Finite Group Databasebeta

← C2×#22620468 #33955615

Subgroups — C2×#22620468 #33955615

Order 18688.

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×#17989217C212yesmaximal
2#22620468C2116yesmaximal, direct product factor
3C2×#17988997C212yesmaximal, complemented
4C2×#17988994C212yesmaximal, complemented
5C2×#17988992C211yesmaximal, characteristic, complemented
6C2×#17988991C211yesmaximal, characteristic, complemented
7C2×#17988988C211yesmaximal, characteristic, complemented
8C2×#17988626C212yesmaximal
9C2×#17988624C211yesmaximal, characteristic
10C2×#107×D73C211yesmaximal, characteristic
11C2×#17988541C211yesmaximal, characteristic
12C2×#499×C73C211yesmaximal, characteristic, complemented
13C22×#11924011C2211yescharacteristic
14C22×C8×D73C2211yescharacteristic
15#17989217—28no—
16#17989217C22116yes—
17C2×#14556591C2212yes—
18C2×#14556590—22no—
19C2×#14556590C2212yes—
20C2×#14556582C2212yes—
21C2×#14556581—22no—
22C2×#14556571—22no—
23C2×#14556569—22no—
24C2×#14556549C2212yes—
25C2×#14556548C2211yescharacteristic
26C2×C4⋊C4×D73C2212yes—
27#17988997C22116yescomplemented
28#17988994C22116yescomplemented
29#17988992C2218yescomplemented
30#17988991C2218yescomplemented
31#17988988C2218yescomplemented
32#17988626C22116yes—
33#17988624C2218yes—
34C2×#14556525C2211yescharacteristic
35C2×#14556525C2211yescharacteristic
36C2×#14556525C2212yes—
37C2×#14556524C2212yes—
38C2×#14556524C2212yes—
39#107×D73C2218yes—
40C2×#14556522C2212yes—
41C2×#14556522C2212yes—
42#17988541C2218yes—
43C2×#14556502C2211yescharacteristic
44C2×#14556501C2211yescharacteristic
45C2×C8×Dic73C2211yescharacteristic
46C2×#125×C73C2212yes—
47#499×C73C2218yescomplemented
48C2×#107×C73C2211yescharacteristic
49C2×#107×C73C2211yescharacteristic
50C2×#106×C73C2212yes—
51C2×C4×C8×C73C2211yescharacteristic
52C22×Dic146—22no—
53C22×Dic146—22no—
54C22×C4×D73—22no—
55C22×C4×D73C2311yescharacteristic
56C2×#11924011Q818yescomplemented
57C2×#11924011C2314yes—
58C22×#10596831C2311yescharacteristic
59C22×#10596831C2311yescharacteristic
60C2×C8×D73Q818yescomplemented
61C2×C8×D73C2314yes—
62#14556591—24no—
63#14556591C2318yes—
64#14556590—216no—
65#14556590—24no—
66#14556590C2318yes—
67#14556582—24no—
68#14556582C2318yes—
69#14556581—216no—
70#14556571—216no—
71#14556569—216no—
72#14556549—24no—
73#14556549C2318yes—
74#14556548D414yes—
75#14556548C2314yes—
76C2×C4⋊Dic73—22no—
77C2×C4⋊Dic73—22no—
78C2×C4⋊Dic73C2312yes—
79C2×C4⋊Dic73C2312yes—
80C2×#11924007—22no—
81C2×#11924007—22no—
82C2×#11924007—22no—
83C2×#11924007D411yescharacteristic
84C2×#11924007D411yescharacteristic
85C4⋊C4×D73—24no—
86C4⋊C4×D73C2318yes—
87C2×#11924005—22no—
88C2×#11924005D411yescharacteristic
89C2×#11924005D411yescharacteristic
90C2×C4×Dic73—22no—
91C2×C4×Dic73C2311yescharacteristic
92#14556525C2314yes—
93#14556525C2314yes—
94#14556525C2318yes—
95#14556524C2318yes—
96#14556524C2318yes—
97#14556522C2318yes—
98#14556522C2318yes—
99#14556502C2314yes—
100#14556501C2314yes—
101C8×Dic73C2314yes—
102C22×C8×C73C2311yescharacteristic
103C22×C8×C73C2311yescharacteristic
104#125×C73—24no—
105#125×C73C2318yes—
106C2×C4⋊C4×C73—22no—
107C2×C4⋊C4×C73—22no—
108C2×C4⋊C4×C73C2312yes—
109C2×C4⋊C4×C73C2312yes—
110C2×C42×C73C2311yescharacteristic
111#107×C73C2314yes—
112#107×C73C2314yes—
113#106×C73C2318yes—
114C4×C8×C73C2314yes—
115C23×D73C2×D411yescharacteristic
116C2×Dic146—28no—
117C2×Dic146—28no—
118C2×Dic146—84no—
119C2×Dic146—84no—
120C22×Dic73—22no—
121C22×Dic73—22no—
122C22×Dic73C2×D411yescharacteristic
123C22×Dic73C2×D411yescharacteristic
124C22×Dic73C2×D411yescharacteristic
125C2×C4×D73—28no—
126C2×C4×D73—84no—
127C2×C4×D73C2×D412yes—
128C2×C4×D73C2×Q814yes—
129C2×C4×D73C2×Q814yes—
130C2×C4×D73C2412yes—
131#11924011C2×Q8116yescomplemented
132C2×#10596831C2×Q814yes—
133C2×#10596831C2×Q814yes—
134C2×#10596831C2412yes—
135C2×#10596831C2412yes—
136C8×D73C2×Q8116yescomplemented
137C4⋊Dic73—22no—
138C4⋊Dic73—28no—
139C4⋊Dic73—22no—
140C4⋊Dic73—28no—
141C4⋊Dic73C2414yes—
142C4⋊Dic73C2414yes—
143#11924007—28no—
144#11924007—28no—
145#11924007—28no—
146#11924007C2×D414yes—
147#11924007C2×D414yes—
148#11924005—28no—
149#11924005C2×D414yes—
150#11924005C2×D414yes—
151C4×Dic73—28no—
152C4×Dic73C2×D412yes—
153C4×Dic73C2412yes—
154C22×C4×C73—22no—
155C22×C4×C73—22no—
156C22×C4×C73C2×D411yescharacteristic
157C22×C4×C73C2×D411yescharacteristic
158C22×C4×C73C2411yescharacteristic
159C2×C8×C73C2×Q814yes—
160C2×C8×C73C2×Q814yes—
161C2×C8×C73C2412yes—
162C2×C8×C73C2412yes—
163C4⋊C4×C73—28no—
164C4⋊C4×C73—28no—
165C4⋊C4×C73—22no—
166C4⋊C4×C73—22no—
167C4⋊C4×C73C2414yes—
168C4⋊C4×C73C2414yes—
169C42×C73C2×D412yes—
170C42×C73C2412yes—
171C23×C73C22×D411yescharacteristic
172C22×D73—22no—
173C22×D73—22no—
174C22×D73C4⋊Q814yes—
175C22×D73C22×D412yes—
176C2×C4×C73—22no—
177C2×C4×C73—22no—
178C2×C4×C73—24no—
179C2×C4×C73—24no—
180C2×C4×C73—44no—
181C2×C4×C73—44no—
182C2×C4×C73C22×D412yes—
183C2×C4×C73C22×D412yes—
184C2×C4×C73C22×D411yescharacteristic
185C2×C4×C73C22×Q812yes—
186C2×C4×C73C22×Q812yes—
187C2×C4×C73C2511yescharacteristic
188C2×Dic73—22no—
189C2×Dic73—22no—
190C2×Dic73—24no—
191C2×Dic73—24no—
192C2×Dic73—44no—
193C2×Dic73—44no—
194C2×Dic73C4⋊Q814yes—
195C2×Dic73C22×D412yes—
196C2×Dic73C22×D412yes—
197C2×Dic73C22×D412yes—
198C4×D73—88no—
199C4×D73C4⋊Q818yes—
200C4×D73C22×Q814yes—
201C4×D73C22×Q814yes—
202Dic146—88no—
203Dic146—88no—
204C8×C73C22×Q814yes—
205C8×C73C22×Q814yes—
206#10596831C22×Q814yes—
207#10596831C22×Q814yes—
208C22×C73C2×C4⋊Q812yes—
209C22×C73#57612yes—
210C22×C73#57812yes—
211C22×C73C23×D411yescharacteristic
212C2×D73—28no—
213C2×D73—22no—
214C2×D73—22no—
215C2×D73C2×C4⋊Q814yes—
216C4×C73—22no—
217C4×C73—22no—
218C4×C73—44no—
219C4×C73—44no—
220C4×C73C2×C4⋊Q812yes—
221C4×C73C23×Q811yescharacteristic
222C4×C73C23×Q811yescharacteristic
223Dic73—22no—
224Dic73—22no—
225Dic73—44no—
226Dic73—44no—
227Dic73C2×C4⋊Q814yes—
228C2×#3164—731nomaximal, Sylow
229C2×C73#316414yescomplemented
230C2×C73C22×C4⋊Q811yescharacteristic
231C2×C73C2×#57611yescharacteristic
232C2×C73C2×#57811yescharacteristic
233D73—24no—
234C2×#544—732no—
235#3164—7316no—
236C2×#501—732no—
237C2×#501—732no—
238C2×#500—731no—
239C2×#500—731no—
240C2×#499—731no—
241C2×#499D7311yescharacteristic, complemented
242C2×#428—732no—
243C2×#427—731no—
244C22×#107—731no—
245C2×#405—731no—
246C73C2×#316411yescharacteristic, complemented, Sylow
247C22×M16—731no—
248C23×C8—731no—
249#544—7316no—
250#544—1468no—
251C2×C4⋊Q8—732no—
252C2×C4⋊Q8—732no—
253C2×C4⋊Q8—1462no—
254C2×#125—732no—
255C2×#125—1462no—
256C2×#125C2×D7312yes—
257C2×C22⋊Q8—1462no—
258C2×C22⋊Q8—1462no—
259C2×#117—731no—
260C2×#117—732no—
261C22×C4⋊C4—732no—
262#501—7316no—
263#501—7316no—
264#500—738no—
265#500—738no—
266#499—738no—
267#499C2×D7318yescomplemented
268#428—7316no—
269#427—738no—
270C2×#107—731no—
271C2×#107—731no—
272C2×#107—732no—
273C2×#107—732no—
274C2×#107—732no—
275C2×#107—738no—
276C2×#107C2×D7311yescharacteristic
277C2×#107C2×D7311yescharacteristic
278C2×#106—732no—
279C2×#106—732no—
280C2×#106C2×D7312yes—
281#405—738no—
282C2×#97—731no—
283C2×#97—731no—
284C2×C4×C8—731no—
285C2×C4×C8C2×D7311yescharacteristic
286C22×Q8—1462no—
287C22×Q8—1462no—
288C23×C4—731no—
289C23×C4—1462no—
290C2×M16—738no—
291C2×M16—734no—
292C22×C8—731no—
293C22×C8—731no—
294C22×C8—738no—
295C22×C8—734no—
296C22×C8C22×D7311yescharacteristic
297C22×C8C22×D7311yescharacteristic
298C4⋊Q8—738no—
299C4⋊Q8—738no—
300C4⋊Q8—1464no—
301C4⋊Q8—14616no—
302C4⋊Q8—1464no—
303#125—24no—
304#125—738no—
305#125—1464no—
306#125—14616no—
307#125C22×D7318yes—
308C22⋊Q8—14616no—
309C22⋊Q8—14616no—
310#117—734no—
311#117—734no—
312#117—738no—
313#117—1464no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—731no—
317C2×C4⋊C4—731no—
318C2×C4⋊C4—732no—
319C2×C4⋊C4—732no—
320C2×C4⋊C4—738no—
321C2×C4⋊C4—1464no—
322C2×C4⋊C4—1462no—
323C2×C4⋊C4—1462no—
324C2×C4⋊C4—1462no—
325C2×C4⋊C4—1462no—
326C2×C4⋊C4—1462no—
327C2×C4⋊C4C22×D7312yes—
328C2×C4⋊C4C22×D7312yes—
329C2×C22⋊C4—731no—
330C2×C22⋊C4—731no—
331C2×C22⋊C4—1462no—
332C2×C42—731no—
333C2×C42—1462no—
334C2×C42C22×D7311yescharacteristic
335#107—734no—
336#107—734no—
337#107—738no—
338#107—738no—
339#107—738no—
340#107C22×D7314yes—
341#107C22×D7314yes—
342#106—738no—
343#106—738no—
344#106C22×D7318yes—
345#97—734no—
346#97—734no—
347C4×C8—734no—
348C4×C8C22×D7314yes—
349C24—731no—
350C2×Q8—5844no—
351C2×Q8—5844no—
352C2×Q8—1468no—
353C2×Q8—1468no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—5844no—
357C22×C4—731no—
358C22×C4—732no—
359C22×C4—734no—
360C22×C4—734no—
361C22×C4—732no—
362C22×C4—731no—
363C22×C4—731no—
364C22×C4—1468no—
365C22×C4—1462no—
366C22×C4—1462no—
367C22×C4D4×D7311yescharacteristic
368C22×C4D4×D7311yescharacteristic
369C22×C4C23×D7311yescharacteristic
370M16—7316no—
371C2×C8—734no—
372C2×C8—734no—
373C2×C8—732no—
374C2×C8—732no—
375C2×C8—7316no—
376C2×C8Q8×D7314yes—
377C2×C8Q8×D7314yes—
378C2×C8C23×D7312yes—
379C2×C8C23×D7312yes—
380C4⋊C4—28no—
381C4⋊C4—28no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—734no—
385C4⋊C4—734no—
386C4⋊C4—734no—
387C4⋊C4—734no—
388C4⋊C4—1468no—
389C4⋊C4—1468no—
390C4⋊C4—1468no—
391C4⋊C4—1468no—
392C4⋊C4—1462no—
393C4⋊C4—1462no—
394C4⋊C4—1468no—
395C4⋊C4C23×D7314yes—
396C4⋊C4C23×D7314yes—
397C22⋊C4—734no—
398C22⋊C4—734no—
399C22⋊C4—1468no—
400C42—732no—
401C42—732no—
402C42—1468no—
403C42D4×D7312yes—
404C42C23×D7312yes—
405C23—734no—
406C23—732no—
407C23—1462no—
408C23—1462no—
409C23C2×D4×D7311yescharacteristic
410Q8—5848no—
411Q8—5848no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—2924no—
419C2×C4—2924no—
420C2×C4—5848no—
421C2×C4—734no—
422C2×C4—732no—
423C2×C4—738no—
424C2×C4—734no—
425C2×C4—734no—
426C2×C4—732no—
427C2×C4—732no—
428C2×C4—1464no—
429C2×C4—1464no—
430C2×C4—1462no—
431C2×C4—1462no—
432C2×C4C2×D4×D7312yes—
433C2×C4C2×D4×D7312yes—
434C2×C4C2×D4×D7311yescharacteristic
435C2×C4C2×Q8×D7312yes—
436C2×C4C2×Q8×D7312yes—
437C2×C4C24×D7311yescharacteristic
438C8—734no—
439C8—734no—
440C8C2×Q8×D7314yes—
441C8C2×Q8×D7314yes—
442C22—734no—
443C22—1468no—
444C22—1462no—
445C22—1462no—
446C22C4⋊Q8×D7312yes—
447C22#1798938912yes—
448C22#1798940112yes—
449C22C22×D4×D7311yescharacteristic
450C4—22no—
451C4—22no—
452C4—44no—
453C4—44no—
454C4—2924no—
455C4—2924no—
456C4—734no—
457C4—1462no—
458C4—1462no—
459C4C4⋊Q8×D7312yes—
460C4C22×Q8×D7311yescharacteristic
461C4C22×Q8×D7311yescharacteristic
462C2—1464no—
463C2#2262046814yesdirect product factor
464C2C2×C4⋊Q8×D7311yescharacteristic
465C2C2×#1798938911yescharacteristic
466C2C2×#1798940111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#499×C73C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenterC2×#499D73
hypocenterC73C2×#3164
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
2. #22620468C2direct (N × H)
3. C2×#17988997C2semidirect
4. C2×#17988994C2semidirect
5. C2×#17988992C2semidirect
6. C2×#17988991C2semidirect
7. C2×#17988988C2semidirect
12. C2×#499×C73C2semidirect
27. #17988997C22semidirect
28. #17988994C22semidirect
29. #17988992C22semidirect
30. #17988991C22semidirect
31. #17988988C22semidirect
47. #499×C73C22semidirect
56. C2×#11924011Q8semidirect
60. C2×C8×D73Q8semidirect
131. #11924011C2×Q8semidirect
136. C8×D73C2×Q8semidirect
229. C2×C73#3164semidirect
241. C2×#499D73semidirect
246. C73C2×#3164semidirect
267. #499C2×D73semidirect
463. C2#22620468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892172
#226204682
C2×#179889972
C2×#179889942
C2×#179889922
C2×#179889912
C2×#179889882
C2×#179886262
C2×#179886242
C2×#107×D732
C2×#179885412
C2×#499×C732
C2×#316473