Finite Group Databasebeta

← C2×#22626840 #34031867

Subgroups — C2×#22626840 #34031867

Order 18688.

1794 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626840C2116yesmaximal, direct product factor
2C2×#17989639C212yesmaximal, complemented
3C2×#17989638C211yesmaximal, characteristic, complemented
4C2×#17989637C211yesmaximal, characteristic, complemented
5C2×#17989636C212yesmaximal, complemented
6C2×#17989636C211yesmaximal, characteristic, complemented
7C2×Q8×#10596833C211yesmaximal, characteristic, complemented
8C2×#17989611C212yesmaximal
9C2×#17989611C212yesmaximal
10C2×#17989604C211yesmaximal, characteristic
11C2×#17989603C211yesmaximal, characteristic
12C2×#17989139C211yesmaximal, characteristic
13#17989639C22116yescomplemented
14#17989638C2218yescomplemented
15#17989637C2218yescomplemented
16#17989636C2218yescomplemented
17#17989636C22116yescomplemented
18Q8×#10596833C2218yescomplemented
19#17989611C22116yes—
20#17989611C22116yes—
21#17989604C2218yes—
22#17989603C2218yes—
23C2×#14556658C2211yescharacteristic
24C2×#14556658C2211yescharacteristic
25C2×#14556658C2212yes—
26C2×#14556658C2212yes—
27C2×C4⋊#10596833C2211yescharacteristic
28C2×C4⋊#10596833C2211yescharacteristic
29C2×C4⋊#10596833C2212yes—
30C2×C4⋊#10596833C2212yes—
31C2×C22⋊#10596833C2212yes—
32C2×C22⋊#10596833C2211yescharacteristic
33C2×C22⋊#10596833C2211yescharacteristic
34C2×#14556646C2212yes—
35C2×#14556646C2212yes—
36C2×C4×#10596833C2212yes—
37C2×C4×#10596833C2211yescharacteristic
38C2×C4×#10596833C2211yescharacteristic
39C2×C4×#10596833C2212yes—
40C2×C4×#10596833C2212yes—
41#17989139C418yes—
42#17989139C2218yes—
43C2×#14556590C411yescharacteristic
44C2×#14556589C411yescharacteristic
45C2×#14556581C412yes—
46C2×#14556570C411yescharacteristic
47C2×#14556568C412yes—
48C2×Q8×Dic73C2211yescharacteristic
49C2×#14556556C2211yescharacteristic
50C2×#14556556C2212yes—
51C2×#14556547C2212yes—
52C22×C4×Dic73C2211yescharacteristic
53C2×C22⋊Q8×C73C411yescharacteristic
54C22×#10596833C2312yes—
55C22×#10596833C2311yescharacteristic
56C22×#10596833C2311yescharacteristic
57C22×#10596833C2312yes—
58C22×#10596833C2311yescharacteristic
59C22×#10596833C2311yescharacteristic
60#14556658C2314yes—
61#14556658C2318yes—
62#14556658C2318yes—
63#14556658C2314yes—
64C4⋊#10596833C2314yes—
65C4⋊#10596833C2318yes—
66C4⋊#10596833C2318yes—
67C4⋊#10596833C2314yes—
68C22⋊#10596833C2318yes—
69C22⋊#10596833C2314yes—
70C22⋊#10596833C2314yes—
71#14556646C2318yes—
72#14556646C2318yes—
73C4×#10596833C2318yes—
74C4×#10596833C2314yes—
75C4×#10596833C2318yes—
76C4×#10596833C2314yes—
77C4×#10596833C2318yes—
78C22×Dic146C2×C411yescharacteristic
79C22×Dic146C2×C412yes—
80C23×Dic73C2×C411yescharacteristic
81C23×Dic73C2311yescharacteristic
82#14556590C2×C418yes—
83#14556589C2×C418yes—
84#14556581C2×C4116yes—
85#14556570C2×C418yes—
86#14556568C2×C4116yes—
87Q8×Dic73C2×C414yes—
88Q8×Dic73C2314yes—
89#14556556C2×C418yes—
90#14556556C2×C414yes—
91#14556556C2314yes—
92#14556556C2318yes—
93#14556547C2×C418yes—
94#14556547C2318yes—
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×C4⋊Dic73C2×C412yes—
97C2×#11924007C2×C412yes—
98C2×#11924007C2×C412yes—
99C2×#11924007C2×C412yes—
100C2×#11924007C2×C412yes—
101C2×#11924007C2×C412yes—
102C2×C22⋊Dic73C2×C412yes—
103C2×C4×Dic73C2×C411yescharacteristic
104C2×C4×Dic73C2×C414yes—
105C2×C4×Dic73C2×C411yescharacteristic
106C2×C4×Dic73C2314yes—
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109C2×C4×Dic73C2312yes—
110C2×C4×Dic73C2312yes—
111C22×Q8×C73C2×C411yescharacteristic
112C23×C4×C73C2×C411yescharacteristic
113C22⋊Q8×C73C2×C418yes—
114C2×C4⋊C4×C73C2×C411yescharacteristic
115C2×C4⋊C4×C73C2×C412yes—
116C2×C22⋊C4×C73C2×C412yes—
117C2×#10596833—24no—
118C2×#10596833—22no—
119C2×#10596833—22no—
120C2×#10596833—24no—
121C2×#10596833—22no—
122C2×#10596833—22no—
123C2×#10596833C2412yes—
124C2×#10596833C2414yes—
125C2×#10596833C2412yes—
126C2×#10596833C2412yes—
127C2×#10596833C2414yes—
128C2×#10596833C2412yes—
129C2×Dic146—24no—
130C2×Dic146—28no—
131C2×Dic146C22×C418yes—
132C2×Dic146C22×C414yes—
133C22×Dic73—24no—
134C22×Dic73—22no—
135C22×Dic73—22no—
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C412yes—
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C414yes—
140C22×Dic73C22×C412yes—
141C22×Dic73C22×C412yes—
142C22×Dic73C22×C411yescharacteristic
143C22×Dic73C2412yes—
144C22×Dic73C2411yescharacteristic
145C4⋊Dic73C22×C418yes—
146C4⋊Dic73C22×C414yes—
147#11924007C22×C418yes—
148#11924007C22×C418yes—
149#11924007C22×C418yes—
150#11924007C22×C418yes—
151#11924007C22×C418yes—
152C22⋊Dic73C22×C418yes—
153C4×Dic73C22×C412yes—
154C4×Dic73C22×C412yes—
155C4×Dic73C22×C414yes—
156C4×Dic73C22×C414yes—
157C4×Dic73C22×C414yes—
158C4×Dic73C22×C414yes—
159C4×Dic73C2412yes—
160C4×Dic73C2412yes—
161C4×Dic73C2414yes—
162C4×Dic73C2414yes—
163C24×C73C22×C411yescharacteristic
164C2×Q8×C73—24no—
165C2×Q8×C73C22×C414yes—
166C22×C4×C73—24no—
167C22×C4×C73C22×C412yes—
168C22×C4×C73C22×C412yes—
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C414yes—
171C22×C4×C73C22×C411yescharacteristic
172C4⋊C4×C73C22×C418yes—
173C4⋊C4×C73C22×C414yes—
174C22⋊C4×C73C22×C418yes—
175C23×C73—22no—
176C23×C73—22no—
177C23×C73—22no—
178C23×C73C23×C412yes—
179C23×C73C23×C411yescharacteristic
180Q8×C73—28no—
181C2×C4×C73—22no—
182C2×C4×C73—24no—
183C2×C4×C73—24no—
184C2×C4×C73—28no—
185C2×C4×C73#13114yes—
186C2×C4×C73C23×C414yes—
187C2×C4×C73C23×C414yes—
188C2×C4×C73C23×C412yes—
189C2×C4×C73C23×C412yes—
190C2×Dic73—22no—
191C2×Dic73—22no—
192C2×Dic73—24no—
193C2×Dic73—24no—
194C2×Dic73—24no—
195C2×Dic73—28no—
196C2×Dic73—22no—
197C2×Dic73—22no—
198C2×Dic73#13114yes—
199C2×Dic73C23×C412yes—
200C2×Dic73C23×C412yes—
201C2×Dic73C23×C414yes—
202C2×Dic73C23×C414yes—
203C2×Dic73C23×C411yescharacteristic
204C2×Dic73C23×C412yes—
205C2×Dic732−1+412yes—
206C2×Dic732−1+412yes—
207C2×Dic73C2511yescharacteristic
208Dic146—28no—
209Dic146—216no—
210#10596833—22no—
211#10596833—24no—
212#10596833—22no—
213#10596833—22no—
214#10596833—24no—
215#10596833—22no—
216C22×C73—22no—
217C22×C73—22no—
218C22×C73—22no—
219C22×C73—44no—
220C22×C73#51912yes—
221C22×C73C2×#13112yes—
222C22×C73C2×#13112yes—
223C22×C73C24×C411yescharacteristic
224C4×C73—24no—
225C4×C73—22no—
226C4×C73—24no—
227C4×C73C2×#13114yes—
228Dic73—22no—
229Dic73—24no—
230Dic73—24no—
231Dic73—22no—
232Dic73#51912yes—
233Dic73C2×#13114yes—
234Dic73C2×2−1+411yescharacteristic
235Dic73C2×2−1+411yescharacteristic
236C2×#2986—731nomaximal, Sylow
237C2×C73—42no—
238C2×C73#298614yescomplemented
239C2×C73C2×#51911yescharacteristic
240C2×C73C22×#13111yescharacteristic
241C2×C73C22×#13111yescharacteristic
242C2×#533—731no—
243#2986—7316no—
244C2×#446—731no—
245C2×#446—731no—
246C2×#446—732no—
247C2×C8×Q8—731no—
248C2×C8×Q8—731no—
249C2×C8×Q8—732no—
250C2×#433—732no—
251C2×#433—732no—
252C2×#431—731no—
253C2×#431—731no—
254C73C2×#298611yescharacteristic, complemented, Sylow
255#533—738no—
256#533—738no—
257C2×C4⋊Q8—731no—
258C2×C4⋊Q8—731no—
259C2×#125—732no—
260C2×C22⋊Q8—731no—
261C2×C22⋊Q8—732no—
262C2×C22⋊Q8#6440811yescharacteristic
263C2×C4×Q8—731no—
264C2×C4×Q8—731no—
265C2×C4×Q8—732no—
266C2×#117—732no—
267C22×C42—731no—
268#446—738no—
269#446—738no—
270#446—7316no—
271C8×Q8—738no—
272C8×Q8—738no—
273C8×Q8—7316no—
274#433—7316no—
275#433—7316no—
276#431—738no—
277#431—738no—
278C2×C4⋊C8—731no—
279C2×C4⋊C8—731no—
280C2×C4⋊C8—731no—
281C2×C4⋊C8—731no—
282C2×C4⋊C8—732no—
283C2×C4⋊C8—732no—
284C2×C4⋊C8—732no—
285C2×C4⋊C8—732no—
286C2×C22⋊C8—732no—
287C2×C22⋊C8—731no—
288C2×C22⋊C8—731no—
289C2×#97—732no—
290C2×#97—732no—
291C2×C4×C8—732no—
292C2×C4×C8—731no—
293C2×C4×C8—731no—
294C2×C4×C8—732no—
295C2×C4×C8—732no—
296C22×Q8—732no—
297C22×Q8—731no—
298C22×Q8C2×#6440811yescharacteristic
299C23×C4—731no—
300C23×C4—731no—
301C23×C4C2×#6440811yescharacteristic
302C22×C8—732no—
303C22×C8—731no—
304C22×C8—731no—
305C22×C8—732no—
306C22×C8—731no—
307C22×C8—731no—
308C4⋊Q8—738no—
309C4⋊Q8—738no—
310#125—7316no—
311C22⋊Q8—738no—
312C22⋊Q8—7316no—
313C22⋊Q8C2×#6440818yes—
314C4×Q8—734no—
315C4×Q8—734no—
316C4×Q8—734no—
317C4×Q8—738no—
318C4×Q8—734no—
319C4×Q8—738no—
320#117—738no—
321#117—738no—
322C2×C4⋊C4—732no—
323C2×C4⋊C4—732no—
324C2×C4⋊C4—732no—
325C2×C4⋊C4—732no—
326C2×C4⋊C4—732no—
327C2×C4⋊C4—732no—
328C2×C4⋊C4—731no—
329C2×C4⋊C4C2×#6440812yes—
330C2×C4⋊C4C2×#6440811yescharacteristic
331C2×C22⋊C4—732no—
332C2×C22⋊C4C2×#6440812yes—
333C2×C42—732no—
334C2×C42—732no—
335C2×C42—731no—
336C2×C42—731no—
337C2×C42—731no—
338C2×C42—731no—
339C2×C42—734no—
340C2×C42—734no—
341C4⋊C8—734no—
342C4⋊C8—734no—
343C4⋊C8—734no—
344C4⋊C8—734no—
345C4⋊C8—738no—
346C4⋊C8—738no—
347C4⋊C8—738no—
348C4⋊C8—738no—
349C22⋊C8—738no—
350C22⋊C8—734no—
351C22⋊C8—734no—
352#97—738no—
353#97—738no—
354C4×C8—738no—
355C4×C8—734no—
356C4×C8—734no—
357C4×C8—738no—
358C4×C8—738no—
359C24C22×#6440811yescharacteristic
360C2×Q8—24no—
361C2×Q8—738no—
362C2×Q8—734no—
363C2×Q8—1468no—
364C2×Q8—1464no—
365C2×Q8C22×#6440814yes—
366C22×C4—24no—
367C22×C4—731no—
368C22×C4—731no—
369C22×C4—732no—
370C22×C4—734no—
371C22×C4—732no—
372C22×C4—731no—
373C22×C4—731no—
374C22×C4—732no—
375C22×C4—732no—
376C22×C4—1462no—
377C22×C4—1462no—
378C22×C4—1464no—
379C22×C4C22×#6440814yes—
380C22×C4C22×#6440811yescharacteristic
381C22×C4C22×#6440812yes—
382C22×C4C22×#6440812yes—
383C22×C4C22×#6440811yescharacteristic
384C2×C8—734no—
385C2×C8—732no—
386C2×C8—732no—
387C2×C8—734no—
388C2×C8—732no—
389C2×C8—732no—
390C2×C8—1464no—
391C2×C8—1462no—
392C2×C8—1462no—
393C2×C8—1464no—
394C2×C8—1462no—
395C2×C8—1462no—
396C4⋊C4—738no—
397C4⋊C4—738no—
398C4⋊C4—738no—
399C4⋊C4—738no—
400C4⋊C4—738no—
401C4⋊C4—738no—
402C4⋊C4—734no—
403C4⋊C4C22×#6440818yes—
404C4⋊C4C22×#6440814yes—
405C22⋊C4—738no—
406C22⋊C4C22×#6440818yes—
407C42—732no—
408C42—732no—
409C42—734no—
410C42—734no—
411C42—734no—
412C42—734no—
413C42—732no—
414C42—732no—
415C42—734no—
416C42—734no—
417C23—22no—
418C23—22no—
419C23—22no—
420C23C23×#6440812yes—
421C23C23×#6440811yescharacteristic
422Q8—28no—
423Q8—14616no—
424Q8—1468no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4—732no—
430C2×C4—732no—
431C2×C4—734no—
432C2×C4—731no—
433C2×C4—731no—
434C2×C4—732no—
435C2×C4—732no—
436C2×C4—732no—
437C2×C4—734no—
438C2×C4—734no—
439C2×C4—1462no—
440C2×C4—1462no—
441C2×C4—1464no—
442C2×C4—1468no—
443C2×C4—1462no—
444C2×C4—1464no—
445C2×C4—1462no—
446C2×C4—1464no—
447C2×C4#1455667814yes—
448C2×C4C23×#6440812yes—
449C2×C4C23×#6440814yes—
450C2×C4C23×#6440814yes—
451C2×C4C23×#6440812yes—
452C8—1464no—
453C8—1462no—
454C8—1462no—
455C8—1464no—
456C8—1462no—
457C8—1462no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—44no—
462C22#1798965512yes—
463C22C2×#1455667812yes—
464C22D73⋊#13112yes—
465C22C24×#6440811yescharacteristic
466C4—22no—
467C4—24no—
468C4—24no—
469C4—731no—
470C4—731no—
471C4—732no—
472C4—734no—
473C4—1462no—
474C4—1464no—
475C4—1462no—
476C4—1464no—
477C4C2×#1455667814yes—
478C2—42no—
479C2#2262684014yesdirect product factor
480C2C2×#1798965511yescharacteristic
481C2C22×#1455667811yescharacteristic
482C2C2×D73⋊#13111yescharacteristic
subgroupG/H
centerC23C23×#64408
commutatorC22×C73C24×C4
FrattiniC22C24×#64408
FittingC2×C22⋊Q8×C73C4
socleC23×C73C23×C4
prime radicalC24×C73C22×C4
cosocleC2×Dic73C25
hypercenterC2×C22⋊Q8#64408
hypocenterC73C2×#2986
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #22626840C2direct (N × H)
2. C2×#17989639C2semidirect
3. C2×#17989638C2semidirect
4. C2×#17989637C2semidirect
5. C2×#17989636C2semidirect
6. C2×#17989636C2semidirect
7. C2×Q8×#10596833C2semidirect
13. #17989639C22semidirect
14. #17989638C22semidirect
15. #17989637C22semidirect
16. #17989636C22semidirect
17. #17989636C22semidirect
18. Q8×#10596833C22semidirect
238. C2×C73#2986semidirect
254. C73C2×#2986semidirect
479. C2#22626840direct (N × H)

Maximal subgroups

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

subgroupindex
#226268402
C2×#179896392
C2×#179896382
C2×#179896372
C2×#179896362
C2×Q8×#105968332
C2×#179896112
C2×#179896042
C2×#179896032
C2×#179891392
C2×#298673