Finite Group Databasebeta

← C2×#11744360 #14262209

Subgroups — C2×#11744360 #14262209

Order 1792.

11126 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×2−1+4C211yesmaximal, characteristic, complemented
2C22×#6554C211yesmaximal, characteristic, complemented
3#11744360C2132yesmaximal, direct product factor
4C2×#90515C2112yesmaximal, complemented
5C2×#90516C213yesmaximal, complemented
6C2×#90523C213yesmaximal, complemented
7C2×#41×Dic7C211yesmaximal, characteristic, complemented
8C2×#90507C213yesmaximal, complemented
9C2×Q8×C22⋊D7C214yesmaximal, complemented
10C22×#6507C213yesmaximal, complemented
11C2×C7×2−1+4—216no—
12C2×C7×2−1+4C22116yescomplemented
13C22×C7×#41C2213yes—
14C22×C7×#41C2216yes—
15C22×C7×#41C2211yescharacteristic
16C23×C7×Q8C2213yes—
17C23×C7×Q8C2212yes—
18C2×#6554—216no—
19C2×#6554C22116yescomplemented
20C22×Q8×D7C2212yes—
21C22×#1159C2216yes—
22C22×#1157C2213yes—
23C23×Dic14C2213yes—
24#90523C22148yescomplemented
25#41×Dic7C22116yescomplemented
26#90516C22148yescomplemented
27#90515C221192yescomplemented
28#90507C22148yescomplemented
29Q8×C22⋊D7C22164yescomplemented
30C2×#6510C2213yes—
31C2×#6509C22112yes—
32C2×Q8×Dic7C2212yes—
33C2×#6507C2213yes—
34C2×#6507C22112yes—
35C2×#6507C2216yes—
36C2×#6507C22148yescomplemented
37C2×#6503C2211yescharacteristic
38C2×#6502C22112yes—
39C2×#6499C2213yes—
40C2×#6498C22112yes—
41C2×D4×Dic7C2216yes—
42C2×#6492C22112yes—
43C2×C4×C22⋊D7C22112yes—
44C2×#6489C2213yes—
45C2×#6487C22112yes—
46C22×Dic7⋊C4C22112yes—
47C22×C4×Dic7C2213yes—
48C2×#3499—71nomaximal, Sylow
49C7×2−1+4—2128no—
50C2×C7×#41—248no—
51C2×C7×#41—224no—
52C2×C7×#41D4116yescomplemented
53C2×C7×#41C23148yes—
54C2×C7×#41C23124yes—
55C2×C7×#41C2318yes—
56C22×C7×Q8—216no—
57C22×C7×Q8—224no—
58C22×C7×Q8C2313yes—
59C22×C7×Q8C2316yes—
60C22×C7×Q8C23124yes—
61C22×C7×Q8C23116yes—
62C22×C7×Q8C2311yescharacteristic
63C22×C7×D4C2316yes—
64C22×C7×D4C2311yescharacteristic
65C22×C7×D4C2313yes—
66C23×C4×C7C2316yes—
67C23×C4×C7C2316yes—
68C23×C4×C7C2313yes—
69C22×C22⋊D7C2314yes—
70C22×C22⋊D7C2316yes—
71C23×Dic7C2316yes—
72C23×Dic7C2316yes—
73#6554—2128no—
74C2×Q8×D7—216no—
75C2×Q8×D7C23116yes—
76C2×#1159—248no—
77C2×#1159C23148yes—
78C2×#1157—224no—
79C2×#1157C23124yes—
80C22×D28C2311yescharacteristic
81C22×C4×D7C2316yes—
82C22×Dic14—224no—
83C22×Dic14C2316yes—
84C22×Dic14C2313yes—
85C22×Dic14C23124yes—
86C2×C22⋊Dic7C23112yes—
87C2×C22⋊Dic7C2316yes—
88#6510C23124yes—
89#6509C23196yes—
90Q8×Dic7C23116yes—
91#6507C23124yes—
92#6507C23196yes—
93#6507C23148yes—
94#6503C2318yes—
95#6502C23196yes—
96#6499C23124yes—
97#6498C23196yes—
98D4×Dic7C23148yes—
99#6492C23196yes—
100C4×C22⋊D7C23196yes—
101C2×(C2×D7)⋊C4C23112yes—
102#6489C23124yes—
103C2×C4⋊Dic7C2316yes—
104#6487C23196yes—
105C2×Dic7⋊C4C23112yes—
106C2×Dic7⋊C4C23124yes—
107C2×Dic7⋊C4C23196yes—
108C2×C4×Dic7C2311yescharacteristic
109C2×C4×Dic7C2313yes—
110C2×C4×Dic7C2316yes—
111C2×C4×Dic7C23124yes—
112C22×2−1+4—71no—
113C22×2−1+4D711yescharacteristic, complemented
114#3499—732no—
115C2×D4×Q8—74no—
116C2×#547—712no—
117C2×#536—73no—
118C2×#536—73no—
119C2×#532—73no—
120C22×C4⋊Q8—73no—
121C2×C4×#41—71no—
122C24×C7C2412yes—
123C24×C7C2413yes—
124C23×D7C2412yes—
125C7×#41—2192no—
126C7×#41—296no—
127C7×#41C2×D4164yescomplemented
128C2×C7×Q8—264no—
129C2×C7×Q8—212no—
130C2×C7×Q8—224no—
131C2×C7×Q8—296no—
132C2×C7×Q8C2×D418yes—
133C2×C7×Q8C24112yes—
134C2×C7×Q8C24124yes—
135C2×C7×Q8C2414yes—
136C2×C7×D4—224no—
137C2×C7×D4—24no—
138C2×C7×D4C2×D4124yes—
139C2×C7×D4C24124yes—
140C2×C7×D4C2414yes—
141C2×C7×D4C24112yes—
142C22×C4×C7—224no—
143C22×C4×C7—224no—
144C22×C4×C7C2×D4124yes—
145C22×C4×C7C2416yes—
146C22×C4×C7C24124yes—
147C22×C4×C7C24124yes—
148C22×C4×C7C2411yescharacteristic
149C22×C4×C7C2413yes—
150C22×C4×C7C24112yes—
151C2×C22⋊D7—224no—
152C2×C22⋊D7—216no—
153C2×C22⋊D7C24116yes—
154C2×C22⋊D7C24124yes—
155C22×Dic7—224no—
156C22×Dic7—224no—
157C22×Dic7C2416yes—
158C22×Dic7C24124yes—
159C22×Dic7C2416yes—
160C22×Dic7C24124yes—
161C22×Dic7C2412yes—
162Q8×D7—264no—
163#1159—2192no—
164#1157—296no—
165C2×D28—24no—
166C2×D28C2414yes—
167C2×C4×D7—224no—
168C2×C4×D7C24124yes—
169C2×Dic14—212no—
170C2×Dic14—224no—
171C2×Dic14—296no—
172C2×Dic14C24124yes—
173C2×Dic14C24112yes—
174C22⋊Dic7C24148yes—
175C22⋊Dic7C24124yes—
176(C2×D7)⋊C4C24148yes—
177C4⋊Dic7C24124yes—
178Dic7⋊C4C24148yes—
179Dic7⋊C4C24196yes—
180C4×Dic7C2414yes—
181C4×Dic7C24112yes—
182C4×Dic7C24124yes—
183C2×2−1+4—216no—
184C2×2−1+4—716no—
185C2×2−1+4—1416no—
186C2×2−1+4C2×D7116yescomplemented
187C22×#41—76no—
188C22×#41—73no—
189C22×#41C2×D713yes—
190C22×#41C2×D716yes—
191C22×#41C2×D711yescharacteristic
192C23×Q8—72no—
193C23×Q8—73no—
194C23×Q8C2×D713yes—
195C23×Q8C2×D712yes—
196D4×Q8—764no—
197#547—7192no—
198#536—748no—
199#536—748no—
200#532—748no—
201C2×C4⋊Q8—73no—
202C2×C4⋊Q8—76no—
203C2×C4⋊Q8—712no—
204C2×C4⋊Q8—748no—
205C2×#127—71no—
206C2×#124—73no—
207C2×#124—73no—
208C2×#123—712no—
209C2×#123—712no—
210C2×C22⋊Q8—712no—
211C2×C22⋊Q8—712no—
212C2×#121—712no—
213C4×#41—716no—
214C2×C4×Q8—72no—
215C2×C4×D4—76no—
216C2×C4×D4—712no—
217C2×#117—73no—
218C22×C4⋊C4—712no—
219C22×C42—73no—
220C23×C7—212no—
221C23×C7—24no—
222C23×C7—28no—
223C23×C7C22×D4112yes—
224C23×C7C2514yes—
225C23×C7C2516yes—
226C23×C7C2511yescharacteristic
227C22×D7—24no—
228C22×D7—28no—
229C22×D7C2514yes—
230C7×Q8—224no—
231C7×Q8—248no—
232C7×Q8C22×D4116yes—
233C7×D4—248no—
234C7×D4—28no—
235C7×D4C22×D4148yes—
236C2×C4×C7—212no—
237C2×C4×C7—248no—
238C2×C4×C7—248no—
239C2×C4×C7C22×D414yes—
240C2×C4×C7C22×D4112yes—
241C2×C4×C7C22×D4148yes—
242C2×C4×C7C25112yes—
243C2×C4×C7C2512yes—
244C2×C4×C7C2516yes—
245C22⋊D7—248no—
246C22⋊D7—232no—
247C2×Dic7—212no—
248C2×Dic7—248no—
249C2×Dic7—212no—
250C2×Dic7—248no—
251C2×Dic72−1+418yescomplemented
252C2×Dic7C25112yes—
253C2×Dic7C25112yes—
254C2×Dic7C2514yes—
255D28—28no—
256C4×D7—248no—
257Dic14—224no—
258Dic14—248no—
2592−1+4—2128no—
2602−1+4—14128no—
261C2×#41—248no—
262C2×#41—224no—
263C2×#41—748no—
264C2×#41—724no—
265C2×#41—1448no—
266C2×#41—1424no—
267C2×#41C22⋊D7116yescomplemented
268C2×#41C22×D7124yes—
269C2×#41C22×D7148yes—
270C2×#41C22×D718yes—
271C22×Q8—216no—
272C22×Q8—224no—
273C22×Q8—716no—
274C22×Q8—76no—
275C22×Q8—73no—
276C22×Q8—724no—
277C22×Q8—1416no—
278C22×Q8—1424no—
279C22×Q8C22×D716yes—
280C22×Q8C22×D713yes—
281C22×Q8C22×D7124yes—
282C22×Q8C22×D7116yes—
283C22×Q8C22×D711yescharacteristic
284C22×D4—74no—
285C22×D4—76no—
286C22×D4—71no—
287C22×D4C22×D716yes—
288C22×D4C22×D711yescharacteristic
289C22×D4C22×D713yes—
290C23×C4—76no—
291C23×C4—76no—
292C23×C4—76no—
293C23×C4C22×D716yes—
294C23×C4C22×D716yes—
295C23×C4C22×D713yes—
296C4⋊Q8—724no—
297C4⋊Q8—748no—
298C4⋊Q8—796no—
299#127—78no—
300#124—724no—
301#124—724no—
302#123—796no—
303#123—796no—
304C22⋊Q8—796no—
305C22⋊Q8—796no—
306#121—796no—
307C4×Q8—716no—
308C4×D4—748no—
309C4×D4—796no—
310#117—724no—
311C2×C4⋊C4—712no—
312C2×C4⋊C4—724no—
313C2×C4⋊C4—796no—
314C2×C4⋊C4—76no—
315C2×C22⋊C4—76no—
316C2×C22⋊C4—712no—
317C2×C22⋊C4—712no—
318C2×C42—73no—
319C2×C42—76no—
320C2×C42—724no—
321C2×C42—71no—
322C22×C7—212no—
323C22×C7—224no—
324C22×C7—24no—
325C22×C7—28no—
326C22×C7—48no—
327C22×C7C23×D4112yes—
328C22×C7C23×D412yes—
329C22×C7C2×2−1+414yes—
330C22×C7C2611yescharacteristic
331C2×D7—24no—
332C2×D7—28no—
333C2×D7—48no—
334C4×C7—212no—
335C4×C7C23×D414yes—
336C4×C7C23×D4112yes—
337Dic7—212no—
338Dic7—212no—
339Dic7C2×2−1+418yescomplemented
340C24—72no—
341C24C23×D712yes—
342C24C23×D713yes—
343#41—2192no—
344#41—296no—
345#41—14192no—
346#41—1496no—
347#41C2×C22⋊D7164yescomplemented
348C2×Q8—264no—
349C2×Q8—224no—
350C2×Q8—212no—
351C2×Q8—296no—
352C2×Q8—724no—
353C2×Q8—712no—
354C2×Q8—1464no—
355C2×Q8—1424no—
356C2×Q8—1412no—
357C2×Q8—1496no—
358C2×Q8C2×C22⋊D718yes—
359C2×Q8C23×D7124yes—
360C2×Q8C23×D7112yes—
361C2×Q8C23×D714yes—
362C2×D4—224no—
363C2×D4—24no—
364C2×D4—716no—
365C2×D4—724no—
366C2×D4—74no—
367C2×D4—1416no—
368C2×D4—1424no—
369C2×D4—144no—
370C2×D4C2×C22⋊D7124yes—
371C2×D4C23×D7124yes—
372C2×D4C23×D714yes—
373C2×D4C23×D7112yes—
374C22×C4—224no—
375C22×C4—224no—
376C22×C4—72no—
377C22×C4—724no—
378C22×C4—724no—
379C22×C4—76no—
380C22×C4—76no—
381C22×C4—724no—
382C22×C4—1424no—
383C22×C4—1424no—
384C22×C4—1424no—
385C22×C4C2×C22⋊D7124yes—
386C22×C4C23×D7124yes—
387C22×C4C23×D7124yes—
388C22×C4C23×D716yes—
389C22×C4C23×D7112yes—
390C22×C4C23×D711yescharacteristic
391C22×C4C23×D713yes—
392C4⋊C4—748no—
393C4⋊C4—796no—
394C4⋊C4—724no—
395C22⋊C4—724no—
396C22⋊C4—748no—
397C22⋊C4—748no—
398C42—74no—
399C42—712no—
400C42—724no—
401C2×C7—212no—
402C2×C7—44no—
403C2×C7#349914yescomplemented
404C2×C7C24×D411yescharacteristic
405C2×C7C22×2−1+412yes—
406D7—44no—
407C23—212no—
408C23—28no—
409C23—24no—
410C23—74no—
411C23—148no—
412C23—144no—
413C23C22×C22⋊D7112yes—
414C23C24×D714yes—
415C23C24×D716yes—
416C23C24×D711yescharacteristic
417Q8—248no—
418Q8—224no—
419Q8—1448no—
420Q8—1424no—
421Q8C22×C22⋊D7116yes—
422D4—248no—
423D4—28no—
424D4—1432no—
425D4—1448no—
426D4—148no—
427D4C22×C22⋊D7148yes—
428C2×C4—212no—
429C2×C4—248no—
430C2×C4—248no—
431C2×C4—74no—
432C2×C4—78no—
433C2×C4—712no—
434C2×C4—712no—
435C2×C4—1448no—
436C2×C4—1412no—
437C2×C4—1412no—
438C2×C4—1448no—
439C2×C4—1448no—
440C2×C4C22×C22⋊D7112yes—
441C2×C4C22×C22⋊D714yes—
442C2×C4C22×C22⋊D7148yes—
443C2×C4C24×D7112yes—
444C2×C4C24×D712yes—
445C2×C4C24×D716yes—
446C7C2×#349911yescharacteristic, complemented, Sylow
447C22—212no—
448C22—224no—
449C22—28no—
450C22—24no—
451C22—48no—
452C22—148no—
453C22—144no—
454C22—288no—
455C22D7×2−1+414yes—
456C22C23×C22⋊D7112yes—
457C22C23×C22⋊D712yes—
458C22C25×D711yescharacteristic
459C4—212no—
460C4—78no—
461C4—1412no—
462C4—1412no—
463C4C23×C22⋊D7112yes—
464C4C23×C22⋊D714yes—
465C2—212no—
466C2—44no—
467C2—284no—
468C2#1174436014yesdirect product factor
469C2C2×D7×2−1+412yes—
470C2C24×C22⋊D711yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC22×C7×2−1+4C2
socleC23×C7C25
hypercenterC22×2−1+4D7
hypocenterC7C2×#3499
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×2−1+4

Complements

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

NH ≅ G/Ntype
1. C22×C7×2−1+4C2semidirect
2. C22×#6554C2semidirect
3. #11744360C2direct (N × H)
4. C2×#90515C2semidirect
5. C2×#90516C2semidirect
6. C2×#90523C2semidirect
7. C2×#41×Dic7C2semidirect
8. C2×#90507C2semidirect
9. C2×Q8×C22⋊D7C2semidirect
10. C22×#6507C2semidirect
12. C2×C7×2−1+4C22semidirect
19. C2×#6554C22semidirect
24. #90523C22semidirect
25. #41×Dic7C22semidirect
26. #90516C22semidirect
27. #90515C22semidirect
28. #90507C22semidirect
29. Q8×C22⋊D7C22semidirect
36. C2×#6507C22semidirect
52. C2×C7×#41D4semidirect
113. C22×2−1+4D7semidirect
127. C7×#41C2×D4semidirect
186. C2×2−1+4C2×D7semidirect
251. C2×Dic72−1+4semidirect
267. C2×#41C22⋊D7semidirect
339. Dic7C2×2−1+4semidirect
347. #41C2×C22⋊D7semidirect
403. C2×C7#3499semidirect
446. C7C2×#3499semidirect
468. C2#11744360direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×2−1+42
C22×#65542
#117443602
C2×#905152
C2×#905162
C2×#905232
C2×#41×Dic72
C2×#905072
C2×Q8×C22⋊D72
C22×#65072
C2×#34997