Finite Group Databasebeta

← C2×#22620452 #33955597

Subgroups — C2×#22620452 #33955597

Order 18688.

1902 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989143C211yesmaximal, characteristic
2C2×#17989142C211yesmaximal, characteristic
3#22620452C2116yesmaximal, direct product factor
4C2×#17988997C211yesmaximal, characteristic, complemented
5C2×#17988996C211yesmaximal, characteristic, complemented
6C2×#17988995C212yesmaximal, complemented
7C2×#17988994C212yesmaximal, complemented
8C2×#17988993C211yesmaximal, characteristic, complemented
9C2×#17988624C212yesmaximal
10C2×#17988622C212yesmaximal
11C2×#97×D73C211yesmaximal, characteristic
12C2×#501×C73C211yesmaximal, characteristic, complemented
13C22×C8×D73C2212yes—
14#17989143—24no—
15#17989143C2218yes—
16#17989142—24no—
17#17989142C2218yes—
18C2×#14556591C2211yescharacteristic
19C2×#14556590C2211yescharacteristic
20C2×#14556590C2211yescharacteristic
21C2×#14556583C2211yescharacteristic
22C2×#14556582C2212yes—
23C2×#14556571—21no—
24C2×#14556569—21no—
25C2×#14556569—21no—
26C2×#14556567—21no—
27C2×Q8×Dic73—21no—
28C2×#14556556—21no—
29C2×#14556556—21no—
30C2×#14556556—21no—
31C2×#14556549C2211yescharacteristic
32C2×#14556549C2212yes—
33C2×#14556549C2211yescharacteristic
34C2×C42×D73C2211yescharacteristic
35#17988997C2218yescomplemented
36#17988996C2218yescomplemented
37#17988995C22116yescomplemented
38#17988994C22116yescomplemented
39#17988993C2218yescomplemented
40#17988624C22116yes—
41#17988622C22116yes—
42C2×#14556525C2212yes—
43C2×#14556524C2212yes—
44C2×#14556524C2212yes—
45C2×#14556523C2212yes—
46C2×#14556522C2212yes—
47C2×#14556522C2212yes—
48C2×#14556502C2211yescharacteristic
49C2×#14556501C2212yes—
50#97×D73C2218yes—
51C2×C4⋊Q8×C73C2211yescharacteristic
52C2×#125×C73C2211yescharacteristic
53#501×C73C2218yescomplemented
54C2×#107×C73C2212yes—
55C2×#106×C73C2212yes—
56C2×#97×C73C2211yescharacteristic
57C22×Dic146—21no—
58C22×Dic146—21no—
59C22×Dic146—21no—
60C22×C4×D73D411yescharacteristic
61C22×C4×D73D411yescharacteristic
62C22×C4×D73C2311yescharacteristic
63C22×#10596831C2312yes—
64C2×C8×D73Q8116yescomplemented
65C2×C8×D73C2318yes—
66#14556591—22no—
67#14556591C2314yes—
68#14556590—22no—
69#14556590—22no—
70#14556590C2314yes—
71#14556590C2314yes—
72#14556583—22no—
73#14556583C2314yes—
74#14556582—24no—
75#14556582C2318yes—
76#14556571—28no—
77#14556569—28no—
78#14556569—28no—
79#14556567—28no—
80Q8×Dic73—28no—
81#14556556—28no—
82#14556556—28no—
83#14556556—28no—
84#14556549—24no—
85#14556549—22no—
86#14556549—22no—
87#14556549C2314yes—
88#14556549C2318yes—
89#14556549C2314yes—
90C2×C4⋊Dic73—22no—
91C2×C4⋊Dic73—21no—
92C2×C4⋊Dic73C2311yescharacteristic
93C2×C4⋊Dic73C2312yes—
94C2×C4⋊Dic73C2311yescharacteristic
95C2×#11924007—21no—
96C2×#11924007—21no—
97C2×#11924007—22no—
98C2×#11924007—21no—
99C2×#11924007—21no—
100C2×#11924005—22no—
101C2×#11924005—21no—
102C2×#11924005—21no—
103C2×C4×Dic73—21no—
104C2×C4×Dic73—21no—
105C2×C4×Dic73—22no—
106C2×C4×Dic73D411yescharacteristic
107C2×C4×Dic73D411yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109C42×D73D414yes—
110C42×D73C2314yes—
111#14556525C2318yes—
112#14556524C2318yes—
113#14556524C2318yes—
114#14556523C2318yes—
115#14556522C2318yes—
116#14556522C2318yes—
117#14556502C2314yes—
118#14556501C2318yes—
119C22×Q8×C73—21no—
120C22×C8×C73C2312yes—
121C4⋊Q8×C73—22no—
122C4⋊Q8×C73C2314yes—
123#125×C73—22no—
124#125×C73C2314yes—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73—21no—
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C4⋊C4×C73C2312yes—
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C42×C73C2311yescharacteristic
132#107×C73C2318yes—
133#106×C73C2318yes—
134#97×C73C2314yes—
135C23×D73C2×D411yescharacteristic
136C2×Dic146—24no—
137C2×Dic146—24no—
138C2×Dic146—24no—
139C2×Dic146—44no—
140C2×Dic146—44no—
141C2×Dic146—44no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—22no—
145C22×Dic73C2×D411yescharacteristic
146C22×Dic73C2×D411yescharacteristic
147C22×Dic73C2×D411yescharacteristic
148C2×C4×D73—42no—
149C2×C4×D73—42no—
150C2×C4×D73C2×D414yes—
151C2×C4×D73C2×D414yes—
152C2×C4×D73C2×D412yes—
153C2×C4×D73C2×Q818yes—
154C2×C4×D73C2412yes—
155C2×#10596831C2×Q818yes—
156C2×#10596831C2414yes—
157C8×D73C2×Q8132yescomplemented
158C4⋊Dic73—24no—
159C4⋊Dic73—22no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—28no—
163C4⋊Dic73C2412yes—
164C4⋊Dic73C2414yes—
165C4⋊Dic73C2412yes—
166#11924007—24no—
167#11924007—24no—
168#11924007—28no—
169#11924007—24no—
170#11924007—24no—
171#11924005—28no—
172#11924005—24no—
173#11924005—24no—
174C4×Dic73—24no—
175C4×Dic73—24no—
176C4×Dic73—28no—
177C4×Dic73C2×D412yes—
178C4×Dic73C2×D414yes—
179C4×Dic73C2×D414yes—
180C4×Dic73C2412yes—
181C2×Q8×C73—24no—
182C2×Q8×C73—44no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—22no—
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2411yescharacteristic
189C2×C8×C73C2×Q818yes—
190C2×C8×C73C2414yes—
191C4⋊C4×C73—24no—
192C4⋊C4×C73—24no—
193C4⋊C4×C73—24no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—22no—
197C4⋊C4×C73C2412yes—
198C4⋊C4×C73C2414yes—
199C4⋊C4×C73C2412yes—
200C42×C73C2×D412yes—
201C42×C73C2412yes—
202C23×C73C22×D411yescharacteristic
203C22×D73—22no—
204C22×D73—22no—
205C22×D73C4⋊Q814yes—
206C22×D73C22×D412yes—
207Q8×C73—48no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—24no—
213C2×C4×C73—44no—
214C2×C4×C73—42no—
215C2×C4×C73—42no—
216C2×C4×C73C22×D412yes—
217C2×C4×C73C22×D412yes—
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C22×Q814yes—
220C2×C4×C73C2511yescharacteristic
221C2×Dic73—22no—
222C2×Dic73—22no—
223C2×Dic73—22no—
224C2×Dic73—22no—
225C2×Dic73—24no—
226C2×Dic73—42no—
227C2×Dic73—42no—
228C2×Dic73—44no—
229C2×Dic73C4⋊Q814yes—
230C2×Dic73C22×D412yes—
231C2×Dic73C22×D412yes—
232C2×Dic73C22×D412yes—
233C4×D73—44no—
234C4×D73—44no—
235C4×D73C4⋊Q818yes—
236C4×D73C22×Q818yes—
237Dic146—48no—
238Dic146—48no—
239Dic146—48no—
240C8×C73C22×Q818yes—
241#10596831C22×Q818yes—
242C22×C73C2×C4⋊Q812yes—
243C22×C73#57512yes—
244C22×C73#57512yes—
245C22×C73C23×D411yescharacteristic
246C2×D73—28no—
247C2×D73—22no—
248C2×D73—22no—
249C2×D73C2×C4⋊Q814yes—
250C4×C73—22no—
251C4×C73—22no—
252C4×C73—42no—
253C4×C73—42no—
254C4×C73—44no—
255C4×C73C2×C4⋊Q812yes—
256C4×C73C23×Q812yes—
257Dic73—22no—
258Dic73—22no—
259Dic73—42no—
260Dic73—42no—
261Dic73—44no—
262Dic73C2×C4⋊Q814yes—
263C2×#3162—731nomaximal, Sylow
264C2×C73#316214yescomplemented
265C2×C73C22×C4⋊Q811yescharacteristic
266C2×C73C2×#57511yescharacteristic
267C2×C73C2×#57511yescharacteristic
268D73—24no—
269C2×#533—731no—
270C2×#533—731no—
271#3162—7316no—
272C2×#501—732no—
273C2×#501—732no—
274C2×#501—731no—
275C2×#501—731no—
276C2×#501—731no—
277C2×#501D7311yescharacteristic, complemented
278C2×#427—732no—
279C2×#427—732no—
280C22×#97—731no—
281C73C2×#316211yescharacteristic, complemented, Sylow
282C23×C8—732no—
283#533—738no—
284#533—738no—
285#533—1464no—
286#533—1464no—
287C2×C4⋊Q8—731no—
288C2×C4⋊Q8—731no—
289C2×C4⋊Q8—731no—
290C2×C4⋊Q8C2×D7311yescharacteristic
291C2×#125—732no—
292C2×#125—731no—
293C2×#125C2×D7311yescharacteristic
294C2×C22⋊Q8—1461no—
295C2×C22⋊Q8—1461no—
296C2×C22⋊Q8—1461no—
297C2×C22⋊Q8—1461no—
298C2×C4×Q8—1461no—
299C2×C4×Q8—1461no—
300C2×C4×Q8—1461no—
301C2×C4×Q8—1461no—
302C2×#117—732no—
303C2×#117—731no—
304C2×#117—731no—
305C22×C42—731no—
306#501—738no—
307#501—738no—
308#501—7316no—
309#501—7316no—
310#501—738no—
311#501C2×D7318yescomplemented
312#427—7316no—
313#427—7316no—
314C2×#107—732no—
315C2×#107—732no—
316C2×#107—732no—
317C2×#107C2×D7312yes—
318C2×#106—732no—
319C2×#106—732no—
320C2×#106—732no—
321C2×#106C2×D7312yes—
322C2×#97—732no—
323C2×#97—731no—
324C2×#97—738no—
325C2×#97C2×D7311yescharacteristic
326C22×Q8—21no—
327C22×Q8—1461no—
328C22×Q8—1461no—
329C22×Q8—1461no—
330C23×C4—731no—
331C23×C4—731no—
332C23×C4—731no—
333C22×C8—732no—
334C22×C8—7316no—
335C22×C8—738no—
336C22×C8C22×D7312yes—
337C4⋊Q8—22no—
338C4⋊Q8—734no—
339C4⋊Q8—734no—
340C4⋊Q8—734no—
341C4⋊Q8—1462no—
342C4⋊Q8—1462no—
343C4⋊Q8—1462no—
344C4⋊Q8C22×D7314yes—
345#125—22no—
346#125—738no—
347#125—734no—
348#125—1464no—
349#125—1462no—
350#125C22×D7314yes—
351C22⋊Q8—1468no—
352C22⋊Q8—1468no—
353C22⋊Q8—1468no—
354C22⋊Q8—1468no—
355C4×Q8—1468no—
356C4×Q8—1468no—
357C4×Q8—1468no—
358C4×Q8—1468no—
359#117—734no—
360#117—738no—
361#117—734no—
362#117—1462no—
363#117—1462no—
364#117—1464no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—732no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—1462no—
372C2×C4⋊C4—1462no—
373C2×C4⋊C4—1461no—
374C2×C4⋊C4—1461no—
375C2×C4⋊C4—1461no—
376C2×C4⋊C4—1461no—
377C2×C4⋊C4—1461no—
378C2×C4⋊C4C22×D7312yes—
379C2×C4⋊C4C22×D7311yescharacteristic
380C2×C4⋊C4C22×D7311yescharacteristic
381C2×C22⋊C4—1461no—
382C2×C22⋊C4—1461no—
383C2×C22⋊C4—1462no—
384C2×C42—731no—
385C2×C42—731no—
386C2×C42—731no—
387C2×C42—734no—
388C2×C42—734no—
389C2×C42—1461no—
390C2×C42—1461no—
391C2×C42—1462no—
392C2×C42C22×D7311yescharacteristic
393#107—738no—
394#107—738no—
395#107—738no—
396#107C22×D7318yes—
397#106—738no—
398#106—738no—
399#106—738no—
400#106C22×D7318yes—
401#97—738no—
402#97—734no—
403#97C22×D7314yes—
404C24—731no—
405C2×Q8—24no—
406C2×Q8—44no—
407C2×Q8—2924no—
408C2×Q8—2924no—
409C2×Q8—2924no—
410C2×Q8—1464no—
411C2×Q8—1464no—
412C2×Q8—1464no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—2922no—
417C22×C4—2922no—
418C22×C4—734no—
419C22×C4—734no—
420C22×C4—731no—
421C22×C4—732no—
422C22×C4—738no—
423C22×C4—732no—
424C22×C4—731no—
425C22×C4—731no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1462no—
429C22×C4D4×D7311yescharacteristic
430C22×C4D4×D7311yescharacteristic
431C22×C4C23×D7311yescharacteristic
432C2×C8—738no—
433C2×C8—734no—
434C2×C8—7332no—
435C2×C8Q8×D7318yes—
436C2×C8C23×D7314yes—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—732no—
444C4⋊C4—734no—
445C4⋊C4—732no—
446C4⋊C4—1468no—
447C4⋊C4—1464no—
448C4⋊C4—1464no—
449C4⋊C4—1468no—
450C4⋊C4—1464no—
451C4⋊C4—1464no—
452C4⋊C4—1462no—
453C4⋊C4—1461no—
454C4⋊C4—1461no—
455C4⋊C4—1464no—
456C4⋊C4C23×D7312yes—
457C4⋊C4C23×D7314yes—
458C4⋊C4C23×D7312yes—
459C22⋊C4—1464no—
460C22⋊C4—1464no—
461C22⋊C4—1468no—
462C42—734no—
463C42—734no—
464C42—732no—
465C42—732no—
466C42—1464no—
467C42—1464no—
468C42—1468no—
469C42D4×D7312yes—
470C42C23×D7312yes—
471C23—734no—
472C23—732no—
473C23—1462no—
474C23—1462no—
475C23C2×D4×D7311yescharacteristic
476Q8—48no—
477Q8—2928no—
478Q8—2928no—
479Q8—2928no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—44no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—2924no—
489C2×C4—2924no—
490C2×C4—2922no—
491C2×C4—2924no—
492C2×C4—2922no—
493C2×C4—734no—
494C2×C4—732no—
495C2×C4—738no—
496C2×C4—738no—
497C2×C4—732no—
498C2×C4—732no—
499C2×C4—1462no—
500C2×C4—1464no—
501C2×C4—1462no—
502C2×C4—1462no—
503C2×C4—1462no—
504C2×C4C2×D4×D7312yes—
505C2×C4C2×D4×D7312yes—
506C2×C4C2×D4×D7311yescharacteristic
507C2×C4C2×Q8×D7314yes—
508C2×C4C24×D7311yescharacteristic
509C8—738no—
510C8C2×Q8×D7318yes—
511C22—734no—
512C22—1468no—
513C22—1462no—
514C22—1462no—
515C22C4⋊Q8×D7312yes—
516C22#1798938312yes—
517C22#1798938612yes—
518C22C22×D4×D7311yescharacteristic
519C4—22no—
520C4—22no—
521C4—44no—
522C4—42no—
523C4—42no—
524C4—2922no—
525C4—2924no—
526C4—2922no—
527C4—734no—
528C4—1462no—
529C4—1462no—
530C4C4⋊Q8×D7312yes—
531C4C22×Q8×D7312yes—
532C2—1464no—
533C2#2262045214yesdirect product factor
534C2C2×C4⋊Q8×D7311yescharacteristic
535C2C2×#1798938311yescharacteristic
536C2C2×#1798938611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#501×C73C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenterC2×#501D73
hypocenterC73C2×#3162
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #22620452C2direct (N × H)
4. C2×#17988997C2semidirect
5. C2×#17988996C2semidirect
6. C2×#17988995C2semidirect
7. C2×#17988994C2semidirect
8. C2×#17988993C2semidirect
12. C2×#501×C73C2semidirect
35. #17988997C22semidirect
36. #17988996C22semidirect
37. #17988995C22semidirect
38. #17988994C22semidirect
39. #17988993C22semidirect
53. #501×C73C22semidirect
64. C2×C8×D73Q8semidirect
157. C8×D73C2×Q8semidirect
264. C2×C73#3162semidirect
277. C2×#501D73semidirect
281. C73C2×#3162semidirect
311. #501C2×D73semidirect
533. C2#22620452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891432
C2×#179891422
#226204522
C2×#179889972
C2×#179889962
C2×#179889952
C2×#179889942
C2×#179889932
C2×#179886242
C2×#179886222
C2×#97×D732
C2×#501×C732
C2×#316273