Finite Group Databasebeta

← C2×#22608468 #33053225

Subgroups — C2×#22608468 #33053225

Order 18688.

1098 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989123C211yesmaximal, characteristic
2C2×#17988641C211yesmaximal, characteristic, complemented
3C2×#17988451C211yesmaximal, characteristic, complemented
4#22608468C218yesmaximal, direct product factor
5C2×#17988324C211yesmaximal, characteristic, complemented
6C2×#17988322C211yesmaximal, characteristic
7C2×#17988320C211yesmaximal, characteristic
8C2×#328×C73C211yesmaximal, characteristic, complemented
9#17989123—22no—
10#17989123—22no—
11#17989123C414yescomplemented
12#17989123C2214yes—
13C2×#14556586—21no—
14C2×#14556582C411yescharacteristic, complemented
15C2×#14556580C411yescharacteristic, complemented
16C2×#14556575—21no—
17C2×#14556565C2211yescharacteristic
18C2×Q8×Dic73C411yescharacteristic, complemented
19C2×#14556553C411yescharacteristic, complemented
20C2×#14556551—21no—
21C2×#14556549—21no—
22C22×#11924007—21no—
23C22×C4×Dic73C2211yescharacteristic
24#17988641—22no—
25#17988641C2214yescomplemented
26C2×#14556520—21no—
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556501—21no—
29#17988451—22no—
30#17988451C2214yescomplemented
31C2×#14556498—21no—
32C2×#14556498C2211yescharacteristic
33#17988324C2214yescomplemented
34#17988322C2214yes—
35#17988320C2214yes—
36C2×C22⋊Q8×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×#95×C73C2211yescharacteristic
39#328×C73C2214yescomplemented
40C22×D292C2×C411yescharacteristic
41C22×C22⋊D73—21no—
42C23×Dic73—21no—
43C23×Dic73D411yescharacteristic
44C23×Dic73D411yescharacteristic
45C22×C4×D73—21no—
46C22×#10596831—21no—
47#14556586—24no—
48#14556586—24no—
49#14556582—22no—
50#14556582C2×C414yescomplemented
51#14556580—22no—
52#14556580C2×C414yescomplemented
53#14556575—24no—
54#14556575—24no—
55#14556565—21no—
56#14556565—21no—
57#14556565C2×C412yes—
58#14556565C2312yes—
59Q8×Dic73—22no—
60Q8×Dic73C2×C414yescomplemented
61#14556553—22no—
62#14556553C2×C414yescomplemented
63#14556551—24no—
64#14556551—24no—
65#14556549—24no—
66#14556549—24no—
67C2×C4⋊Dic73—21no—
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73C2×C411yescharacteristic
70C2×#11924007—21no—
71C2×#11924007—24no—
72C2×#11924007—44no—
73C2×#11924005—21no—
74C2×#11924005—21no—
75C2×#11924005—21no—
76C2×#11924005—21no—
77C2×C4×Dic73—21no—
78C2×C4×Dic73C2×C412yes—
79C2×C4×Dic73C2×C411yescharacteristic
80C2×C4×Dic73C2×C411yescharacteristic
81C2×C4×Dic73D412yes—
82C2×C4×Dic73D412yes—
83C2×C4×Dic73D411yescharacteristic
84C2×C4×Dic73D411yescharacteristic
85C2×C4×Dic73C2312yes—
86#14556520—24no—
87C22⋊#10596831—21no—
88C22⋊#10596831C2312yes—
89#14556501—24no—
90#14556498—24no—
91#14556498—21no—
92#14556498C2312yes—
93C22×Q8×C73C2×C411yescharacteristic
94C23×C4×C73—21no—
95C23×C4×C73C2311yescharacteristic
96C22×C8×C73—21no—
97C22⋊Q8×C73—21no—
98C22⋊Q8×C73—21no—
99C22⋊Q8×C73C2×C412yes—
100C22⋊Q8×C73C2312yes—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73C2×C411yescharacteristic
103C2×C22⋊C4×C73—21no—
104C22⋊C8×C73—21no—
105C22⋊C8×C73C2312yes—
106#95×C73—21no—
107#95×C73C2312yes—
108C23×D73—21no—
109C2×D292—21no—
110C2×D292—42no—
111C2×D292C22×C412yes—
112C2×C22⋊D73—22no—
113C2×C22⋊D73—22no—
114C2×C22⋊D73—42no—
115C2×C22⋊D73—42no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—21no—
119C22×Dic73—22no—
120C22×Dic73—42no—
121C22×Dic73—42no—
122C22×Dic73—42no—
123C22×Dic73—42no—
124C22×Dic73C22⋊C411yescharacteristic
125C22×Dic73C22⋊C411yescharacteristic
126C22×Dic73C22⋊C411yescharacteristic
127C22×Dic73C22⋊C411yescharacteristic
128C22×Dic73C22⋊C412yes—
129C22×Dic73C22⋊C412yes—
130C22×Dic73C2×D412yes—
131C22×Dic73C2×D412yes—
132C2×C4×D73—24no—
133C2×C4×D73—44no—
134C2×#10596831—22no—
135C2×#10596831—42no—
136C4⋊Dic73—21no—
137C4⋊Dic73—24no—
138C4⋊Dic73—24no—
139C4⋊Dic73C22×C412yes—
140#11924007—24no—
141#11924007—48no—
142#11924005—22no—
143#11924005—22no—
144#11924005—24no—
145#11924005—24no—
146#11924005—24no—
147C4×Dic73—24no—
148C4×Dic73C22⋊C412yes—
149C4×Dic73C22⋊C412yes—
150C4×Dic73C22⋊C412yes—
151C4×Dic73C22⋊C412yes—
152C4×Dic73C22×C412yes—
153C4×Dic73C22×C412yes—
154C4×Dic73C2×D412yes—
155C4×Dic73C2×D412yes—
156C24×C73C2×D411yescharacteristic
157C2×Q8×C73—21no—
158C2×Q8×C73—42no—
159C2×Q8×C73C22×C412yes—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—22no—
163C22×C4×C73—42no—
164C22×C4×C73—42no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73C22×C411yescharacteristic
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2411yescharacteristic
173C2×C8×C73—22no—
174C2×C8×C73—42no—
175C4⋊C4×C73—22no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—22no—
178C4⋊C4×C73C22×C412yes—
179C22⋊C4×C73—22no—
180C22⋊C4×C73—22no—
181C23×C73—22no—
182C23×C73—22no—
183C23×C73C2×C22⋊C411yescharacteristic
184C23×C73C2×C22⋊C411yescharacteristic
185C23×C73AGL(1,ℤ/8)12yes—
186C23×C73#13712yes—
187C23×C73C22×D411yescharacteristic
188C22×D73—22no—
189C22×D73—42no—
190C22×D73—42no—
191C22×D73—42no—
192Q8×C73—42no—
193Q8×C73—42no—
194C2×C4×C73—22no—
195C2×C4×C73—22no—
196C2×C4×C73—22no—
197C2×C4×C73—22no—
198C2×C4×C73—41no—
199C2×C4×C73—41no—
200C2×C4×C73—41no—
201C2×C4×C73—41no—
202C2×C4×C73—42no—
203C2×C4×C73—42no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×C4×C73—42no—
207C2×C4×C73—84no—
208C2×C4×C73C2×C22⋊C411yescharacteristic
209C2×C4×C73C2×C22⋊C411yescharacteristic
210C2×C4×C73C23×C411yescharacteristic
211C2×C4×C73C22×D411yescharacteristic
212C22⋊D73—42no—
213C22⋊D73—42no—
214C22⋊D73—44no—
215C2×Dic73—22no—
216C2×Dic73—22no—
217C2×Dic73—24no—
218C2×Dic73—22no—
219C2×Dic73—22no—
220C2×Dic73—22no—
221C2×Dic73—22no—
222C2×Dic73—22no—
223C2×Dic73—42no—
224C2×Dic73—42no—
225C2×Dic73—42no—
226C2×Dic73—42no—
227C2×Dic73—42no—
228C2×Dic73—42no—
229C2×Dic73—84no—
230C2×Dic73C2×C22⋊C412yes—
231C2×Dic73C2×C22⋊C412yes—
232C2×Dic73C2×C22⋊C412yes—
233C2×Dic73C2×C22⋊C412yes—
234D292—42no—
235D292—42no—
236C4×D73—48no—
237C8×C73—42no—
238#10596831—42no—
239C22×C73—21no—
240C22×C73—21no—
241C22×C73—21no—
242C22×C73—21no—
243C22×C73—24no—
244C22×C73—24no—
245C22×C73#41012yes—
246C22×C73#41712yes—
247C22×C73#41712yes—
248C22×C73#42112yes—
249C22×C73C22×C22⋊C411yescharacteristic
250C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C73C2×#13711yescharacteristic
252C2×D73—42no—
253C2×D73—42no—
254C2×D73—42no—
255C2×D73—84no—
256C4×C73—21no—
257C4×C73—21no—
258C4×C73—21no—
259C4×C73—21no—
260C4×C73—42no—
261C4×C73—42no—
262C4×C73—82no—
263Dic73—22no—
264Dic73—22no—
265Dic73—22no—
266Dic73—22no—
267Dic73—42no—
268Dic73—82no—
269C2×#1512—731nomaximal, Sylow
270C2×C73—21no—
271C2×C73—21no—
272C2×C73—22no—
273C2×C73#151214yescomplemented
274C2×C73C2×#41011yescharacteristic
275C2×C73C2×#41711yescharacteristic
276C2×C73C2×#42111yescharacteristic
277D73—82no—
278C2×#529—731no—
279C2×#432—731no—
280C2×#382—731no—
281#1512—738no—
282C2×#328—731no—
283C2×#328D7311yescharacteristic, complemented
284C2×#327—731no—
285C2×#327—731no—
286C73C2×#151211yescharacteristic, complemented, Sylow
287#529—734no—
288#529—734no—
289#529—1462no—
290#529—1462no—
291C2×#126—1461no—
292C2×#125—731no—
293C2×#124—731no—
294C2×#123—1461no—
295C2×C22⋊Q8C2×D7311yescharacteristic
296C2×#121—731no—
297C2×C4×Q8—731no—
298C2×C4×D4—731no—
299C2×C4×D4—1461no—
300C2×#117—1461no—
301C22×C4⋊C4—1461no—
302C22×C42—731no—
303#432—734no—
304#432—1462no—
305C2×C4⋊C8—1461no—
306C2×C22⋊C8—731no—
307C2×C22⋊C8C2×D7311yescharacteristic
308C2×#97—1461no—
309#382—734no—
310#382—1462no—
311C2×#95—731no—
312C2×#95—1461no—
313C2×#95C2×D7311yescharacteristic
314#328—734no—
315#328C2×D7314yescomplemented
316#327—734no—
317#327—734no—
318C22×Q8C4×D7311yescharacteristic
319C22×D4—731no—
320C22×D4—1461no—
321C23×C4—21no—
322C23×C4—731no—
323C23×C4—731no—
324C23×C4—1461no—
325C23×C4—1461no—
326C23×C4C22×D7311yescharacteristic
327C22×C8—21no—
328C22×C8—1461no—
329#126—1464no—
330#126—1464no—
331#125—734no—
332#125—1462no—
333#124—734no—
334#124—1462no—
335#123—1464no—
336#123—1464no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8C4×D7312yes—
340C22⋊Q8C22×D7312yes—
341#121—732no—
342#121—732no—
343#121—1461no—
344#121—1461no—
345C4×Q8—734no—
346C4×Q8—1462no—
347C4×D4—734no—
348C4×D4—1462no—
349C4×D4—1464no—
350C4×D4—1464no—
351#117—1464no—
352#117—1464no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—2924no—
355C2×C4⋊C4—731no—
356C2×C4⋊C4—1464no—
357C2×C4⋊C4—1461no—
358C2×C4⋊C4—1461no—
359C2×C4⋊C4—1461no—
360C2×C4⋊C4C4×D7311yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—1461no—
363C2×C22⋊C4—1461no—
364C2×C22⋊C4—1461no—
365C2×C22⋊C4—1461no—
366C2×C42—731no—
367C2×C42—731no—
368C2×C42—732no—
369C2×C42—731no—
370C2×C42—731no—
371C2×C42—732no—
372C2×C42—732no—
373C2×C42—732no—
374C2×C42—1461no—
375C4⋊C8—1464no—
376C22⋊C8—21no—
377C22⋊C8—732no—
378C22⋊C8—1461no—
379C22⋊C8C22×D7312yes—
380#97—1464no—
381#95—21no—
382#95—732no—
383#95—1464no—
384#95—1461no—
385#95C22×D7312yes—
386C24—1461no—
387C24D4×D7311yescharacteristic
388C2×Q8—21no—
389C2×Q8—42no—
390C2×Q8C2×C4×D7312yes—
391C2×D4—2922no—
392C2×D4—2922no—
393C2×D4—2922no—
394C2×D4—732no—
395C2×D4—1462no—
396C2×D4—1462no—
397C2×D4—1461no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—2924no—
406C22×C4—2922no—
407C22×C4—2922no—
408C22×C4—2922no—
409C22×C4—2922no—
410C22×C4—732no—
411C22×C4—732no—
412C22×C4—732no—
413C22×C4—731no—
414C22×C4—731no—
415C22×C4—731no—
416C22×C4—731no—
417C22×C4—732no—
418C22×C4—1464no—
419C22×C4—1462no—
420C22×C4—1461no—
421C22×C4—1462no—
422C22×C4—1462no—
423C22×C4C2×C4×D7311yescharacteristic
424C22×C4C2×C4×D7311yescharacteristic
425C22×C4D4×D7311yescharacteristic
426C22×C4D4×D7311yescharacteristic
427C22×C4D4×D7311yescharacteristic
428C22×C4C23×D7311yescharacteristic
429C2×C8—22no—
430C2×C8—42no—
431C2×C8—2922no—
432C2×C8—1462no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—2928no—
437C4⋊C4—732no—
438C4⋊C4—1464no—
439C4⋊C4—1464no—
440C4⋊C4—1464no—
441C4⋊C4—1461no—
442C4⋊C4C2×C4×D7312yes—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—1464no—
446C22⋊C4—1464no—
447C22⋊C4—1464no—
448C22⋊C4—1462no—
449C22⋊C4—1462no—
450C42—732no—
451C42—732no—
452C42—732no—
453C42—732no—
454C42—732no—
455C42—732no—
456C42—732no—
457C42—732no—
458C42—1464no—
459C23—22no—
460C23—22no—
461C23—2922no—
462C23—2922no—
463C23—2922no—
464C23—1462no—
465C23C22⋊C4×D7311yescharacteristic
466C23C22⋊C4×D7311yescharacteristic
467C23#1455661812yes—
468C23#1455662312yes—
469C23C2×D4×D7311yescharacteristic
470Q8—42no—
471Q8—42no—
472D4—2922no—
473D4—2922no—
474D4—2922no—
475D4—2924no—
476D4—2922no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—84no—
491C2×C4—2928no—
492C2×C4—2922no—
493C2×C4—2922no—
494C2×C4—2922no—
495C2×C4—2922no—
496C2×C4—2922no—
497C2×C4—2922no—
498C2×C4—5844no—
499C2×C4—732no—
500C2×C4—732no—
501C2×C4—732no—
502C2×C4—732no—
503C2×C4—1462no—
504C2×C4—1462no—
505C2×C4—1464no—
506C2×C4—1462no—
507C2×C4—1462no—
508C2×C4—1462no—
509C2×C4—1462no—
510C2×C4—1462no—
511C2×C4C22⋊C4×D7311yescharacteristic
512C2×C4C22⋊C4×D7311yescharacteristic
513C2×C4C22×C4×D7311yescharacteristic
514C2×C4C2×D4×D7311yescharacteristic
515C8—42no—
516C8—2922no—
517C22—21no—
518C22—21no—
519C22—24no—
520C22—24no—
521C22—21no—
522C22—21no—
523C22—2922no—
524C22—2922no—
525C22—2922no—
526C22—5844no—
527C22#1798855912yes—
528C22#1798858712yes—
529C22#1798858712yes—
530C22#1798860212yes—
531C22C2×C22⋊C4×D7311yescharacteristic
532C22C2×#1455661811yescharacteristic
533C22C2×#1455662311yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—42no—
540C4—82no—
541C4—2922no—
542C4—5842no—
543C4—1462no—
544C4—1462no—
545C4—1462no—
546C4—1462no—
547C2—21no—
548C2—21no—
549C2—22no—
550C2—5842no—
551C2#2260846814yesdirect product factor
552C2C2×#1798855911yescharacteristic
553C2C2×#1798858711yescharacteristic
554C2C2×#1798860211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#328×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556565C22
cosocleC22×C4×C73C24
hypercenterC2×#328D73
hypocenterC73C2×#1512
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#17988641C2semidirect
3. C2×#17988451C2semidirect
4. #22608468C2direct (N × H)
5. C2×#17988324C2semidirect
8. C2×#328×C73C2semidirect
11. #17989123C4semidirect
14. C2×#14556582C4semidirect
15. C2×#14556580C4semidirect
18. C2×Q8×Dic73C4semidirect
19. C2×#14556553C4semidirect
25. #17988641C22semidirect
30. #17988451C22semidirect
33. #17988324C22semidirect
39. #328×C73C22semidirect
50. #14556582C2×C4semidirect
52. #14556580C2×C4semidirect
60. Q8×Dic73C2×C4semidirect
62. #14556553C2×C4semidirect
273. C2×C73#1512semidirect
283. C2×#328D73semidirect
286. C73C2×#1512semidirect
315. #328C2×D73semidirect
551. C2#22608468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891232
C2×#179886412
C2×#179884512
#226084682
C2×#179883242
C2×#179883222
C2×#179883202
C2×#328×C732
C2×#151273