Finite Group Databasebeta

← C2×#22622810 #33966427

Subgroups — C2×#22622810 #33966427

Order 18688.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989312C211yesmaximal, characteristic, complemented
2C2×#17989294C211yesmaximal, characteristic
3#22622810C2116yesmaximal, direct product factor
4C2×#17988988C212yesmaximal, complemented
5C2×#17988983C211yesmaximal, characteristic, complemented
6C2×#17988893C212yesmaximal, complemented
7C2×#17988883C211yesmaximal, characteristic, complemented
8C2×#17988885C212yesmaximal
9C2×#17988711C211yesmaximal, characteristic, complemented
10C2×#17988678C212yesmaximal
11C2×C4×#11924016C211yesmaximal, characteristic
12C2×#474×C73C211yesmaximal, characteristic
13C22×#11924016C2211yescharacteristic
14#17989312—24no—
15#17989312C2218yescomplemented
16#17989294—24no—
17#17989294C2218yes—
18C2×#14556591C2211yescharacteristic
19C2×#14556589—21no—
20C2×#14556582C2212yes—
21C2×#14556582C2212yes—
22C2×#14556581—22no—
23C2×#14556570—21no—
24C2×#14556568—22no—
25C2×Q8×Dic73—21no—
26C2×C4×Dic146C2211yescharacteristic
27C2×C4×Dic146C2211yescharacteristic
28C2×#14556556C2212yes—
29C2×D4×Dic73C2212yes—
30C22×C4⋊Dic73—21no—
31#17988988C22116yescomplemented
32#17988983C2218yescomplemented
33#17988893C22116yescomplemented
34#17988885C22116yes—
35#17988883C2218yescomplemented
36#17988711C2218yescomplemented
37#17988678C22116yes—
38C4×#11924016C2218yes—
39C2×#14556525C2212yes—
40C2×#14556522C2212yes—
41C2×#14556522C2212yes—
42C2×#14556522C2211yescharacteristic
43C2×#14556520C2212yes—
44C2×#14556516C2212yes—
45C2×#14556514C2211yescharacteristic
46C2×#14556512C2211yescharacteristic
47C2×C4×#10596831C2211yescharacteristic
48C2×C8×Dic73C2212yes—
49C2×C4⋊Q8×C73C2211yescharacteristic
50C2×C4×D4×C73C2211yescharacteristic
51#474×C73C2218yes—
52C2×#107×C73C2212yes—
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×#102×C73C2212yes—
55C22×Dic146—21no—
56C22×Dic146D411yescharacteristic
57C22×Dic146C2311yescharacteristic
58C23×Dic73—22no—
59C2×#11924016Q818yescomplemented
60C2×#11924016C2314yes—
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63#14556591—22no—
64#14556591C2314yes—
65#14556589—28no—
66#14556582—24no—
67#14556582—24no—
68#14556582C2318yes—
69#14556582C2318yes—
70#14556581—216no—
71#14556570—28no—
72#14556568—216no—
73Q8×Dic73—28no—
74C4×Dic146—22no—
75C4×Dic146D414yes—
76C4×Dic146C2314yes—
77C4×Dic146C2314yes—
78#14556556—24no—
79#14556556C2318yes—
80D4×Dic73—24no—
81D4×Dic73C2318yes—
82C2×C4⋊Dic73—22no—
83C2×C4⋊Dic73—22no—
84C2×C4⋊Dic73—28no—
85C2×C4⋊Dic73—21no—
86C2×C4⋊Dic73D411yescharacteristic
87C2×C4⋊Dic73C2312yes—
88C2×C4⋊Dic73C2311yescharacteristic
89C2×#11924007—22no—
90C2×#11924007—22no—
91C2×#11924007—22no—
92C2×#11924007—21no—
93C2×#11924007D412yes—
94C2×C22⋊Dic73—22no—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—21no—
97C2×C4×Dic73C2312yes—
98#14556525C2318yes—
99#14556522C2318yes—
100#14556522C2314yes—
101#14556522C2318yes—
102#14556520C2318yes—
103#14556516C2318yes—
104#14556514C2314yes—
105#14556512C2314yes—
106C4×#10596831C2314yes—
107C8×Dic73C2318yes—
108C22×Q8×C73—21no—
109C22×D4×C73C2311yescharacteristic
110C23×C4×C73—21no—
111C22×C8×C73C2312yes—
112C4⋊Q8×C73—22no—
113C4⋊Q8×C73C2314yes—
114C4×D4×C73—22no—
115C4×D4×C73C2314yes—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73C2312yes—
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C22⋊C4×C73—21no—
120C2×C42×C73C2311yescharacteristic
121#107×C73C2318yes—
122C4⋊C8×C73C2314yes—
123#102×C73C2318yes—
124C2×Dic146—24no—
125C2×Dic146—21no—
126C2×Dic146—22no—
127C2×Dic146—24no—
128C2×Dic146—82no—
129C2×Dic146C2×D414yes—
130C2×Dic146C2×Q814yes—
131C2×Dic146C2412yes—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—22no—
135C22×Dic73—28no—
136C22×Dic73—84no—
137C22×Dic73C2×D412yes—
138C22×Dic73C2×D412yes—
139#11924016C2×Q8116yescomplemented
140C2×#10596831—22no—
141C2×#10596831C2×Q814yes—
142C2×#10596831C2412yes—
143C2×#10596831C2412yes—
144C4⋊Dic73—24no—
145C4⋊Dic73—22no—
146C4⋊Dic73—21no—
147C4⋊Dic73—28no—
148C4⋊Dic73—28no—
149C4⋊Dic73C2×D414yes—
150C4⋊Dic73C2412yes—
151C4⋊Dic73C2414yes—
152#11924007—24no—
153#11924007—28no—
154#11924007—28no—
155#11924007—28no—
156#11924007C2×D418yes—
157C22⋊Dic73—28no—
158C4×Dic73—24no—
159C4×Dic73—28no—
160C4×Dic73C2×D414yes—
161C4×Dic73C2414yes—
162C24×C73—21no—
163C2×Q8×C73—24no—
164C2×Q8×C73—44no—
165C2×D4×C73—21no—
166C2×D4×C73—22no—
167C2×D4×C73C2×Q814yes—
168C2×D4×C73C2412yes—
169C22×C4×C73—21no—
170C22×C4×C73—22no—
171C22×C4×C73—24no—
172C22×C4×C73—44no—
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2411yescharacteristic
176C2×C8×C73—24no—
177C2×C8×C73C2414yes—
178C4⋊C4×C73—24no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—22no—
181C4⋊C4×C73C2414yes—
182C4⋊C4×C73C2412yes—
183C22⋊C4×C73—24no—
184C42×C73C2×D412yes—
185C42×C73C2412yes—
186C23×C73—24no—
187C23×C73—22no—
188C23×C73—42no—
189C23×C73—42no—
190C23×C73C22×D411yescharacteristic
191Q8×C73—48no—
192D4×C73—24no—
193D4×C73—22no—
194D4×C73C22×Q814yes—
195C2×C4×C73—22no—
196C2×C4×C73—22no—
197C2×C4×C73—24no—
198C2×C4×C73—42no—
199C2×C4×C73—44no—
200C2×C4×C73—48no—
201C2×C4×C73#13514yes—
202C2×C4×C73C22×D412yes—
203C2×C4×C73C22×D411yescharacteristic
204C2×C4×C73C22×D412yes—
205C2×C4×C73C22×Q812yes—
206C2×C4×C732−1+412yes—
207C2×C4×C73C2511yescharacteristic
208C2×Dic73—24no—
209C2×Dic73—24no—
210C2×Dic73—24no—
211C2×Dic73—22no—
212C2×Dic73—22no—
213C2×Dic73—24no—
214C2×Dic73—42no—
215C2×Dic73—44no—
216C2×Dic73—88no—
217C2×Dic73C22×D414yes—
218C2×Dic73C22×D414yes—
219Dic146—24no—
220Dic146—28no—
221Dic146—22no—
222Dic146—84no—
223Dic146C22×Q814yes—
224C8×C73—24no—
225#10596831—22no—
226#10596831C22×Q814yes—
227C22×C73—24no—
228C22×C73—48no—
229C22×C73—42no—
230C22×C73—42no—
231C22×C73D4×Q812yes—
232C22×C73C2×#13512yes—
233C22×C73#57712yes—
234C22×C73C23×D411yescharacteristic
235C4×C73—22no—
236C4×C73—42no—
237C4×C73—44no—
238C4×C73D4×Q812yes—
239C4×C73C2×#13514yes—
240C4×C73C23×Q811yescharacteristic
241C4×C73C2×2−1+411yescharacteristic
242Dic73—24no—
243Dic73—24no—
244Dic73—24no—
245Dic73—44no—
246Dic73—42no—
247C2×#3381—731nomaximal, Sylow
248C2×C73—44no—
249C2×C73#338114yescomplemented
250C2×C73C2×D4×Q811yescharacteristic
251C2×C73C22×#13511yescharacteristic
252C2×C73C2×#57711yescharacteristic
253C2×#557—731no—
254C2×#554—731no—
255#3381—7316no—
256C2×#499—732no—
257C2×#498—731no—
258C2×#479—732no—
259C2×#477—731no—
260C2×#478—732no—
261C2×#474D7311yescharacteristic
262C2×C8×Q8—731no—
263C2×C4×SD16—732no—
264C2×C4×SD16—731no—
265C73C2×#338111yescharacteristic, complemented, Sylow
266C22×SD16—731no—
267#557—738no—
268#557—1464no—
269#554—738no—
270#554—1464no—
271C2×C4⋊Q8—731no—
272C2×C4⋊Q8—1461no—
273C2×C4⋊Q8C2×D7311yescharacteristic
274C2×#125—732no—
275C2×#125—732no—
276C2×#125—1462no—
277C2×C22⋊Q8—1462no—
278C2×C22⋊Q8—1461no—
279C2×C4×Q8—731no—
280C2×C4×Q8—732no—
281C2×C4×Q8—731no—
282C2×C4×Q8—1461no—
283C2×C4×D4—732no—
284C2×C4×D4C2×D7311yescharacteristic
285C22×C4⋊C4—1461no—
286#499—7316no—
287#498—738no—
288#479—7316no—
289#478—7316no—
290#477—738no—
291#474C2×D7318yes—
292C8×Q8—738no—
293C4×SD16—738no—
294C4×SD16—7316no—
295C2×#107—732no—
296C2×#107C2×D7312yes—
297C2×#106—732no—
298C2×#106—732no—
299C2×#106—731no—
300C2×C4⋊C8—732no—
301C2×C4⋊C8C2×D7311yescharacteristic
302C2×#103—732no—
303C2×#103—731no—
304C2×#102—731no—
305C2×#102C2×D7312yes—
306C2×C4×C8—732no—
307C2×C4×C8—731no—
308C22×Q8—21no—
309C22×Q8—731no—
310C22×Q8—731no—
311C22×Q8—1461no—
312C22×D4C22×D7311yescharacteristic
313C23×C4—21no—
314C23×C4—1462no—
315C2×SD16—738no—
316C2×SD16—734no—
317C22×C8—731no—
318C22×C8—731no—
319C22×C8C22×D7312yes—
320C4⋊Q8—22no—
321C4⋊Q8—734no—
322C4⋊Q8—1468no—
323C4⋊Q8—1462no—
324C4⋊Q8C22×D7314yes—
325#125—738no—
326#125—738no—
327#125—1464no—
328#125—1464no—
329#125—14616no—
330C22⋊Q8—14616no—
331C22⋊Q8—1468no—
332C4×Q8—734no—
333C4×Q8—734no—
334C4×Q8—738no—
335C4×Q8—734no—
336C4×Q8—1464no—
337C4×Q8—1468no—
338C4×Q8—1462no—
339C4×D4—22no—
340C4×D4—738no—
341C4×D4—1464no—
342C4×D4C22×D7314yes—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—731no—
345C2×C4⋊C4—732no—
346C2×C4⋊C4—732no—
347C2×C4⋊C4—731no—
348C2×C4⋊C4—1468no—
349C2×C4⋊C4—1462no—
350C2×C4⋊C4—1462no—
351C2×C4⋊C4—1462no—
352C2×C4⋊C4—1462no—
353C2×C4⋊C4—1462no—
354C2×C4⋊C4—1461no—
355C2×C4⋊C4—1461no—
356C2×C4⋊C4C22×D7311yescharacteristic
357C2×C4⋊C4C22×D7312yes—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—1462no—
360C2×C42—732no—
361C2×C42—1462no—
362C2×C42—1461no—
363C2×C42C22×D7311yescharacteristic
364#107—738no—
365#107C22×D7318yes—
366#106—738no—
367#106—734no—
368#106—738no—
369C4⋊C8—738no—
370C4⋊C8C22×D7314yes—
371#103—738no—
372#103—734no—
373#102—734no—
374#102C22×D7318yes—
375C4×C8—738no—
376C4×C8—734no—
377C24—21no—
378C2×Q8—24no—
379C2×Q8—44no—
380C2×Q8—5842no—
381C2×Q8—734no—
382C2×Q8—734no—
383C2×Q8—732no—
384C2×Q8—1464no—
385C2×Q8—1464no—
386C2×Q8—1461no—
387C2×Q8—1462no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4Q8×D7314yes—
391C2×D4C23×D7312yes—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—24no—
395C22×C4—44no—
396C22×C4—5844no—
397C22×C4—732no—
398C22×C4—732no—
399C22×C4—1461no—
400C22×C4—1462no—
401C22×C4—1468no—
402C22×C4—1461no—
403C22×C4D4×D7311yescharacteristic
404C22×C4D4×D7311yescharacteristic
405C22×C4C23×D7311yescharacteristic
406SD16—7316no—
407C2×C8—24no—
408C2×C8—734no—
409C2×C8—732no—
410C2×C8—732no—
411C2×C8—1462no—
412C2×C8C23×D7314yes—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—738no—
417C4⋊C4—734no—
418C4⋊C4—732no—
419C4⋊C4—734no—
420C4⋊C4—1468no—
421C4⋊C4—1468no—
422C4⋊C4—1468no—
423C4⋊C4—1468no—
424C4⋊C4—1468no—
425C4⋊C4—1464no—
426C4⋊C4—1462no—
427C4⋊C4—1461no—
428C4⋊C4—1464no—
429C4⋊C4C23×D7314yes—
430C4⋊C4C23×D7312yes—
431C22⋊C4—24no—
432C22⋊C4—1468no—
433C42—734no—
434C42—734no—
435C42—1468no—
436C42—1464no—
437C42D4×D7312yes—
438C42C23×D7312yes—
439C23—22no—
440C23—24no—
441C23—42no—
442C23—42no—
443C23C2×D4×D7311yescharacteristic
444Q8—48no—
445Q8—5844no—
446Q8—734no—
447Q8—1462no—
448Q8—1464no—
449Q8—1468no—
450D4—22no—
451D4—24no—
452D4C2×Q8×D7314yes—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—48no—
459C2×C4—2924no—
460C2×C4—2922no—
461C2×C4—5848no—
462C2×C4—734no—
463C2×C4—734no—
464C2×C4—1462no—
465C2×C4—1464no—
466C2×C4—1464no—
467C2×C4—1462no—
468C2×C4—1464no—
469C2×C4—1464no—
470C2×C4#1455661014yes—
471C2×C4C2×D4×D7312yes—
472C2×C4C2×D4×D7311yescharacteristic
473C2×C4C2×D4×D7312yes—
474C2×C4C2×Q8×D7312yes—
475C2×C4#1455663812yes—
476C2×C4C24×D7311yescharacteristic
477C8—24no—
478C8—734no—
479C8—1462no—
480C22—24no—
481C22—48no—
482C22—42no—
483C22—42no—
484C22#1798925012yes—
485C22C2×#1455661012yes—
486C22#1798939612yes—
487C22C22×D4×D7311yescharacteristic
488C4—22no—
489C4—42no—
490C4—44no—
491C4—2924no—
492C4—2922no—
493C4—1464no—
494C4—1464no—
495C4—1464no—
496C4#1798925012yes—
497C4C2×#1455661014yes—
498C4C22×Q8×D7311yescharacteristic
499C4C2×#1455663811yescharacteristic
500C2—44no—
501C2#2262281014yesdirect product factor
502C2C2×#1798925011yescharacteristic
503C2C22×#1455661011yescharacteristic
504C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#474×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
hypercenterC2×#474D73
hypocenterC73C2×#3381
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#17989312C2semidirect
3. #22622810C2direct (N × H)
4. C2×#17988988C2semidirect
5. C2×#17988983C2semidirect
6. C2×#17988893C2semidirect
7. C2×#17988883C2semidirect
9. C2×#17988711C2semidirect
15. #17989312C22semidirect
31. #17988988C22semidirect
32. #17988983C22semidirect
33. #17988893C22semidirect
35. #17988883C22semidirect
36. #17988711C22semidirect
59. C2×#11924016Q8semidirect
139. #11924016C2×Q8semidirect
249. C2×C73#3381semidirect
265. C73C2×#3381semidirect
501. C2#22622810direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893122
C2×#179892942
#226228102
C2×#179889882
C2×#179889832
C2×#179888932
C2×#179888832
C2×#179888852
C2×#179887112
C2×#179886782
C2×C4×#119240162
C2×#474×C732
C2×#338173