—
90D7×C4⋊C4—24no—
91D7×C4⋊C4C2318yes—
92#6453—24no—
93#6453C2318yes—
94#6452—216no—
95#6451—216no—
96#6451—24no—
97#6451C2318yes—
98#6435D414yes—
99#6435C2314yes—
100#6432—24no—
101#6432C2318yes—
102C7×#107C2314yes—
103C7×#107C2314yes—
104C7×#106C2318yes—
105C4×C7×C8C2314yes—
106#6392C2318yes—
107#6392C2314yes—
108#6392C2314yes—
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×#500—71no—
122C2×#499—71no—
123C2×#499D711yescharacteristic, complemented
124C2×#428—72no—
125C2×#427—71no—
126C22×#107—71no—
127C2×#405—71no—
128C23×D7C2×D411yescharacteristic
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2411yescharacteristic
134C22×Dic7—22no—
135C22×Dic7—22no—
136C22×Dic7C2×D411yescharacteristic
137C22×Dic7C2×D411yescharacteristic
138C22×Dic7C2×D411yescharacteristic
139C2×C4×D7—28no—
140C2×C4×D7—84no—
141C2×C4×D7C2×D412yes—
142C2×C4×D7C2×Q814yes—
143C2×C4×D7C2×Q814yes—
144C2×C4×D7C2412yes—
145C2×Dic14—28no—
146C2×Dic14—28no—
147C2×Dic14—84no—
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—28no—
156C7×C4⋊C4—22no—
157C7×C4⋊C4C2414yes—
158C7×C4⋊C4C2414yes—
159C42×C7C2×D412yes—
160C42×C7C2412yes—
161(C2×D7)⋊C4—28no—
162(C2×D7)⋊C4C2×D414yes—
163(C2×D7)⋊C4C2×D414yes—
164C4⋊Dic7—22no—
165C4⋊Dic7—22no—
166C4⋊Dic7—28no—
167C4⋊Dic7—28no—
168C4⋊Dic7C2414yes—
169C4⋊Dic7C2414yes—
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—72no—
190C2×C4⋊Q8—142no—
191C2×#125—72no—
192C2×#125—142no—
193C2×#125C2×D712yes—
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#500—78no—
203#499—78no—
204#499C2×D718yescomplemented
205#428—716no—
206#427—78no—
207C2×#107—71no—
208C2×#107—71no—
209C2×#107—72no—
210C2×#107—72no—
211C2×#107—72no—
212C2×#107—78no—
213C2×#107C2×D711yescharacteristic
214C2×#107C2×D711yescharacteristic
215C2×#106—72no—
216C2×#106—72no—
217C2×#106C2×D712yes—
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—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—24no—
231C2×C4×C7—24no—
232C2×C4×C7—44no—
233C2×C4×C7—44no—
234C2×C4×C7C22×D412yes—
235C2×C4×C7C22×D412yes—
236C2×C4×C7C22×D411yescharacteristic
237C2×C4×C7C22×Q812yes—
238C2×C4×C7C22×Q812yes—
239C2×C4×C7C2511yescharacteristic
240C2×Dic7—22no—
241C2×Dic7—22no—
242C2×Dic7—24no—
243C2×Dic7—24no—
244C2×Dic7—44no—
245C2×Dic7—44no—
246C2×Dic7C4⋊Q814yes—
247C2×Dic7C22×D412yes—
248C2×Dic7C22×D412yes—
249C2×Dic7C22×D412yes—
250C4×D7—88no—
251C4×D7C4⋊Q818yes—
252C4×D7C22×Q814yes—
253C4×D7C22×Q814yes—
254Dic14—88no—
255Dic14—88no—
256C7×C8C22×Q814yes—
257C7×C8C22×Q814yes—
258C7⋊C8C22×Q814yes—
259C7⋊C8C22×Q814yes—
260C22×Q8—142no—
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—78no—
273C4⋊Q8—78no—
274C4⋊Q8—144no—
275C4⋊Q8—1416no—
276C4⋊Q8—144no—
277#125—24no—
278#125—78no—
279#125—144no—
280#125—1416no—
281#125C22×D718yes—
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—22no—
290C2×C4⋊C4—71no—
291C2×C4⋊C4—71no—
292C2×C4⋊C4—72no—
293C2×C4⋊C4—72no—
294C2×C4⋊C4—78no—
295C2×C4⋊C4—144no—
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#107—78no—
314#107C22×D714yes—
315#107C22×D714yes—
316#106—78no—
317#106—78no—
318#106C22×D718yes—
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—148no—
345C2×Q8—148no—
346C2×Q8—564no—
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—28no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—74no—
379C4⋊C4—74no—
380C4⋊C4—74no—
381C4⋊C4—74no—
382C4⋊C4—148no—
383C4⋊C4—148no—
384C4⋊C4—148no—
385C4⋊C4—148no—
386C4⋊C4—142no—
387C4⋊C4—142no—
388C4⋊C4—148no—
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—568no—
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—148no—
444C22—142no—
445C22—142no—
446C22D7×C4⋊Q812yes—
447C22#9046012yes—
448C22#9046212yes—
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#1173936314yesdirect product factor
464C2C2×D7×C4⋊Q811yescharacteristic
465C2C2×#9046011yescharacteristic
466C2C2×#9046211yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#499C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#499D7
hypocenterC7C2×#3164
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
2. C2×C7×#499C2semidirect
3. C2×#89837C2semidirect
4. #11739363C2direct (N × H)
7. C2×#89650C2semidirect
8. C2×#89646C2semidirect
10. C2×#89628C2semidirect
12. C2×#89454C2semidirect
28. C7×#499C22semidirect
38. #89837C22semidirect
46. #89650C22semidirect
47. #89646C22semidirect
49. #89628C22semidirect
51. #89454C22semidirect
82. C2×#1131Q8semidirect
84. C2×C8×D7Q8semidirect
123. C2×#499D7semidirect
182. #1131C2×Q8semidirect
183. C8×D7C2×Q8semidirect
204. #499C2×D7semidirect
399. C2×C7#3164semidirect
441. C7C2×#3164semidirect
463. C2#11739363direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903802
C2×C7×#4992
C2×#898372
#117393632
C2×#896522
C2×D7×#1072
C2×#896502
C2×#896462
C2×#896332
C2×#896282
C2×#894612
C2×#894542
C2×#31647