Finite Group Databasebeta

← C2×#22619789 #33953573

Subgroups — C2×#22619789 #33953573

Order 18688.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989067C211yesmaximal, characteristic
2#22619789C2116yesmaximal, direct product factor
3C2×#17988891C212yesmaximal, complemented
4C2×#17988869C212yesmaximal, complemented
5C2×#17988884C212yesmaximal, complemented
6C2×#17988874C212yesmaximal, complemented
7C2×#17988630C211yesmaximal, characteristic, complemented
8C22×#14556522C211yesmaximal, characteristic, complemented
9C2×#17988614C211yesmaximal, characteristic, complemented
10C2×#17988586C211yesmaximal, characteristic
11C2×#17988581C211yesmaximal, characteristic
12C2×#544×C73C211yesmaximal, characteristic, complemented
13C22×#11924028C2211yescharacteristic
14C22×#11924012C2211yescharacteristic
15C23×#10596831C2211yescharacteristic
16#17989067—24no—
17#17989067C2218yes—
18C2×C4×Dic146C2212yes—
19C2×C4×D292C2212yes—
20C2×#14556551—22no—
21C2×#14556549—21no—
22C22×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊C4×D73—21no—
24#17988891C22116yescomplemented
25#17988884C22116yescomplemented
26#17988874C22116yescomplemented
27#17988869C22116yescomplemented
28#17988630C2218yescomplemented
29C2×#14556524C2212yes—
30C2×#14556522C2212yes—
31C2×#14556522C2212yes—
32C2×#14556522C2212yes—
33C2×#14556522C2218yescomplemented
34#17988614C2218yescomplemented
35C2×C4⋊#10596831C2212yes—
36C2×C4⋊#10596831C2212yes—
37#17988586C2218yes—
38#17988581C2218yes—
39C2×#14556514C2211yescharacteristic
40C2×#14556514C2212yes—
41C2×#14556514C2211yescharacteristic
42C2×#14556511C2211yescharacteristic
43C2×#14556511C2212yes—
44C2×#14556511C2211yescharacteristic
45#544×C73—24no—
46#544×C73C2218yescomplemented
47C2×C4⋊Q8×C73—21no—
48C2×C4⋊Q8×C73C2212yes—
49C2×#125×C73—21no—
50C2×#125×C73C2212yes—
51C2×C22⋊Q8×C73—22no—
52C2×#117×C73C2211yescharacteristic
53C2×#117×C73C2211yescharacteristic
54C22×C4⋊C4×C73C2211yescharacteristic
55C2×#11924028—22no—
56C2×#11924028—24no—
57C2×#11924028Q818yescomplemented
58C2×#11924028C2314yes—
59C22×Dic146C2311yescharacteristic
60C22×D292C2311yescharacteristic
61C22×C22⋊D73—21no—
62C23×Dic73—21no—
63C22×C4×D73—21no—
64C22×C4×D73—22no—
65C2×#11924012—24no—
66C2×#11924012C2314yes—
67C22×#10596831—24no—
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2312yes—
71C22×#10596831C2314yes—
72C4×Dic146—24no—
73C4×Dic146C2318yes—
74C4×D292—24no—
75C4×D292C2318yes—
76#14556551—216no—
77#14556549—28no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—22no—
80C2×C4⋊Dic73C2312yes—
81C2×C4⋊Dic73C2314yes—
82C2×#11924007—22no—
83C4⋊C4×D73—28no—
84C2×#11924005—22no—
85C2×C4×Dic73—22no—
86#14556524C2318yes—
87#14556522C2318yes—
88#14556522C2318yes—
89#14556522C2318yes—
90C4⋊#10596831C2318yes—
91C4⋊#10596831C2318yes—
92#14556514C2314yes—
93#14556514C2318yes—
94#14556514C2314yes—
95#14556511C2314yes—
96#14556511C2318yes—
97#14556511C2314yes—
98C22×Q8×C73—22no—
99C23×C4×C73—21no—
100C23×C4×C73C2311yescharacteristic
101C4⋊Q8×C73—28no—
102C4⋊Q8×C73—24no—
103C4⋊Q8×C73C2318yes—
104#125×C73—28no—
105#125×C73—24no—
106#125×C73C2318yes—
107C22⋊Q8×C73—216no—
108#117×C73—22no—
109#117×C73D414yes—
110#117×C73C2314yes—
111#117×C73C2314yes—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73—22no—
114C2×C4⋊C4×C73—22no—
115C2×C4⋊C4×C73—22no—
116C2×C4⋊C4×C73—22no—
117C2×C4⋊C4×C73D411yescharacteristic
118C2×C4⋊C4×C73D411yescharacteristic
119C2×C4⋊C4×C73C2312yes—
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2314yes—
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73D412yes—
125C2×C42×C73—21no—
126C2×C42×C73C2312yes—
127C23×D73—21no—
128#11924028—216no—
129#11924028—28no—
130#11924028C2×Q8116yescomplemented
131C2×Dic146—21no—
132C2×Dic146—22no—
133C2×Dic146C2×Q814yes—
134C2×Dic146C2412yes—
135C2×D292—21no—
136C2×D292—22no—
137C2×D292C2×Q814yes—
138C2×D292C2412yes—
139C2×C22⋊D73—28no—
140C2×C22⋊D73—24no—
141C22×Dic73—21no—
142C22×Dic73—22no—
143C22×Dic73—24no—
144C22×Dic73—82no—
145C2×C4×D73—28no—
146C2×C4×D73—24no—
147C2×C4×D73—28no—
148C2×C4×D73—84no—
149#11924012—28no—
150C2×#10596831—22no—
151C2×#10596831—22no—
152C2×#10596831—28no—
153C2×#10596831—24no—
154C2×#10596831C2412yes—
155C2×#10596831C2412yes—
156C2×#10596831C2414yes—
157C4⋊Dic73—24no—
158C4⋊Dic73—22no—
159C4⋊Dic73C2414yes—
160#11924007—28no—
161#11924005—28no—
162C4×Dic73—28no—
163C24×C73C2×D411yescharacteristic
164C2×Q8×C73—28no—
165C2×Q8×C73—84no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—22no—
169C22×C4×C73—24no—
170C22×C4×C73—82no—
171C22×C4×C73C2×D412yes—
172C22×C4×C73C2×D412yes—
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D412yes—
175C22×C4×C73C2×Q814yes—
176C22×C4×C73#4114yes—
177C22×C4×C73C2411yescharacteristic
178C22×C4×C73C2412yes—
179C4⋊C4×C73—24no—
180C4⋊C4×C73—22no—
181C4⋊C4×C73—28no—
182C4⋊C4×C73—28no—
183C4⋊C4×C73—28no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73C2×D414yes—
187C4⋊C4×C73C2×D414yes—
188C4⋊C4×C73C2414yes—
189C4⋊C4×C73C2412yes—
190C4⋊C4×C73C2412yes—
191C22⋊C4×C73—24no—
192C22⋊C4×C73C2×D418yes—
193C42×C73—24no—
194C42×C73C2×D414yes—
195C42×C73C2414yes—
196C23×C73—22no—
197C23×C73—22no—
198C23×C73C22⋊Q814yes—
199C23×C73C22×D412yes—
200C23×C73C22×D411yescharacteristic
201C22×D73—24no—
202C22×D73—22no—
203C22×D73—42no—
204C22×D73—42no—
205Q8×C73—88no—
206C2×C4×C73—24no—
207C2×C4×C73—24no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—24no—
211C2×C4×C73—42no—
212C2×C4×C73—44no—
213C2×C4×C73—42no—
214C2×C4×C73—84no—
215C2×C4×C73C22⋊Q814yes—
216C2×C4×C73C22⋊Q818yes—
217C2×C4×C73C22×D414yes—
218C2×C4×C73C22×D414yes—
219C2×C4×C73C22×D412yes—
220C2×C4×C73C22×D411yescharacteristic
221C2×C4×C73C22×Q812yes—
222C2×C4×C73C22×Q814yes—
223C2×C4×C73C2×#4112yes—
224C2×C4×C73C2×#4114yes—
225C2×C4×C73C2511yescharacteristic
226C22⋊D73—216no—
227C2×Dic73—24no—
228C2×Dic73—22no—
229C2×Dic73—24no—
230C2×Dic73—44no—
231C2×Dic73—84no—
232D292—24no—
233D292—22no—
234D292C22×Q814yes—
235C4×D73—216no—
236C4×D73—88no—
237Dic146—24no—
238Dic146—22no—
239Dic146C22×Q814yes—
240#10596831—22no—
241#10596831—22no—
242#10596831—24no—
243C22×C73—28no—
244C22×C73—22no—
245C22×C73—22no—
246C22×C73C2×C22⋊Q814yes—
247C22×C73C2×C22⋊Q812yes—
248C22×C73#57712yes—
249C22×C73#57712yes—
250C22×C73C23×D411yescharacteristic
251C2×D73—24no—
252C2×D73—48no—
253C2×D73—42no—
254C2×D73—42no—
255C4×C73—24no—
256C4×C73—24no—
257C4×C73—42no—
258C4×C73—44no—
259C4×C73—42no—
260C4×C73C2×C22⋊Q812yes—
261C4×C73C2×C22⋊Q814yes—
262C4×C73C23×Q811yescharacteristic
263C4×C73C22×#4111yescharacteristic
264Dic73—24no—
265Dic73—44no—
266C2×#3084—731nomaximal, Sylow
267C2×C73—24no—
268C2×C73#308414yescomplemented
269C2×C73C22×C22⋊Q811yescharacteristic
270C2×C73C2×#57711yescharacteristic
271C2×C73C2×#57711yescharacteristic
272D73—44no—
273C2×#544D7311yescharacteristic, complemented
274C2×#520—731no—
275#3084—7316no—
276C2×#479—732no—
277C2×#475—732no—
278C2×#478—732no—
279C2×#476—732no—
280C2×#428—731no—
281C22×#106—731no—
282C2×#424—731no—
283C2×#417—731no—
284C2×#416—731no—
285C73C2×#308411yescharacteristic, complemented, Sylow
286C22×#41—731no—
287C22×M16—731no—
288C23×C8—731no—
289#544—24no—
290#544C2×D7318yescomplemented
291C2×C4⋊Q8—21no—
292C2×C4⋊Q8C2×D7312yes—
293C2×#125—21no—
294C2×#125C2×D7312yes—
295C2×C22⋊Q8—22no—
296#520—738no—
297#520—1464no—
298C2×C4×Q8—732no—
299C2×C4×D4—732no—
300C2×C4×D4—1462no—
301C2×#117—1461no—
302C2×#117C2×D7311yescharacteristic
303C2×#117C2×D7311yescharacteristic
304C22×C4⋊C4—731no—
305C22×C4⋊C4—1461no—
306C22×C4⋊C4C2×D7311yescharacteristic
307#479—7316no—
308#478—7316no—
309#476—7316no—
310#475—7316no—
311#428—738no—
312C2×#107—732no—
313C2×#106—732no—
314C2×#106—732no—
315C2×#106—732no—
316C2×#106—738no—
317#424—738no—
318C2×C4⋊C8—732no—
319C2×C4⋊C8—732no—
320#417—738no—
321#416—738no—
322C2×#103—731no—
323C2×#103—732no—
324C2×#103—731no—
325C2×#102—731no—
326C2×#102—732no—
327C2×#102—731no—
328C2×#41—738no—
329C2×#41—734no—
330C2×#41—1462no—
331C2×#41—1464no—
332C22×Q8—22no—
333C22×Q8—731no—
334C22×D4—731no—
335C22×D4—1461no—
336C23×C4—21no—
337C23×C4—1461no—
338C23×C4—1462no—
339C23×C4—1461no—
340C23×C4C22×D7311yescharacteristic
341C2×M16—734no—
342C2×M16—1464no—
343C22×C8—731no—
344C22×C8—731no—
345C22×C8—734no—
346C22×C8—732no—
347C22×C8—1464no—
348C4⋊Q8—28no—
349C4⋊Q8—24no—
350C4⋊Q8C22×D7318yes—
351#125—28no—
352#125—24no—
353#125C22×D7318yes—
354C22⋊Q8—216no—
355C4×Q8—738no—
356C4×Q8—1464no—
357C4×D4—738no—
358C4×D4—14616no—
359C4×D4—1464no—
360#117—22no—
361#117—1468no—
362#117C22⋊D7314yes—
363#117C22×D7314yes—
364#117C22×D7314yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—732no—
371C2×C4⋊C4—734no—
372C2×C4⋊C4—1461no—
373C2×C4⋊C4—1462no—
374C2×C4⋊C4—1462no—
375C2×C4⋊C4—1468no—
376C2×C4⋊C4C22⋊D7311yescharacteristic
377C2×C4⋊C4C22⋊D7311yescharacteristic
378C2×C4⋊C4C22×D7312yes—
379C2×C4⋊C4C22×D7314yes—
380C2×C4⋊C4C22×D7311yescharacteristic
381C2×C4⋊C4C22×D7311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—1462no—
384C2×C22⋊C4C22⋊D7312yes—
385C2×C42—21no—
386C2×C42—1462no—
387C2×C42C22×D7312yes—
388#107—738no—
389#106—738no—
390#106—738no—
391#106—738no—
392C4⋊C8—738no—
393C4⋊C8—738no—
394#103—734no—
395#103—734no—
396#103—738no—
397#102—734no—
398#102—734no—
399#102—738no—
400C24—1461no—
401C24C2×C22⋊D7311yescharacteristic
402#41—7316no—
403#41—14616no—
404#41—1468no—
405C2×Q8—28no—
406C2×Q8—84no—
407C2×Q8—734no—
408C2×Q8—732no—
409C2×Q8—1461no—
410C2×Q8—1462no—
411C2×D4—734no—
412C2×D4—732no—
413C2×D4—1468no—
414C2×D4—1464no—
415C2×D4—1461no—
416C2×D4—1462no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—82no—
422C22×C4—5844no—
423C22×C4—5842no—
424C22×C4—1462no—
425C22×C4—1464no—
426C22×C4—1468no—
427C22×C4—1461no—
428C22×C4—1468no—
429C22×C4—1464no—
430C22×C4C2×C22⋊D7312yes—
431C22×C4C2×C22⋊D7312yes—
432C22×C4C2×C22⋊D7312yes—
433C22×C4C2×C22⋊D7311yescharacteristic
434C22×C4Q8×D7314yes—
435C22×C4#1192402914yes—
436C22×C4C23×D7312yes—
437C22×C4C23×D7311yescharacteristic
438M16—1468no—
439C2×C8—732no—
440C2×C8—732no—
441C2×C8—734no—
442C2×C8—1462no—
443C2×C8—1462no—
444C2×C8—1468no—
445C2×C8—1464no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—28no—
449C4⋊C4—28no—
450C4⋊C4—28no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—734no—
454C4⋊C4—1468no—
455C4⋊C4—1464no—
456C4⋊C4—1462no—
457C4⋊C4C2×C22⋊D7314yes—
458C4⋊C4C2×C22⋊D7314yes—
459C4⋊C4C23×D7314yes—
460C4⋊C4C23×D7312yes—
461C4⋊C4C23×D7312yes—
462C22⋊C4—24no—
463C22⋊C4—1468no—
464C22⋊C4C2×C22⋊D7318yes—
465C42—24no—
466C42—1468no—
467C42C2×C22⋊D7314yes—
468C42C23×D7314yes—
469C23—22no—
470C23—22no—
471C23—2922no—
472C23—2922no—
473C23—1462no—
474C23—1464no—
475C23#1455656714yes—
476C23C22×C22⋊D7312yes—
477C23C22×C22⋊D7311yescharacteristic
478Q8—88no—
479Q8—734no—
480Q8—1462no—
481Q8—1464no—
482D4—734no—
483D4—14616no—
484D4—1462no—
485D4—1464no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—84no—
495C2×C4—2924no—
496C2×C4—5848no—
497C2×C4—5844no—
498C2×C4—1464no—
499C2×C4—1462no—
500C2×C4—1464no—
501C2×C4—14616no—
502C2×C4#1455656714yes—
503C2×C4#1455656718yes—
504C2×C4C22×C22⋊D7314yes—
505C2×C4C22×C22⋊D7314yes—
506C2×C4C22×C22⋊D7312yes—
507C2×C4C22×C22⋊D7311yescharacteristic
508C2×C4C2×Q8×D7312yes—
509C2×C4C2×Q8×D7314yes—
510C2×C4C2×#1192402912yes—
511C2×C4C2×#1192402914yes—
512C2×C4C24×D7311yescharacteristic
513C8—1462no—
514C8—1462no—
515C8—1464no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—2928no—
520C22—2922no—
521C22—2922no—
522C22—1464no—
523C22C2×#1455656714yes—
524C22C2×#1455656712yes—
525C22#1798939512yes—
526C22#1798939812yes—
527C22C23×C22⋊D7311yescharacteristic
528C4—24no—
529C4—24no—
530C4—42no—
531C4—44no—
532C4—42no—
533C4—2924no—
534C4—1464no—
535C4C2×#1455656714yes—
536C4C2×#1455656712yes—
537C4C22×Q8×D7311yescharacteristic
538C4C22×#1192402911yescharacteristic
539C2—24no—
540C2—2924no—
541C2#2261978914yesdirect product factor
542C2C22×#1455656711yescharacteristic
543C2C2×#1798939511yescharacteristic
544C2C2×#1798939811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#544×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924028C22
hypercenterC2×#544D73
hypocenterC73C2×#3084
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #22619789C2direct (N × H)
3. C2×#17988891C2semidirect
4. C2×#17988869C2semidirect
5. C2×#17988884C2semidirect
6. C2×#17988874C2semidirect
7. C2×#17988630C2semidirect
8. C22×#14556522C2semidirect
9. C2×#17988614C2semidirect
12. C2×#544×C73C2semidirect
24. #17988891C22semidirect
25. #17988884C22semidirect
26. #17988874C22semidirect
27. #17988869C22semidirect
28. #17988630C22semidirect
33. C2×#14556522C22semidirect
34. #17988614C22semidirect
46. #544×C73C22semidirect
57. C2×#11924028Q8semidirect
130. #11924028C2×Q8semidirect
268. C2×C73#3084semidirect
273. C2×#544D73semidirect
285. C73C2×#3084semidirect
290. #544C2×D73semidirect
541. C2#22619789direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890672
#226197892
C2×#179888912
C2×#179888692
C2×#179888842
C2×#179888742
C2×#179886302
C22×#145565222
C2×#179886142
C2×#179885862
C2×#179885812
C2×#544×C732
C2×#308473