Finite Group Databasebeta

← C2×#22619797 #33953581

Subgroups — C2×#22619797 #33953581

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×#17989218C211yesmaximal, characteristic, complemented
2C2×#17989070C211yesmaximal, characteristic
3#22619797C2116yesmaximal, direct product factor
4C2×#17988896C212yesmaximal, complemented
5C2×#17988870C212yesmaximal, complemented
6C2×#17988885C212yesmaximal, complemented
7C2×#17988875C212yesmaximal, complemented
8C2×#17988629C211yesmaximal, characteristic, complemented
9C22×#14556522C211yesmaximal, characteristic, complemented
10C2×#17988615C211yesmaximal, characteristic, complemented
11C2×#17988583C211yesmaximal, characteristic
12C2×#417×C73C211yesmaximal, characteristic
13C23×#10596831C2211yescharacteristic
14#17989218—24no—
15#17989218C2218yescomplemented
16C2×#14556590—21no—
17C2×#14556590C2212yes—
18C2×#14556582—21no—
19C2×#14556582C2212yes—
20C2×#14556570—22no—
21#17989070—24no—
22#17989070C2218yes—
23C2×Q8×Dic73C2212yes—
24C2×D4×Dic73—22no—
25C2×D4×Dic73C2212yes—
26C2×#14556550—21no—
27C2×#14556550C2211yescharacteristic
28C2×#14556550C2211yescharacteristic
29C22×C4⋊Dic73—21no—
30C22×C4⋊Dic73C2211yescharacteristic
31#17988896C22116yescomplemented
32#17988885C22116yescomplemented
33#17988875C22116yescomplemented
34#17988870C22116yescomplemented
35#17988629C2218yescomplemented
36C2×#14556525C2212yes—
37C2×#14556523C2212yes—
38C2×#14556522C2212yes—
39C2×#14556522C2212yes—
40C2×#14556522C2218yescomplemented
41#17988615C2218yescomplemented
42C2×#14556520C2212yes—
43C2×#14556520C2212yes—
44#17988583C2218yes—
45C2×#14556515C2211yescharacteristic
46C2×#14556515C2211yescharacteristic
47C2×#14556512C2211yescharacteristic
48C2×#14556512C2211yescharacteristic
49C22×#41×C73C2211yescharacteristic
50C22×M16×C73C2211yescharacteristic
51C22×C4⋊C4×C73C2211yescharacteristic
52#417×C73C2218yes—
53C2×#103×C73C2212yes—
54C2×#102×C73C2212yes—
55C22×Dic146—22no—
56C23×Dic73—22no—
57C23×Dic73—21no—
58C22×#10596831—24no—
59C22×#10596831C2314yes—
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62#14556590—28no—
63#14556590—24no—
64#14556590C2318yes—
65#14556582—28no—
66#14556582—24no—
67#14556582C2318yes—
68#14556570—216no—
69Q8×Dic73—24no—
70Q8×Dic73C2318yes—
71D4×Dic73—216no—
72D4×Dic73—24no—
73D4×Dic73C2318yes—
74#14556550—28no—
75#14556550—22no—
76#14556550D414yes—
77#14556550C2314yes—
78#14556550C2314yes—
79C2×C4⋊Dic73—22no—
80C2×C4⋊Dic73—22no—
81C2×C4⋊Dic73—28no—
82C2×C4⋊Dic73—21no—
83C2×C4⋊Dic73—22no—
84C2×C4⋊Dic73D411yescharacteristic
85C2×C4⋊Dic73D411yescharacteristic
86C2×C4⋊Dic73C2312yes—
87C2×C4⋊Dic73C2314yes—
88C2×C4⋊Dic73C2311yescharacteristic
89C2×C4⋊Dic73C2311yescharacteristic
90C2×#11924007—22no—
91C2×#11924007—22no—
92C2×C22⋊Dic73—22no—
93C2×C22⋊Dic73—21no—
94C2×C22⋊Dic73D412yes—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—21no—
97C2×C4×Dic73C2312yes—
98#14556525C2318yes—
99#14556523C2318yes—
100#14556522C2318yes—
101#14556522C2318yes—
102#14556520C2318yes—
103#14556520C2318yes—
104#14556515C2314yes—
105#14556515C2314yes—
106#14556512C2314yes—
107#14556512C2314yes—
108C2×#41×C73—22no—
109C2×#41×C73—24no—
110C2×#41×C73Q818yescomplemented
111C2×#41×C73C2314yes—
112C22×Q8×C73C2311yescharacteristic
113C22×D4×C73—21no—
114C22×D4×C73C2311yescharacteristic
115C23×C4×C73—21no—
116C23×C4×C73—21no—
117C23×C4×C73C2311yescharacteristic
118C2×M16×C73—24no—
119C2×M16×C73C2314yes—
120C22×C8×C73C2312yes—
121C2×C4⋊C4×C73—21no—
122C2×C4⋊C4×C73—22no—
123C2×C4⋊C4×C73C2312yes—
124C2×C4⋊C4×C73C2314yes—
125#103×C73C2318yes—
126#102×C73C2318yes—
127C2×Dic146—28no—
128C2×Dic146—84no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—22no—
132C22×Dic73—24no—
133C22×Dic73—28no—
134C22×Dic73—84no—
135C22×Dic73—82no—
136C22×Dic73C2×D412yes—
137C22×Dic73C2×D412yes—
138C2×#10596831—22no—
139C2×#10596831—22no—
140C2×#10596831—28no—
141C2×#10596831C2412yes—
142C2×#10596831C2412yes—
143C4⋊Dic73—24no—
144C4⋊Dic73—22no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—28no—
148C4⋊Dic73—28no—
149C4⋊Dic73C2×D414yes—
150C4⋊Dic73C2×D414yes—
151C4⋊Dic73C2412yes—
152C4⋊Dic73C2412yes—
153C4⋊Dic73C2414yes—
154#11924007—28no—
155#11924007—28no—
156C22⋊Dic73—24no—
157C22⋊Dic73—28no—
158C22⋊Dic73C2×D418yes—
159C4×Dic73—24no—
160C4×Dic73—28no—
161C4×Dic73C2×D414yes—
162C4×Dic73C2414yes—
163C24×C73—21no—
164C24×C73C2×D411yescharacteristic
165#41×C73—216no—
166#41×C73—28no—
167#41×C73C2×Q8116yescomplemented
168C2×Q8×C73—21no—
169C2×Q8×C73—22no—
170C2×Q8×C73C2×Q814yes—
171C2×Q8×C73C2412yes—
172C2×D4×C73—28no—
173C2×D4×C73—24no—
174C2×D4×C73—21no—
175C2×D4×C73—22no—
176C2×D4×C73C2×Q814yes—
177C2×D4×C73C2412yes—
178C22×C4×C73—21no—
179C22×C4×C73—28no—
180C22×C4×C73—24no—
181C22×C4×C73—22no—
182C22×C4×C73—24no—
183C22×C4×C73—82no—
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D412yes—
186C22×C4×C73C2×Q814yes—
187C22×C4×C73#4114yes—
188C22×C4×C73C2411yescharacteristic
189C22×C4×C73C2412yes—
190M16×C73—28no—
191C2×C8×C73—24no—
192C2×C8×C73C2414yes—
193C4⋊C4×C73—24no—
194C4⋊C4×C73—22no—
195C4⋊C4×C73C2414yes—
196C23×C73—22no—
197C23×C73—22no—
198C23×C73—24no—
199C23×C73—22no—
200C23×C73—42no—
201C23×C73—42no—
202C23×C73C22⋊Q814yes—
203C23×C73C22×D412yes—
204C23×C73C22×D411yescharacteristic
205Q8×C73—24no—
206Q8×C73—22no—
207Q8×C73C22×Q814yes—
208D4×C73—216no—
209D4×C73—24no—
210D4×C73—22no—
211D4×C73C22×Q814yes—
212C2×C4×C73—24no—
213C2×C4×C73—22no—
214C2×C4×C73—216no—
215C2×C4×C73—24no—
216C2×C4×C73—44no—
217C2×C4×C73—84no—
218C2×C4×C73C22⋊Q814yes—
219C2×C4×C73C22⋊Q818yes—
220C2×C4×C73C22×D412yes—
221C2×C4×C73C22×D411yescharacteristic
222C2×C4×C73C22×Q812yes—
223C2×C4×C73C22×Q814yes—
224C2×C4×C73C2×#4112yes—
225C2×C4×C73C2×#4114yes—
226C2×C4×C73C2511yescharacteristic
227C2×Dic73—24no—
228C2×Dic73—24no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—24no—
232C2×Dic73—42no—
233C2×Dic73—44no—
234C2×Dic73—42no—
235C2×Dic73—88no—
236C2×Dic73—84no—
237C2×Dic73C22×D414yes—
238C2×Dic73C22×D414yes—
239Dic146—88no—
240C8×C73—24no—
241#10596831—22no—
242#10596831—22no—
243C22×C73—28no—
244C22×C73—22no—
245C22×C73—22no—
246C22×C73—24no—
247C22×C73—48no—
248C22×C73—42no—
249C22×C73—42no—
250C22×C73C2×C22⋊Q814yes—
251C22×C73C2×C22⋊Q812yes—
252C22×C73#57712yes—
253C22×C73#57712yes—
254C22×C73C23×D411yescharacteristic
255C4×C73—24no—
256C4×C73—44no—
257C4×C73C2×C22⋊Q814yes—
258C4×C73C2×C22⋊Q812yes—
259C4×C73C23×Q811yescharacteristic
260C4×C73C22×#4111yescharacteristic
261Dic73—24no—
262Dic73—24no—
263Dic73—42no—
264Dic73—42no—
265Dic73—44no—
266C2×#3084—731nomaximal, Sylow
267C2×C73—24no—
268C2×C73—44no—
269C2×C73#308414yescomplemented
270C2×C73C22×C22⋊Q811yescharacteristic
271C2×C73C2×#57711yescharacteristic
272C2×C73C2×#57711yescharacteristic
273C2×#544—731no—
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×#417D7311yescharacteristic
284C2×#416—731no—
285C73C2×#308411yescharacteristic, complemented, Sylow
286C22×#41C2×D7311yescharacteristic
287C22×M16C2×D7311yescharacteristic
288C23×C8—731no—
289#544—738no—
290#544—1464no—
291C2×C4⋊Q8—732no—
292C2×C4⋊Q8—1461no—
293C2×#125—732no—
294C2×#125—1461no—
295C2×C22⋊Q8—1462no—
296#520—738no—
297#520—1464no—
298C2×C4×Q8—732no—
299C2×C4×D4—732no—
300C2×C4×D4—1462no—
301C2×#117—731no—
302C2×#117—731no—
303C2×#117—1461no—
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#417C2×D7318yes—
321#416—738no—
322C2×#103—731no—
323C2×#103—731no—
324C2×#103C2×D7312yes—
325C2×#102—731no—
326C2×#102—731no—
327C2×#102C2×D7312yes—
328C2×#41—22no—
329C2×#41—24no—
330C2×#41Dic14618yescomplemented
331C2×#41C22×D7314yes—
332C22×Q8—1462no—
333C22×Q8C22×D7311yescharacteristic
334C22×D4—21no—
335C22×D4C22×D7311yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—1462no—
339C23×C4—1461no—
340C23×C4C22×D7311yescharacteristic
341C2×M16—24no—
342C2×M16C22×D7314yes—
343C22×C8—731no—
344C22×C8—731no—
345C22×C8—734no—
346C22×C8—1464no—
347C22×C8C22×D7312yes—
348C4⋊Q8—738no—
349C4⋊Q8—1464no—
350C4⋊Q8—1468no—
351#125—738no—
352#125—1464no—
353#125—1468no—
354C22⋊Q8—14616no—
355C4×Q8—738no—
356C4×Q8—1464no—
357C4×D4—738no—
358C4×D4—1464no—
359C4×D4—14616no—
360#117—734no—
361#117—734no—
362#117—734no—
363#117—1468no—
364#117—1462no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—731no—
369C2×C4⋊C4—732no—
370C2×C4⋊C4—734no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—1468no—
374C2×C4⋊C4—1462no—
375C2×C4⋊C4—1462no—
376C2×C4⋊C4—1462no—
377C2×C4⋊C4—1462no—
378C2×C4⋊C4—1461no—
379C2×C4⋊C4—1462no—
380C2×C4⋊C4C22×D7312yes—
381C2×C4⋊C4C22×D7314yes—
382C2×C22⋊C4—732no—
383C2×C22⋊C4—1462no—
384C2×C22⋊C4—1461no—
385C2×C42—732no—
386C2×C42—1462no—
387C2×C42—1461no—
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#103C22×D7318yes—
397#102—734no—
398#102—734no—
399#102C22×D7318yes—
400C24—21no—
401C24D4×D7311yescharacteristic
402#41—216no—
403#41—28no—
404#41C2×Dic146116yescomplemented
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—5844no—
408C2×Q8—1468no—
409C2×Q8C2×Dic14614yes—
410C2×Q8C23×D7312yes—
411C2×D4—28no—
412C2×D4—24no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4C2×Dic14614yes—
416C2×D4C23×D7312yes—
417C22×C4—21no—
418C22×C4—28no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—82no—
423C22×C4—5842no—
424C22×C4—5844no—
425C22×C4—732no—
426C22×C4—732no—
427C22×C4—1461no—
428C22×C4—1462no—
429C22×C4—1461no—
430C22×C4—1468no—
431C22×C4—1464no—
432C22×C4D4×D7312yes—
433C22×C4D4×D7311yescharacteristic
434C22×C4C2×Dic14614yes—
435C22×C4#1192402714yes—
436C22×C4C23×D7312yes—
437C22×C4C23×D7311yescharacteristic
438M16—28no—
439C2×C8—24no—
440C2×C8—732no—
441C2×C8—732no—
442C2×C8—1462no—
443C2×C8—1462no—
444C2×C8—1468no—
445C2×C8C23×D7314yes—
446C4⋊C4—22no—
447C4⋊C4—24no—
448C4⋊C4—734no—
449C4⋊C4—734no—
450C4⋊C4—732no—
451C4⋊C4—732no—
452C4⋊C4—734no—
453C4⋊C4—1468no—
454C4⋊C4—1468no—
455C4⋊C4—1468no—
456C4⋊C4—1468no—
457C4⋊C4—1464no—
458C4⋊C4—1462no—
459C4⋊C4—1461no—
460C4⋊C4—1461no—
461C4⋊C4C23×D7314yes—
462C22⋊C4—738no—
463C22⋊C4—1468no—
464C22⋊C4—1464no—
465C42—734no—
466C42—734no—
467C42—1468no—
468C42—1464no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—24no—
473C23—42no—
474C23—42no—
475C23#1455656814yes—
476C23C2×D4×D7312yes—
477C23C2×D4×D7311yescharacteristic
478Q8—22no—
479Q8—24no—
480Q8—5848no—
481Q8C22×Dic14614yes—
482D4—216no—
483D4—22no—
484D4—24no—
485D4C22×Dic14614yes—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—216no—
489C2×C4—24no—
490C2×C4—44no—
491C2×C4—84no—
492C2×C4—2924no—
493C2×C4—2922no—
494C2×C4—2922no—
495C2×C4—5844no—
496C2×C4—5848no—
497C2×C4—734no—
498C2×C4—734no—
499C2×C4—1462no—
500C2×C4—1464no—
501C2×C4—1462no—
502C2×C4—1464no—
503C2×C4—1464no—
504C2×C4#1455656814yes—
505C2×C4#1455656818yes—
506C2×C4C2×D4×D7311yescharacteristic
507C2×C4C2×D4×D7312yes—
508C2×C4C22×Dic14612yes—
509C2×C4C22×Dic14614yes—
510C2×C4C2×#1192402712yes—
511C2×C4C2×#1192402714yes—
512C2×C4C24×D7311yescharacteristic
513C8—24no—
514C8—1462no—
515C8—1462no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—48no—
521C22—42no—
522C22—42no—
523C22C2×#1455656814yes—
524C22C2×#1455656812yes—
525C22#1798939612yes—
526C22#1798939712yes—
527C22C22×D4×D7311yescharacteristic
528C4—24no—
529C4—44no—
530C4—2924no—
531C4—2922no—
532C4—2922no—
533C4—1464no—
534C4—1464no—
535C4C2×#1455656814yes—
536C4C2×#1455656812yes—
537C4C23×Dic14611yescharacteristic
538C4C22×#1192402711yescharacteristic
539C2—24no—
540C2—44no—
541C2#2261979714yesdirect product factor
542C2C22×#1455656811yescharacteristic
543C2C2×#1798939611yescharacteristic
544C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#417×C73C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
hypercenterC2×#417D73
hypocenterC73C2×#3084
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#17989218C2semidirect
3. #22619797C2direct (N × H)
4. C2×#17988896C2semidirect
5. C2×#17988870C2semidirect
6. C2×#17988885C2semidirect
7. C2×#17988875C2semidirect
8. C2×#17988629C2semidirect
9. C22×#14556522C2semidirect
10. C2×#17988615C2semidirect
15. #17989218C22semidirect
31. #17988896C22semidirect
32. #17988885C22semidirect
33. #17988875C22semidirect
34. #17988870C22semidirect
35. #17988629C22semidirect
40. C2×#14556522C22semidirect
41. #17988615C22semidirect
110. C2×#41×C73Q8semidirect
167. #41×C73C2×Q8semidirect
269. C2×C73#3084semidirect
285. C73C2×#3084semidirect
330. C2×#41Dic146semidirect
404. #41C2×Dic146semidirect
541. C2#22619797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892182
C2×#179890702
#226197972
C2×#179888962
C2×#179888702
C2×#179888852
C2×#179888752
C2×#179886292
C22×#145565222
C2×#179886152
C2×#179885832
C2×#417×C732
C2×#308473