Finite Group Databasebeta

← C2×#22608507 #33053304

Subgroups — C2×#22608507 #33053304

Order 18688.

1074 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989123C211yesmaximal, characteristic
2C2×#17988637C211yesmaximal, characteristic, complemented
3C2×#17988454C211yesmaximal, characteristic, complemented
4#22608507C218yesmaximal, 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×C4×Dic73C2211yescharacteristic
23#17988637—22no—
24#17988637C2214yescomplemented
25C2×#14556520—21no—
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C8×Dic73—21no—
28#17988454—22no—
29#17988454C2214yescomplemented
30C2×#14556498—21no—
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×#11924005—21no—
72C2×#11924005—21no—
73C2×#11924005—21no—
74C2×#11924005—21no—
75C2×C4×Dic73—21no—
76C2×C4×Dic73C2×C412yes—
77C2×C4×Dic73C2×C411yescharacteristic
78C2×C4×Dic73C2×C411yescharacteristic
79C2×C4×Dic73D412yes—
80C2×C4×Dic73D412yes—
81C2×C4×Dic73D411yescharacteristic
82C2×C4×Dic73D411yescharacteristic
83C2×C4×Dic73C2312yes—
84#14556520—24no—
85C22⋊#10596831—21no—
86C22⋊#10596831C2312yes—
87C8×Dic73—24no—
88#14556498—24no—
89#14556498—24no—
90#14556498—21no—
91#14556498C2312yes—
92C22×Q8×C73C2×C411yescharacteristic
93C23×C4×C73—21no—
94C23×C4×C73C2311yescharacteristic
95C22×C8×C73—21no—
96C22⋊Q8×C73—21no—
97C22⋊Q8×C73—21no—
98C22⋊Q8×C73C2×C412yes—
99C22⋊Q8×C73C2312yes—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73C2×C411yescharacteristic
102C2×C22⋊C4×C73—21no—
103C22⋊C8×C73—21no—
104C22⋊C8×C73C2312yes—
105#95×C73—21no—
106#95×C73C2312yes—
107C23×D73—21no—
108C2×D292—21no—
109C2×D292—42no—
110C2×D292C22×C412yes—
111C2×C22⋊D73—22no—
112C2×C22⋊D73—22no—
113C2×C22⋊D73—42no—
114C2×C22⋊D73—42no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—21no—
118C22×Dic73—22no—
119C22×Dic73—42no—
120C22×Dic73—42no—
121C22×Dic73—42no—
122C22×Dic73—42no—
123C22×Dic73C22⋊C411yescharacteristic
124C22×Dic73C22⋊C411yescharacteristic
125C22×Dic73C22⋊C411yescharacteristic
126C22×Dic73C22⋊C411yescharacteristic
127C22×Dic73C22⋊C412yes—
128C22×Dic73C22⋊C412yes—
129C22×Dic73C2×D412yes—
130C22×Dic73C2×D412yes—
131C2×C4×D73—24no—
132C2×C4×D73—44no—
133C2×#10596831—22no—
134C2×#10596831—42no—
135C4⋊Dic73—21no—
136C4⋊Dic73—24no—
137C4⋊Dic73—24no—
138C4⋊Dic73C22×C412yes—
139#11924007—24no—
140#11924005—22no—
141#11924005—22no—
142#11924005—24no—
143#11924005—24no—
144#11924005—24no—
145C4×Dic73—24no—
146C4×Dic73C22⋊C412yes—
147C4×Dic73C22⋊C412yes—
148C4×Dic73C22⋊C412yes—
149C4×Dic73C22⋊C412yes—
150C4×Dic73C22×C412yes—
151C4×Dic73C22×C412yes—
152C4×Dic73C2×D412yes—
153C4×Dic73C2×D412yes—
154C24×C73C2×D411yescharacteristic
155C2×Q8×C73—21no—
156C2×Q8×C73—42no—
157C2×Q8×C73C22×C412yes—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—22no—
161C22×C4×C73—42no—
162C22×C4×C73—42no—
163C22×C4×C73—42no—
164C22×C4×C73—42no—
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C22×C411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2411yescharacteristic
171C2×C8×C73—22no—
172C2×C8×C73—42no—
173C4⋊C4×C73—22no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—22no—
176C4⋊C4×C73C22×C412yes—
177C22⋊C4×C73—22no—
178C22⋊C4×C73—22no—
179C23×C73—22no—
180C23×C73—22no—
181C23×C73C2×C22⋊C411yescharacteristic
182C23×C73C2×C22⋊C411yescharacteristic
183C23×C73#13512yes—
184C23×C73#13512yes—
185C23×C73C22×D411yescharacteristic
186C22×D73—22no—
187C22×D73—42no—
188C22×D73—42no—
189C22×D73—42no—
190Q8×C73—42no—
191Q8×C73—42no—
192C2×C4×C73—22no—
193C2×C4×C73—22no—
194C2×C4×C73—22no—
195C2×C4×C73—22no—
196C2×C4×C73—41no—
197C2×C4×C73—41no—
198C2×C4×C73—41no—
199C2×C4×C73—41no—
200C2×C4×C73—42no—
201C2×C4×C73—42no—
202C2×C4×C73—42no—
203C2×C4×C73—42no—
204C2×C4×C73—42no—
205C2×C4×C73—84no—
206C2×C4×C73C2×C22⋊C411yescharacteristic
207C2×C4×C73C2×C22⋊C411yescharacteristic
208C2×C4×C73C23×C411yescharacteristic
209C2×C4×C73C22×D411yescharacteristic
210C22⋊D73—42no—
211C22⋊D73—42no—
212C22⋊D73—44no—
213C2×Dic73—22no—
214C2×Dic73—22no—
215C2×Dic73—24no—
216C2×Dic73—22no—
217C2×Dic73—22no—
218C2×Dic73—22no—
219C2×Dic73—22no—
220C2×Dic73—22no—
221C2×Dic73—42no—
222C2×Dic73—42no—
223C2×Dic73—42no—
224C2×Dic73—42no—
225C2×Dic73—42no—
226C2×Dic73—42no—
227C2×Dic73—84no—
228C2×Dic73C2×C22⋊C412yes—
229C2×Dic73C2×C22⋊C412yes—
230C2×Dic73C2×C22⋊C412yes—
231C2×Dic73C2×C22⋊C412yes—
232D292—42no—
233D292—42no—
234C4×D73—48no—
235C8×C73—42no—
236#10596831—42no—
237C22×C73—21no—
238C22×C73—21no—
239C22×C73—21no—
240C22×C73—21no—
241C22×C73—24no—
242C22×C73—24no—
243C22×C73#41012yes—
244C22×C73#41612yes—
245C22×C73#41612yes—
246C22×C73#42112yes—
247C22×C73C22×C22⋊C411yescharacteristic
248C22×C73C2×#13511yescharacteristic
249C22×C73C2×#13511yescharacteristic
250C2×D73—42no—
251C2×D73—42no—
252C2×D73—42no—
253C2×D73—84no—
254C4×C73—21no—
255C4×C73—21no—
256C4×C73—21no—
257C4×C73—21no—
258C4×C73—42no—
259C4×C73—42no—
260C4×C73—82no—
261Dic73—22no—
262Dic73—22no—
263Dic73—22no—
264Dic73—22no—
265Dic73—42no—
266Dic73—82no—
267C2×#1521—731nomaximal, Sylow
268C2×C73—21no—
269C2×C73—21no—
270C2×C73—22no—
271C2×C73#152114yescomplemented
272C2×C73C2×#41011yescharacteristic
273C2×C73C2×#41611yescharacteristic
274C2×C73C2×#42111yescharacteristic
275D73—82no—
276C2×#529—731no—
277C2×#431—731no—
278C2×#383—731no—
279#1521—738no—
280C2×#328—731no—
281C2×#328D7311yescharacteristic, complemented
282C2×#327—731no—
283C2×#327—731no—
284C73C2×#152111yescharacteristic, complemented, Sylow
285#529—734no—
286#529—734no—
287#529—1462no—
288#529—1462no—
289C2×#126—1461no—
290C2×#125—731no—
291C2×#124—731no—
292C2×#123—1461no—
293C2×C22⋊Q8C2×D7311yescharacteristic
294C2×#121—731no—
295C2×C4×Q8—731no—
296C2×C4×D4—731no—
297C2×C4×D4—1461no—
298C2×#117—1461no—
299C22×C42—731no—
300#431—734no—
301#431—1462no—
302C2×C4⋊C8—1461no—
303C2×C22⋊C8—731no—
304C2×C22⋊C8C2×D7311yescharacteristic
305C2×C4×C8—1461no—
306#383—734no—
307#383—1462no—
308C2×#95—731no—
309C2×#95—1461no—
310C2×#95—1461no—
311C2×#95C2×D7311yescharacteristic
312#328—734no—
313#328C2×D7314yescomplemented
314#327—734no—
315#327—734no—
316C22×Q8C4×D7311yescharacteristic
317C22×D4—731no—
318C22×D4—1461no—
319C23×C4—21no—
320C23×C4—731no—
321C23×C4—731no—
322C23×C4—1461no—
323C23×C4—1461no—
324C23×C4C22×D7311yescharacteristic
325C22×C8—21no—
326C22×C8—1461no—
327#126—1464no—
328#126—1464no—
329#125—734no—
330#125—1462no—
331#124—734no—
332#124—1462no—
333#123—1464no—
334#123—1464no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8C4×D7312yes—
338C22⋊Q8C22×D7312yes—
339#121—732no—
340#121—732no—
341#121—1461no—
342#121—1461no—
343C4×Q8—734no—
344C4×Q8—1462no—
345C4×D4—734no—
346C4×D4—1462no—
347C4×D4—1464no—
348C4×D4—1464no—
349#117—1464no—
350#117—1464no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—731no—
353C2×C4⋊C4—1461no—
354C2×C4⋊C4—1461no—
355C2×C4⋊C4—1461no—
356C2×C4⋊C4C4×D7311yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—1461no—
359C2×C22⋊C4—1461no—
360C2×C22⋊C4—1461no—
361C2×C22⋊C4—1461no—
362C2×C42—731no—
363C2×C42—731no—
364C2×C42—732no—
365C2×C42—731no—
366C2×C42—731no—
367C2×C42—732no—
368C2×C42—732no—
369C2×C42—732no—
370C2×C42—1461no—
371C4⋊C8—1464no—
372C22⋊C8—21no—
373C22⋊C8—732no—
374C22⋊C8—1461no—
375C22⋊C8C22×D7312yes—
376C4×C8—1464no—
377#95—21no—
378#95—732no—
379#95—1464no—
380#95—1464no—
381#95—1461no—
382#95C22×D7312yes—
383C24—1461no—
384C24D4×D7311yescharacteristic
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8C2×C4×D7312yes—
388C2×D4—2922no—
389C2×D4—2922no—
390C2×D4—2922no—
391C2×D4—732no—
392C2×D4—1462no—
393C2×D4—1462no—
394C2×D4—1461no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—2924no—
403C22×C4—2922no—
404C22×C4—2922no—
405C22×C4—2922no—
406C22×C4—2922no—
407C22×C4—732no—
408C22×C4—732no—
409C22×C4—732no—
410C22×C4—731no—
411C22×C4—731no—
412C22×C4—731no—
413C22×C4—731no—
414C22×C4—732no—
415C22×C4—1464no—
416C22×C4—1462no—
417C22×C4—1461no—
418C22×C4—1462no—
419C22×C4—1462no—
420C22×C4C2×C4×D7311yescharacteristic
421C22×C4C2×C4×D7311yescharacteristic
422C22×C4D4×D7311yescharacteristic
423C22×C4D4×D7311yescharacteristic
424C22×C4D4×D7311yescharacteristic
425C22×C4C23×D7311yescharacteristic
426C2×C8—22no—
427C2×C8—42no—
428C2×C8—2922no—
429C2×C8—1462no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—732no—
434C4⋊C4—1464no—
435C4⋊C4—1464no—
436C4⋊C4—1464no—
437C4⋊C4—1461no—
438C4⋊C4C2×C4×D7312yes—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—1464no—
442C22⋊C4—1464no—
443C22⋊C4—1464no—
444C22⋊C4—1462no—
445C22⋊C4—1462no—
446C42—732no—
447C42—732no—
448C42—732no—
449C42—732no—
450C42—732no—
451C42—732no—
452C42—732no—
453C42—732no—
454C42—1464no—
455C23—22no—
456C23—22no—
457C23—2922no—
458C23—2922no—
459C23—2922no—
460C23—1462no—
461C23C22⋊C4×D7311yescharacteristic
462C23C22⋊C4×D7311yescharacteristic
463C23#1455661212yes—
464C23#1455661412yes—
465C23C2×D4×D7311yescharacteristic
466Q8—42no—
467Q8—42no—
468D4—2922no—
469D4—2922no—
470D4—2924no—
471D4—2922no—
472D4—2922no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—84no—
487C2×C4—2928no—
488C2×C4—2922no—
489C2×C4—2922no—
490C2×C4—2922no—
491C2×C4—2922no—
492C2×C4—2922no—
493C2×C4—2922no—
494C2×C4—5844no—
495C2×C4—732no—
496C2×C4—732no—
497C2×C4—732no—
498C2×C4—732no—
499C2×C4—1462no—
500C2×C4—1464no—
501C2×C4—1462no—
502C2×C4—1462no—
503C2×C4—1462no—
504C2×C4—1462no—
505C2×C4—1462no—
506C2×C4—1462no—
507C2×C4C22⋊C4×D7311yescharacteristic
508C2×C4C22⋊C4×D7311yescharacteristic
509C2×C4C22×C4×D7311yescharacteristic
510C2×C4C2×D4×D7311yescharacteristic
511C8—42no—
512C8—2922no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—24no—
518C22—24no—
519C22—2922no—
520C22—2922no—
521C22—2922no—
522C22—5844no—
523C22#1798855912yes—
524C22#1798858212yes—
525C22#1798858212yes—
526C22#1798860212yes—
527C22C2×C22⋊C4×D7311yescharacteristic
528C22C2×#1455661211yescharacteristic
529C22C2×#1455661411yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—42no—
535C4—42no—
536C4—82no—
537C4—2922no—
538C4—5842no—
539C4—1462no—
540C4—1462no—
541C4—1462no—
542C4—1462no—
543C2—21no—
544C2—21no—
545C2—22no—
546C2—5842no—
547C2#2260850714yesdirect product factor
548C2C2×#1798855911yescharacteristic
549C2C2×#1798858211yescharacteristic
550C2C2×#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×#1521
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×#17988637C2semidirect
3. C2×#17988454C2semidirect
4. #22608507C2direct (N × H)
5. C2×#17988324C2semidirect
8. C2×#328×C73C2semidirect
11. #17989123C4semidirect
14. C2×#14556582C4semidirect
15. C2×#14556580C4semidirect
18. C2×Q8×Dic73C4semidirect
19. C2×#14556553C4semidirect
24. #17988637C22semidirect
29. #17988454C22semidirect
33. #17988324C22semidirect
39. #328×C73C22semidirect
50. #14556582C2×C4semidirect
52. #14556580C2×C4semidirect
60. Q8×Dic73C2×C4semidirect
62. #14556553C2×C4semidirect
271. C2×C73#1521semidirect
281. C2×#328D73semidirect
284. C73C2×#1521semidirect
313. #328C2×D73semidirect
547. C2#22608507direct (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×#179886372
C2×#179884542
#226085072
C2×#179883242
C2×#179883222
C2×#179883202
C2×#328×C732
C2×#152173