Finite Group Databasebeta

← C2×#22622546 #33964722

Subgroups — C2×#22622546 #33964722

Order 18688.

1866 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989307C211yesmaximal, characteristic
2#22622546C2116yesmaximal, direct product factor
3C2×#17988983C211yesmaximal, characteristic, complemented
4C2×#17988925C212yesmaximal, complemented
5C2×#17988917C212yesmaximal, complemented
6C2×#17988879C211yesmaximal, characteristic, complemented
7C2×#17988872C211yesmaximal, characteristic, complemented
8C2×#17988843C212yesmaximal, complemented
9C2×C4×#11924018C211yesmaximal, characteristic, complemented
10C2×#17988665C211yesmaximal, characteristic
11C2×#17988627C212yesmaximal, complemented
12C2×#554×C73C211yesmaximal, characteristic
13C22×#11924018C2211yescharacteristic
14C22×#11924012C2212yes—
15#17989307—24no—
16#17989307C2218yes—
17C2×#14556591C2211yescharacteristic
18C2×#14556584—22no—
19C2×#14556578—21no—
20C2×#14556570C2212yes—
21C2×C4×Dic146C2211yescharacteristic
22C2×#14556556—21no—
23C2×#14556550C2212yes—
24#17988983C2218yescomplemented
25#17988925C22116yescomplemented
26#17988917C22116yescomplemented
27#17988879C2218yescomplemented
28#17988872C2218yescomplemented
29#17988843C22116yescomplemented
30C4×#11924018C2218yescomplemented
31#17988665C2218yes—
32#17988627C22116yescomplemented
33C2×#14556524C2212yes—
34C2×#14556524C2211yescharacteristic
35C2×#14556522C2212yes—
36C2×#14556522C2212yes—
37C2×#14556522C2212yes—
38C2×C4⋊#10596831C2211yescharacteristic
39C2×#14556515C2212yes—
40C2×#14556515C2211yescharacteristic
41C2×#14556514C2212yes—
42C2×#14556514C2211yescharacteristic
43C2×C22⋊#10596831C2212yes—
44C2×C4×#10596831C2211yescharacteristic
45#554×C73—24no—
46#554×C73C2218yes—
47C2×C4⋊Q8×C73C2211yescharacteristic
48C2×#125×C73—21no—
49C2×C22⋊Q8×C73—22no—
50C2×C22⋊Q8×C73C2212yes—
51C2×C4×Q8×C73C2211yescharacteristic
52C2×C4×D4×C73—21no—
53C2×C4×D4×C73C2211yescharacteristic
54C22×C4⋊C4×C73C2212yes—
55C22×Dic146—21no—
56C22×Dic146C2311yescharacteristic
57C2×#11924018—24no—
58C2×#11924018C2314yes—
59C2×#11924012—28no—
60C2×#11924012C2318yes—
61C22×#10596831C2312yes—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64#14556591—22no—
65#14556591C2314yes—
66#14556584—216no—
67#14556578—28no—
68#14556570—24no—
69#14556570C2318yes—
70C4×Dic146—22no—
71C4×Dic146C2314yes—
72#14556556—28no—
73#14556550—24no—
74#14556550C2318yes—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73C2312yes—
77C2×C4⋊Dic73C2311yescharacteristic
78C2×#11924007—22no—
79C2×#11924007—21no—
80C2×C22⋊Dic73—22no—
81C2×C22⋊Dic73—22no—
82C2×C4×Dic73—22no—
83C2×C4×Dic73—21no—
84#14556524C2318yes—
85#14556524C2314yes—
86#14556522C2318yes—
87#14556522C2318yes—
88#14556522C2318yes—
89C4⋊#10596831C2314yes—
90#14556515C2318yes—
91#14556515C2314yes—
92#14556514C2318yes—
93#14556514C2314yes—
94C22⋊#10596831C2318yes—
95C4×#10596831C2314yes—
96C22×Q8×C73—21no—
97C22×Q8×C73C2311yescharacteristic
98C22×D4×C73D411yescharacteristic
99C23×C4×C73—22no—
100C23×C4×C73C2312yes—
101C4⋊Q8×C73—22no—
102C4⋊Q8×C73C2314yes—
103#125×C73—28no—
104C22⋊Q8×C73—24no—
105C22⋊Q8×C73—216no—
106C22⋊Q8×C73C2318yes—
107C4×Q8×C73—22no—
108C4×Q8×C73C2314yes—
109C4×D4×C73—28no—
110C4×D4×C73D414yes—
111C4×D4×C73C2314yes—
112C2×C4⋊C4×C73—22no—
113C2×C4⋊C4×C73—24no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73—22no—
117C2×C4⋊C4×C73D411yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2312yes—
120C2×C4⋊C4×C73C2318yes—
121C2×C22⋊C4×C73—22no—
122C2×C22⋊C4×C73D412yes—
123C2×C42×C73—21no—
124C2×C42×C73C2311yescharacteristic
125C2×Dic146—22no—
126C2×Dic146—22no—
127C2×Dic146—24no—
128C2×Dic146—21no—
129C2×Dic146—44no—
130C2×Dic146C2412yes—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—22no—
134#11924018—28no—
135#11924012—216no—
136C2×#10596831—24no—
137C2×#10596831—22no—
138C2×#10596831#4114yes—
139C2×#10596831C2412yes—
140C2×#10596831C2414yes—
141C2×#10596831C2412yes—
142C4⋊Dic73—24no—
143C4⋊Dic73—21no—
144C4⋊Dic73—22no—
145C4⋊Dic73C2414yes—
146C4⋊Dic73C2412yes—
147#11924007—28no—
148#11924007—24no—
149C22⋊Dic73—28no—
150C22⋊Dic73—28no—
151C4×Dic73—28no—
152C4×Dic73—24no—
153C24×C73C2×D412yes—
154C2×Q8×C73—21no—
155C2×Q8×C73—24no—
156C2×Q8×C73—22no—
157C2×Q8×C73—22no—
158C2×Q8×C73—82no—
159C2×Q8×C73C2412yes—
160C2×D4×C73—24no—
161C2×D4×C73C2×D414yes—
162C22×C4×C73—24no—
163C22×C4×C73—24no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—22no—
167C22×C4×C73—28no—
168C22×C4×C73—84no—
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D412yes—
171C22×C4×C73C2×D414yes—
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2414yes—
174C22×C4×C73C2411yescharacteristic
175C4⋊C4×C73—21no—
176C4⋊C4×C73—28no—
177C4⋊C4×C73—22no—
178C4⋊C4×C73—24no—
179C4⋊C4×C73—24no—
180C4⋊C4×C73—28no—
181C4⋊C4×C73C2×D414yes—
182C4⋊C4×C73C2412yes—
183C4⋊C4×C73C2414yes—
184C22⋊C4×C73—28no—
185C22⋊C4×C73C2×D418yes—
186C42×C73—24no—
187C42×C73C2×D412yes—
188C42×C73C2412yes—
189C23×C73—24no—
190C23×C73—24no—
191C23×C73—24no—
192C23×C73C22×D414yes—
193C23×C73C22×D411yescharacteristic
194Q8×C73—22no—
195Q8×C73—22no—
196Q8×C73—42no—
197Q8×C73—84no—
198D4×C73—28no—
199C2×C4×C73—24no—
200C2×C4×C73—22no—
201C2×C4×C73—28no—
202C2×C4×C73—24no—
203C2×C4×C73—24no—
204C2×C4×C73—22no—
205C2×C4×C73—22no—
206C2×C4×C73—24no—
207C2×C4×C73—42no—
208C2×C4×C73—42no—
209C2×C4×C73—44no—
210C2×C4×C73—88no—
211C2×C4×C73#13714yes—
212C2×C4×C73C22×D412yes—
213C2×C4×C73C22×D414yes—
214C2×C4×C73C22×D411yescharacteristic
215C2×C4×C73C22×D412yes—
216C2×C4×C73C2×#4112yes—
217C2×C4×C732−1+412yes—
218C2×C4×C73C2511yescharacteristic
219C2×Dic73—22no—
220C2×Dic73—22no—
221C2×Dic73—24no—
222C2×Dic73—42no—
223C2×Dic73—44no—
224C2×Dic73—42no—
225Dic146—22no—
226Dic146—22no—
227Dic146—42no—
228Dic146—48no—
229#10596831—24no—
230#10596831—22no—
231#10596831C2×#4114yes—
232C22×C73—24no—
233C22×C73—24no—
234C22×C73—24no—
235C22×C73—48no—
236C22×C73#54712yes—
237C22×C73C2×#13712yes—
238C22×C73#57712yes—
239C22×C73C23×D411yescharacteristic
240C4×C73—24no—
241C4×C73—22no—
242C4×C73—42no—
243C4×C73—42no—
244C4×C73—44no—
245C4×C73#54712yes—
246C4×C73C2×#13714yes—
247C4×C73C22×#4111yescharacteristic
248C4×C73C2×2−1+411yescharacteristic
249Dic73—42no—
250Dic73—44no—
251Dic73—42no—
252C2×#3356—731nomaximal, Sylow
253C2×C73—44no—
254C2×C73#335614yescomplemented
255C2×C73C2×#54711yescharacteristic
256C2×C73C22×#13711yescharacteristic
257C2×C73C2×#57711yescharacteristic
258C2×#556—731no—
259C2×#554D7311yescharacteristic
260#3356—7316no—
261C2×#498—731no—
262C2×#485—732no—
263C2×#483—732no—
264C2×#477—731no—
265C2×#475—731no—
266C2×#470—732no—
267C2×C4×Q16—731no—
268C2×#436—731no—
269C2×#428—732no—
270C73C2×#335611yescharacteristic, complemented, Sylow
271C22×Q16—731no—
272C22×M16—732no—
273#556—738no—
274#556—1464no—
275#554—24no—
276#554C2×D7318yes—
277C2×C4⋊Q8—731no—
278C2×C4⋊Q8C2×D7311yescharacteristic
279C2×#126—1462no—
280C2×#125—21no—
281C2×#124—1461no—
282C2×C22⋊Q8—22no—
283C2×C22⋊Q8—732no—
284C2×C22⋊Q8C2×D7312yes—
285C2×C4×Q8—731no—
286C2×C4×Q8—1461no—
287C2×C4×Q8C2×D7311yescharacteristic
288C2×C4×D4—21no—
289C2×C4×D4C2×D7311yescharacteristic
290C2×#117—732no—
291C22×C4⋊C4C2×D7312yes—
292#498—738no—
293#485—7316no—
294#483—7316no—
295#477—738no—
296#475—738no—
297#470—7316no—
298C4×Q16—738no—
299#436—738no—
300#428—7316no—
301C2×#107—732no—
302C2×#107—731no—
303C2×#106—732no—
304C2×#106—732no—
305C2×#106—732no—
306C2×C4⋊C8—731no—
307C2×#103—732no—
308C2×#103—731no—
309C2×#103—732no—
310C2×#103—731no—
311C2×C22⋊C8—732no—
312C2×C4×C8—731no—
313C22×Q8—21no—
314C22×Q8—731no—
315C22×Q8—1461no—
316C22×Q8C22×D7311yescharacteristic
317C22×D4C22⋊D7311yescharacteristic
318C23×C4—22no—
319C23×C4C22×D7312yes—
320C2×Q16—734no—
321C2×Q16—1464no—
322C2×M16—738no—
323C2×M16—1468no—
324C22×C8—731no—
325C22×C8—732no—
326C22×C8—731no—
327C4⋊Q8—22no—
328C4⋊Q8—734no—
329C4⋊Q8—1462no—
330C4⋊Q8C22×D7314yes—
331#126—14616no—
332#125—28no—
333#124—1468no—
334C22⋊Q8—24no—
335C22⋊Q8—216no—
336C22⋊Q8—738no—
337C22⋊Q8—1464no—
338C22⋊Q8C22×D7318yes—
339C4×Q8—22no—
340C4×Q8—734no—
341C4×Q8—1468no—
342C4×Q8—1462no—
343C4×Q8C22×D7314yes—
344C4×D4—28no—
345C4×D4C22⋊D7314yes—
346C4×D4C22×D7314yes—
347#117—738no—
348#117—1464no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—731no—
355C2×C4⋊C4—732no—
356C2×C4⋊C4—1461no—
357C2×C4⋊C4—1462no—
358C2×C4⋊C4—1461no—
359C2×C4⋊C4C22⋊D7311yescharacteristic
360C2×C4⋊C4C22×D7311yescharacteristic
361C2×C4⋊C4C22×D7312yes—
362C2×C4⋊C4C22×D7318yes—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—1462no—
365C2×C22⋊C4—1462no—
366C2×C22⋊C4C22⋊D7312yes—
367C2×C42—21no—
368C2×C42—1462no—
369C2×C42—1461no—
370C2×C42C22×D7311yescharacteristic
371#107—734no—
372#107—738no—
373#106—738no—
374#106—738no—
375#106—738no—
376C4⋊C8—734no—
377#103—734no—
378#103—738no—
379#103—734no—
380#103—738no—
381C22⋊C8—738no—
382C4×C8—734no—
383C24C2×C22⋊D7312yes—
384C2×Q8—21no—
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—82no—
389C2×Q8—2924no—
390C2×Q8—732no—
391C2×Q8—1462no—
392C2×Q8—1462no—
393C2×Q8—1461no—
394C2×Q8—1464no—
395C2×Q8C23×D7312yes—
396C2×D4—24no—
397C2×D4C2×C22⋊D7314yes—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—28no—
404C22×C4—84no—
405C22×C4—1461no—
406C22×C4—1462no—
407C22×C4—1461no—
408C22×C4C2×C22⋊D7314yes—
409C22×C4C2×C22⋊D7312yes—
410C22×C4C2×C22⋊D7311yescharacteristic
411C22×C4C2×C22⋊D7311yescharacteristic
412C22×C4C23×D7314yes—
413C22×C4C23×D7311yescharacteristic
414Q16—1468no—
415M16—14616no—
416C2×C8—734no—
417C2×C8—732no—
418C2×C8—732no—
419C2×C8—734no—
420C2×C8—1464no—
421C2×C8—1462no—
422C4⋊C4—21no—
423C4⋊C4—28no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—28no—
428C4⋊C4—734no—
429C4⋊C4—732no—
430C4⋊C4—1464no—
431C4⋊C4—1468no—
432C4⋊C4—1461no—
433C4⋊C4—1462no—
434C4⋊C4—1464no—
435C4⋊C4C2×C22⋊D7314yes—
436C4⋊C4C23×D7312yes—
437C4⋊C4C23×D7314yes—
438C22⋊C4—28no—
439C22⋊C4—1468no—
440C22⋊C4—1468no—
441C22⋊C4C2×C22⋊D7318yes—
442C42—24no—
443C42—1468no—
444C42—1464no—
445C42C2×C22⋊D7312yes—
446C42C23×D7312yes—
447C23—24no—
448C23—24no—
449C23—24no—
450C23C22×C22⋊D7314yes—
451C23C22×C22⋊D7311yescharacteristic
452Q8—22no—
453Q8—22no—
454Q8—42no—
455Q8—84no—
456Q8—2928no—
457Q8—2922no—
458Q8—1462no—
459Q8—1462no—
460D4—28no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—28no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—42no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—88no—
473C2×C4—2924no—
474C2×C4—2922no—
475C2×C4—2922no—
476C2×C4—1462no—
477C2×C4—1464no—
478C2×C4—1462no—
479C2×C4#1455662214yes—
480C2×C4C22×C22⋊D7314yes—
481C2×C4C22×C22⋊D7312yes—
482C2×C4C22×C22⋊D7312yes—
483C2×C4C22×C22⋊D7311yescharacteristic
484C2×C4#41×D7312yes—
485C2×C4#1455663812yes—
486C2×C4C24×D7311yescharacteristic
487C8—734no—
488C8—1464no—
489C8—1462no—
490C22—24no—
491C22—24no—
492C22—24no—
493C22—48no—
494C22#1798923612yes—
495C22C2×#1455662212yes—
496C22#1798939812yes—
497C22C23×C22⋊D7311yescharacteristic
498C4—24no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—44no—
503C4—2922no—
504C4—2924no—
505C4—2922no—
506C4#1798923612yes—
507C4C2×#1455662214yes—
508C4C2×#41×D7311yescharacteristic
509C4C2×#1455663811yescharacteristic
510C2—44no—
511C2#2262254614yesdirect product factor
512C2C2×#1798923611yescharacteristic
513C2C22×#1455662211yescharacteristic
514C2C2×#1798939811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#554×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
hypercenterC2×#554D73
hypocenterC73C2×#3356
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #22622546C2direct (N × H)
3. C2×#17988983C2semidirect
4. C2×#17988925C2semidirect
5. C2×#17988917C2semidirect
6. C2×#17988879C2semidirect
7. C2×#17988872C2semidirect
8. C2×#17988843C2semidirect
9. C2×C4×#11924018C2semidirect
11. C2×#17988627C2semidirect
24. #17988983C22semidirect
25. #17988925C22semidirect
26. #17988917C22semidirect
27. #17988879C22semidirect
28. #17988872C22semidirect
29. #17988843C22semidirect
30. C4×#11924018C22semidirect
32. #17988627C22semidirect
254. C2×C73#3356semidirect
270. C73C2×#3356semidirect
511. C2#22622546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893072
#226225462
C2×#179889832
C2×#179889252
C2×#179889172
C2×#179888792
C2×#179888722
C2×#179888432
C2×C4×#119240182
C2×#179886652
C2×#179886272
C2×#554×C732
C2×#335673