Finite Group Databasebeta

← C2×#22622967 #33966957

Subgroups — C2×#22622967 #33966957

Order 18688.

1906 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989312C211yesmaximal, characteristic, complemented
2C2×#17989311C211yesmaximal, characteristic
3#22622967C2116yesmaximal, direct product factor
4C2×#17988980C212yesmaximal
5C2×#17988811C212yesmaximal
6C2×#17988795C212yesmaximal, complemented
7C2×#17988794C211yesmaximal, characteristic, complemented
8C2×#17988789C211yesmaximal, characteristic
9C2×#17988717C211yesmaximal, characteristic, complemented
10C2×#17988694C212yesmaximal, complemented
11C2×C4×#11924017C211yesmaximal, characteristic
12C2×#494×C73C211yesmaximal, characteristic, complemented
13C22×#11924018C2212yes—
14C22×#11924017C2211yescharacteristic
15C22×#11924015C2212yes—
16#17989312—24no—
17#17989312C2218yescomplemented
18#17989311—24no—
19#17989311C2218yes—
20C2×#14556589C2212yes—
21C2×#14556586—22no—
22C2×#14556582—21no—
23C2×#14556581—22no—
24C2×#14556580C2212yes—
25C2×#14556571—21no—
26C2×Q8×Dic73C2212yes—
27C2×Q8×Dic73C2212yes—
28C2×C4×Dic146C2211yescharacteristic
29C2×C4×Dic146C2211yescharacteristic
30C2×#14556556—21no—
31C2×C4×D292C2211yescharacteristic
32C2×#14556549—21no—
33#17988980C22116yes—
34#17988811C22116yes—
35#17988795C22116yescomplemented
36#17988794C2218yescomplemented
37#17988789C2218yes—
38#17988717C2218yescomplemented
39#17988694C22116yescomplemented
40C4×#11924017C2218yes—
41C2×#14556523C2211yescharacteristic
42C2×C4⋊#10596831C2211yescharacteristic
43C2×#14556520C2212yes—
44C2×#14556516C2211yescharacteristic
45C2×#14556515C2212yes—
46C2×#14556515C2212yes—
47C2×#14556513C2211yescharacteristic
48C2×#14556501C2212yes—
49C22×Q16×C73C2212yes—
50C22×Q16×C73C2212yes—
51C2×C4⋊Q8×C73C2211yescharacteristic
52C2×C4⋊Q8×C73C2211yescharacteristic
53#494×C73C2218yescomplemented
54C2×C4×C8×C73C2211yescharacteristic
55C22×Dic146D411yescharacteristic
56C22×Dic146C2311yescharacteristic
57C22×D292C2311yescharacteristic
58C22×C4×D73—21no—
59C2×#11924018—44no—
60C2×#11924018C2318yes—
61C2×#11924017—24no—
62C2×#11924017C2314yes—
63C2×#11924015—44no—
64C2×#11924015C2318yes—
65C22×#10596831C2312yes—
66#14556589—24no—
67#14556589C2318yes—
68#14556586—216no—
69#14556582—28no—
70#14556581—216no—
71#14556580—24no—
72#14556580C2318yes—
73#14556571—28no—
74Q8×Dic73—24no—
75Q8×Dic73—24no—
76Q8×Dic73C2318yes—
77Q8×Dic73C2318yes—
78C4×Dic146—22no—
79C4×Dic146D414yes—
80C4×Dic146C2314yes—
81C4×Dic146C2314yes—
82#14556556—28no—
83C4×D292—22no—
84C4×D292C2314yes—
85#14556549—28no—
86C2×C4⋊Dic73—22no—
87C2×C4⋊Dic73—22no—
88C2×C4⋊Dic73D411yescharacteristic
89C2×C4⋊Dic73C2311yescharacteristic
90C2×C4⋊Dic73C2311yescharacteristic
91C2×#11924007—22no—
92C2×#11924007—22no—
93C2×#11924007—21no—
94C2×#11924007D412yes—
95C2×#11924005—22no—
96C2×#11924005—22no—
97C2×#11924005—21no—
98C2×C4×Dic73—22no—
99C2×C4×Dic73—22no—
100C2×C4×Dic73—21no—
101C2×C4×Dic73C2312yes—
102#14556523C2314yes—
103C4⋊#10596831C2314yes—
104#14556520C2318yes—
105#14556516C2314yes—
106#14556515C2318yes—
107#14556515C2318yes—
108#14556513C2314yes—
109#14556501C2318yes—
110C22×Q8×C73C2312yes—
111C22×Q8×C73C2312yes—
112C2×Q16×C73—28no—
113C2×Q16×C73—44no—
114C2×Q16×C73C2318yes—
115C2×Q16×C73C2318yes—
116C22×C8×C73C2311yescharacteristic
117C22×C8×C73C2311yescharacteristic
118C4⋊Q8×C73—22no—
119C4⋊Q8×C73—22no—
120C4⋊Q8×C73C2314yes—
121C4⋊Q8×C73C2314yes—
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73—21no—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—21no—
126C2×C42×C73C2311yescharacteristic
127C4×C8×C73C2314yes—
128C23×D73—21no—
129C2×Dic146—24no—
130C2×Dic146—22no—
131C2×Dic146—22no—
132C2×Dic146—21no—
133C2×Dic146C2×D414yes—
134C2×Dic146C2412yes—
135C2×D292—22no—
136C2×D292—22no—
137C2×D292—21no—
138C2×D292C2412yes—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73C2×D412yes—
143C22×Dic73C2×D412yes—
144C2×C4×D73—24no—
145C2×C4×D73—44no—
146#11924018—48no—
147#11924017—28no—
148#11924015—48no—
149C2×#10596831—24no—
150C2×#10596831C2414yes—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—28no—
154C4⋊Dic73—28no—
155C4⋊Dic73C2×D414yes—
156C4⋊Dic73C2412yes—
157C4⋊Dic73C2412yes—
158#11924007—24no—
159#11924007—28no—
160#11924007—28no—
161#11924007C2×D418yes—
162#11924005—24no—
163#11924005—28no—
164#11924005—28no—
165C4×Dic73—24no—
166C4×Dic73—28no—
167C4×Dic73—28no—
168C4×Dic73C2×D414yes—
169C4×Dic73C2414yes—
170C2×Q8×C73—22no—
171C2×Q8×C73—22no—
172C2×Q8×C73—24no—
173C2×Q8×C73—24no—
174C2×Q8×C73—24no—
175C2×Q8×C73—24no—
176C2×Q8×C73C2414yes—
177C2×Q8×C73C2414yes—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2411yescharacteristic
183Q16×C73—216no—
184Q16×C73—48no—
185C2×C8×C73—22no—
186C2×C8×C73#4114yes—
187C2×C8×C73C2412yes—
188C2×C8×C73C2412yes—
189C4⋊C4×C73—24no—
190C4⋊C4×C73—24no—
191C4⋊C4×C73—24no—
192C4⋊C4×C73—24no—
193C42×C73C2×D412yes—
194C42×C73C2412yes—
195C23×C73C22×D411yescharacteristic
196C22×D73—22no—
197C22×D73—42no—
198C22×D73—42no—
199C22×D73—42no—
200Q8×C73—24no—
201Q8×C73—24no—
202Q8×C73—24no—
203Q8×C73—24no—
204Q8×C73—44no—
205Q8×C73—44no—
206C2×C4×C73—22no—
207C2×C4×C73—24no—
208C2×C4×C73—24no—
209C2×C4×C73—44no—
210C2×C4×C73—44no—
211C2×C4×C73#13714yes—
212C2×C4×C73C22×D412yes—
213C2×C4×C73C22×D411yescharacteristic
214C2×C4×C73C22×D412yes—
215C2×C4×C73C2×#4112yes—
216C2×C4×C73H(5,𝔽2)12yes—
217C2×C4×C73C2511yescharacteristic
218C2×Dic73—24no—
219C2×Dic73—24no—
220C2×Dic73—22no—
221C2×Dic73—22no—
222C2×Dic73—22no—
223C2×Dic73—42no—
224C2×Dic73—42no—
225C2×Dic73—42no—
226C2×Dic73C22×D414yes—
227C2×Dic73C22×D414yes—
228D292—22no—
229D292—22no—
230D292—42no—
231C4×D73—48no—
232Dic146—28no—
233Dic146—22no—
234Dic146—22no—
235Dic146—42no—
236C8×C73—22no—
237C8×C73C2×#4114yes—
238#10596831—24no—
239C22×C73#55012yes—
240C22×C73C2×#13712yes—
241C22×C73#57812yes—
242C22×C73C23×D411yescharacteristic
243C2×D73—42no—
244C2×D73—42no—
245C2×D73—42no—
246C2×D73—84no—
247C4×C73—22no—
248C4×C73—44no—
249C4×C73—44no—
250C4×C73#55012yes—
251C4×C73C2×#13714yes—
252C4×C73C22×#4111yescharacteristic
253C4×C73C2×H(5,𝔽2)11yescharacteristic
254Dic73—24no—
255Dic73—24no—
256Dic73—42no—
257Dic73—42no—
258Dic73—42no—
259C2×#3398—731nomaximal, Sylow
260C2×C73#339814yescomplemented
261C2×C73C2×#55011yescharacteristic
262C2×C73C22×#13711yescharacteristic
263C2×C73C2×#57811yescharacteristic
264D73—82no—
265C2×#557—731no—
266C2×#556—731no—
267#3398—7316no—
268C2×#497—732no—
269C2×#494D7311yescharacteristic, complemented
270C2×#464—732no—
271C2×#462—732no—
272C2×#462—731no—
273C2×#461—731no—
274C2×#446—731no—
275C2×#441—732no—
276C2×C4×SD16—731no—
277C73C2×#339811yescharacteristic, complemented, Sylow
278C22×Q16—732no—
279C22×Q16C2×D7312yes—
280C22×Q16C2×D7312yes—
281C22×SD16—732no—
282C22×SD16—731no—
283#557—738no—
284#557—1464no—
285#556—738no—
286#556—1464no—
287C2×C4⋊Q8—732no—
288C2×C4⋊Q8C2×D7311yescharacteristic
289C2×C4⋊Q8C2×D7311yescharacteristic
290C2×#126—1462no—
291C2×#125—1462no—
292C2×#125—1461no—
293C2×#124—732no—
294C2×C22⋊Q8—1461no—
295C2×C4×Q8—731no—
296C2×C4×Q8—732no—
297C2×C4×Q8—732no—
298C2×C4×Q8—731no—
299C2×C4×Q8—1461no—
300C2×C4×D4—731no—
301C2×#117—1461no—
302#497—7316no—
303#494C2×D7318yescomplemented
304#464—7316no—
305#462—7316no—
306#462—738no—
307#461—738no—
308#446—738no—
309#441—7316no—
310C4×SD16—738no—
311C2×#106—731no—
312C2×C4⋊C8—732no—
313C2×C4⋊C8—731no—
314C2×#103—732no—
315C2×#103—732no—
316C2×#103—731no—
317C2×#102—731no—
318C2×#97—732no—
319C2×C4×C8C2×D7311yescharacteristic
320C22×Q8—731no—
321C22×Q8—731no—
322C22×Q8C22×D7312yes—
323C22×Q8C22×D7312yes—
324C22×D4—731no—
325C23×C4—1461no—
326C2×Q16—28no—
327C2×Q16—44no—
328C2×Q16—2924no—
329C2×Q16—738no—
330C2×Q16C22×D7318yes—
331C2×Q16C22×D7318yes—
332C2×SD16—2924no—
333C2×SD16—738no—
334C2×SD16—734no—
335C2×SD16—1464no—
336C22×C8—732no—
337C22×C8C22×D7311yescharacteristic
338C22×C8C22×D7311yescharacteristic
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—738no—
342C4⋊Q8—1464no—
343C4⋊Q8C22×D7314yes—
344C4⋊Q8C22×D7314yes—
345#126—14616no—
346#125—14616no—
347#125—1468no—
348#124—738no—
349#124—1464no—
350C22⋊Q8—1468no—
351C4×Q8—734no—
352C4×Q8—734no—
353C4×Q8—738no—
354C4×Q8—738no—
355C4×Q8—734no—
356C4×Q8—1464no—
357C4×Q8—1464no—
358C4×Q8—1468no—
359C4×Q8—1462no—
360C4×D4—734no—
361C4×D4—1462no—
362#117—1468no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—732no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—1462no—
372C2×C4⋊C4—1462no—
373C2×C4⋊C4—1462no—
374C2×C4⋊C4—1462no—
375C2×C4⋊C4—1461no—
376C2×C22⋊C4—1462no—
377C2×C22⋊C4—1462no—
378C2×C22⋊C4—1461no—
379C2×C42—732no—
380C2×C42—1462no—
381C2×C42—1462no—
382C2×C42—1461no—
383C2×C42C22×D7311yescharacteristic
384#106—734no—
385C4⋊C8—738no—
386C4⋊C8—734no—
387#103—738no—
388#103—738no—
389#103—734no—
390#102—734no—
391#97—738no—
392C4×C8C22×D7314yes—
393C24—1461no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—24no—
397C2×Q8—24no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—734no—
401C2×Q8—732no—
402C2×Q8—1462no—
403C2×Q8—1462no—
404C2×Q8—1464no—
405C2×Q8—1461no—
406C2×Q8C23×D7314yes—
407C2×Q8C23×D7314yes—
408C2×D4—732no—
409C2×D4—1461no—
410C2×D4—1462no—
411C2×D4—1462no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—2924no—
415C22×C4—732no—
416C22×C4—732no—
417C22×C4—1461no—
418C22×C4—1461no—
419C22×C4—1461no—
420C22×C4—1464no—
421C22×C4D4×D7311yescharacteristic
422C22×C4D4×D7311yescharacteristic
423C22×C4C23×D7311yescharacteristic
424Q16—216no—
425Q16—48no—
426Q16—2928no—
427SD16—2928no—
428SD16—1468no—
429C2×C8—22no—
430C2×C8—734no—
431C2×C8—1464no—
432C2×C8#1192402714yes—
433C2×C8C23×D7312yes—
434C2×C8C23×D7312yes—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—738no—
440C4⋊C4—734no—
441C4⋊C4—732no—
442C4⋊C4—732no—
443C4⋊C4—1468no—
444C4⋊C4—1468no—
445C4⋊C4—1468no—
446C4⋊C4—1468no—
447C4⋊C4—1464no—
448C4⋊C4—1461no—
449C4⋊C4—1461no—
450C22⋊C4—1468no—
451C22⋊C4—1468no—
452C22⋊C4—1464no—
453C42—734no—
454C42—734no—
455C42—1468no—
456C42—1468no—
457C42—1464no—
458C42D4×D7312yes—
459C42C23×D7312yes—
460C23—2922no—
461C23—2922no—
462C23—2922no—
463C23—1462no—
464C23C2×D4×D7311yescharacteristic
465Q8—24no—
466Q8—24no—
467Q8—24no—
468Q8—24no—
469Q8—44no—
470Q8—44no—
471Q8—2922no—
472Q8—1462no—
473Q8—1462no—
474Q8—1468no—
475D4—2922no—
476D4—1462no—
477D4—1462no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—2922no—
484C2×C4—2922no—
485C2×C4—2922no—
486C2×C4—2928no—
487C2×C4—734no—
488C2×C4—734no—
489C2×C4—1462no—
490C2×C4—1462no—
491C2×C4—1462no—
492C2×C4—1464no—
493C2×C4—1464no—
494C2×C4#1455662314yes—
495C2×C4C2×D4×D7312yes—
496C2×C4C2×D4×D7312yes—
497C2×C4C2×D4×D7311yescharacteristic
498C2×C4C2×#1192402712yes—
499C2×C4#1455663612yes—
500C2×C4C24×D7311yescharacteristic
501C8—22no—
502C8—1464no—
503C8C2×#1192402714yes—
504C22—2922no—
505C22—2922no—
506C22—2922no—
507C22—5844no—
508C22#1798925712yes—
509C22C2×#1455662312yes—
510C22#1798940012yes—
511C22C22×D4×D7311yescharacteristic
512C4—22no—
513C4—44no—
514C4—44no—
515C4—2922no—
516C4—2922no—
517C4—2922no—
518C4—1464no—
519C4—1464no—
520C4#1798925712yes—
521C4C2×#1455662314yes—
522C4C22×#1192402711yescharacteristic
523C4C2×#1455663611yescharacteristic
524C2—5842no—
525C2#2262296714yesdirect product factor
526C2C2×#1798925711yescharacteristic
527C2C22×#1455662311yescharacteristic
528C2C2×#1798940011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#494×C73C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenterC2×#494D73
hypocenterC73C2×#3398
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
1. C2×#17989312C2semidirect
3. #22622967C2direct (N × H)
6. C2×#17988795C2semidirect
7. C2×#17988794C2semidirect
9. C2×#17988717C2semidirect
10. C2×#17988694C2semidirect
12. C2×#494×C73C2semidirect
17. #17989312C22semidirect
35. #17988795C22semidirect
36. #17988794C22semidirect
38. #17988717C22semidirect
39. #17988694C22semidirect
53. #494×C73C22semidirect
260. C2×C73#3398semidirect
269. C2×#494D73semidirect
277. C73C2×#3398semidirect
303. #494C2×D73semidirect
525. C2#22622967direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893122
C2×#179893112
#226229672
C2×#179889802
C2×#179888112
C2×#179887952
C2×#179887942
C2×#179887892
C2×#179887172
C2×#179886942
C2×C4×#119240172
C2×#494×C732
C2×#339873