Finite Group Databasebeta

← C2×#22611997 #33240353

Subgroups — C2×#22611997 #33240353

Order 18688.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989028C211yesmaximal, characteristic, complemented
2C2×#17989023C211yesmaximal, characteristic
3C2×#17988705C211yesmaximal, characteristic, complemented
4#22611997C218yesmaximal, direct product factor
5C2×#17988408C211yesmaximal, characteristic, complemented
6C2×#17988403C211yesmaximal, characteristic, complemented
7C2×#17988400C211yesmaximal, characteristic, complemented
8C2×#495×C73C211yesmaximal, characteristic, complemented
9C2×#14556613C2211yescharacteristic
10C2×#14556597—21no—
11#17989028—22no—
12#17989028C2214yescomplemented
13#17989023—22no—
14#17989023C2214yes—
15C2×#14556537—21no—
16C2×#14556535—21no—
17C2×#14556534—21no—
18C2×#14556532—21no—
19C2×#14556531C2211yescharacteristic
20C2×#14556531C2211yescharacteristic
21#17988705—22no—
22#17988705C2214yescomplemented
23C2×#14556527C2211yescharacteristic
24C2×#14556519—21no—
25#17988408C2214yescomplemented
26#17988403C2214yescomplemented
27#17988400C2214yescomplemented
28C22×Q16×C73C2211yescharacteristic
29C22×SD16×C73—21no—
30C22×D8×C73C2211yescharacteristic
31C2×#124×C73—21no—
32#495×C73—22no—
33#495×C73C2214yescomplemented
34C2×C4×C8×C73C2211yescharacteristic
35C2×#11924028—21no—
36#14556613—21no—
37#14556613—21no—
38#14556613D412yes—
39#14556613C2312yes—
40C2×Dic292D411yescharacteristic
41C2×#11924017—21no—
42C2×D584D411yescharacteristic
43#14556597—24no—
44#14556597—42no—
45C2×#11924012—21no—
46C2×#11924011—41no—
47C2×C8×D73—41no—
48#14556537—24no—
49#14556535—24no—
50#14556534—24no—
51#14556532—24no—
52#14556531—21no—
53#14556531—21no—
54#14556531C2312yes—
55#14556531C2312yes—
56C2×#11924003—21no—
57C2×#11924003—21no—
58#14556527—21no—
59#14556527C2312yes—
60#14556519—24no—
61C22×Q8×C73—21no—
62C22×D4×C73—21no—
63C2×Q16×C73—21no—
64C2×Q16×C73—21no—
65C2×Q16×C73—21no—
66C2×Q16×C73—21no—
67C2×Q16×C73—21no—
68C2×Q16×C73C2312yes—
69C2×SD16×C73—24no—
70C2×SD16×C73—41no—
71C2×SD16×C73—41no—
72C2×SD16×C73—42no—
73C2×D8×C73—21no—
74C2×D8×C73—21no—
75C2×D8×C73—21no—
76C2×D8×C73—21no—
77C2×D8×C73—21no—
78C2×D8×C73C2312yes—
79C22×C8×C73D411yescharacteristic
80C22×C8×C73C2311yescharacteristic
81#124×C73—24no—
82#124×C73—42no—
83C2×C22⋊C4×C73—42no—
84C2×C42×C73D411yescharacteristic
85C4×C8×C73D412yes—
86C4×C8×C73C2312yes—
87#11924028—22no—
88#11924028—22no—
89#11924028—41no—
90#11924028—41no—
91C2×Dic146—21no—
92C2×D292—21no—
93C2×C22⋊D73—41no—
94C2×C4×D73—41no—
95Dic292—21no—
96Dic292C2×D412yes—
97#11924017—22no—
98#11924017—22no—
99D584—21no—
100D584C2×D412yes—
101#11924012—22no—
102#11924012—41no—
103#11924011—44no—
104C2×#10596831—41no—
105C8×D73—44no—
106#11924003—22no—
107#11924003—22no—
108C24×C73—41no—
109C2×Q8×C73—22no—
110C2×Q8×C73—41no—
111C2×Q8×C73—41no—
112C2×Q8×C73—41no—
113C2×Q8×C73—41no—
114C2×Q8×C73—41no—
115C2×D4×C73—22no—
116C2×D4×C73—41no—
117C2×D4×C73—41no—
118C2×D4×C73—41no—
119C2×D4×C73—41no—
120C2×D4×C73—41no—
121C22×C4×C73—21no—
122C22×C4×C73—41no—
123C22×C4×C73C2×D411yescharacteristic
124Q16×C73—22no—
125Q16×C73—22no—
126Q16×C73—41no—
127Q16×C73—41no—
128SD16×C73—44no—
129SD16×C73—44no—
130D8×C73—22no—
131D8×C73—22no—
132D8×C73—41no—
133D8×C73—41no—
134C2×C8×C73D811yescharacteristic
135C2×C8×C73D811yescharacteristic
136C2×C8×C73D812yes—
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D411yescharacteristic
140C2×C8×C73C2×D412yes—
141C2×C8×C73#4111yescharacteristic
142C2×C8×C73#4111yescharacteristic
143C2×C8×C73C2411yescharacteristic
144C22⋊C4×C73—48no—
145C42×C73—21no—
146C42×C73C2×D412yes—
147C23×C73—42no—
148C23×C73—84no—
149C23×C73—81no—
150C23×C73—81no—
151C23×C73AGL(1,ℤ/8)11yescharacteristic
152C22×D73—41no—
153Q8×C73—42no—
154Q8×C73—42no—
155Q8×C73—81no—
156Q8×C73—81no—
157D4×C73—42no—
158D4×C73—42no—
159D4×C73—81no—
160D4×C73—81no—
161C2×C4×C73—22no—
162C2×C4×C73—42no—
163C2×C4×C73—42no—
164C2×C4×C73—81no—
165C2×C4×C73—81no—
166C2×C4×C73#12111yescharacteristic
167C2×C4×C73#12111yescharacteristic
168C2×C4×C73C2×D811yescharacteristic
169C2×C4×C73C2×D811yescharacteristic
170C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C73C22×D411yescharacteristic
172C22⋊D73—42no—
173C22⋊D73—42no—
174C2×Dic73—41no—
175D292—22no—
176D292—41no—
177C4×D73—42no—
178C4×D73—42no—
179Dic146—22no—
180Dic146—41no—
181C8×C73#12111yescharacteristic
182C8×C73#12111yescharacteristic
183C8×C73C2×D812yes—
184C8×C73C2×D812yes—
185C8×C73C22×D411yescharacteristic
186C8×C73C2×#4111yescharacteristic
187#10596831—42no—
188C22×C73—22no—
189C22×C73—84no—
190C22×C73—82no—
191C22×C73—162no—
192C22×C73—162no—
193C22×C73#45911yescharacteristic
194C22×C73#45911yescharacteristic
195C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
196C2×D73—42no—
197C2×D73—82no—
198C4×C73—42no—
199C4×C73—82no—
200C4×C73#45911yescharacteristic
201C4×C73#45911yescharacteristic
202C4×C73C2×#12111yescharacteristic
203C4×C73C22×D811yescharacteristic
204Dic73—42no—
205C2×#2212—731nomaximal, Sylow
206C2×C73—21no—
207C2×C73—21no—
208C2×C73—162no—
209C2×C73#221212yescomplemented
210C2×C73C2×#45911yescharacteristic
211D73—82no—
212C2×#510—731no—
213C2×#509—731no—
214C2×#495D7311yescharacteristic, complemented
215C2×#443—731no—
216#2212—738no—
217C2×#364—731no—
218C2×#362—731no—
219C2×#361—731no—
220C73C2×#221211yescharacteristic, complemented, Sylow
221C2×#135—731no—
222C22×Q16C2×D7311yescharacteristic
223C22×SD16—21no—
224C22×D8C2×D7311yescharacteristic
225C2×#131—1461no—
226C2×#124—21no—
227#510—734no—
228#510—1462no—
229#509—734no—
230#509—1462no—
231C2×Q32—1461no—
232C2×SD32—1461no—
233C2×SD32—1461no—
234C2×D16—1461no—
235C2×M32—731no—
236C2×M32—731no—
237#495—22no—
238#495C2×D7314yescomplemented
239#443—734no—
240#443—1462no—
241C2×#108—731no—
242C2×#104—1461no—
243C2×C4×C8C2×D7311yescharacteristic
244#364—734no—
245#362—734no—
246#361—734no—
247C2×#41—1461no—
248C22×Q8—21no—
249C22×D4—21no—
250#135—732no—
251#135—732no—
252#135—1461no—
253#135—1461no—
254C2×Q16—21no—
255C2×Q16—21no—
256C2×Q16—21no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16—731no—
260C2×Q16C22×D7312yes—
261C2×SD16—24no—
262C2×SD16—41no—
263C2×SD16—41no—
264C2×SD16—42no—
265C2×SD16—1461no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—21no—
270C2×D8—21no—
271C2×D8—731no—
272C2×D8C22×D7312yes—
273#131—2922no—
274#131—1464no—
275C2×M16—2921no—
276C2×M16—1461no—
277C22×C8—2921no—
278C22×C8C22⋊D7311yescharacteristic
279C22×C8C22×D7311yescharacteristic
280#124—24no—
281#124—42no—
282C2×C22⋊C4—42no—
283C2×C42C22⋊D7311yescharacteristic
284Q32—1464no—
285SD32—1464no—
286SD32—1464no—
287D16—1464no—
288M32—732no—
289M32—732no—
290M32—1461no—
291M32—1461no—
292C2×C16—1461no—
293C2×C16—1461no—
294#108—732no—
295#108—1461no—
296#104—1464no—
297C4×C8C22⋊D7312yes—
298C4×C8C22×D7312yes—
299C24—41no—
300#41—2921no—
301#41—2921no—
302#41—1462no—
303#41—1462no—
304C2×Q8—22no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—1461no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—2921no—
318C2×D4—1461no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—2921no—
322C22×C4C2×C22⋊D7311yescharacteristic
323Q16—22no—
324Q16—22no—
325Q16—41no—
326Q16—41no—
327Q16—732no—
328Q16—1461no—
329SD16—44no—
330SD16—44no—
331SD16—1462no—
332SD16—1462no—
333D8—22no—
334D8—22no—
335D8—41no—
336D8—41no—
337D8—732no—
338D8—1461no—
339M16—2921no—
340M16—2924no—
341M16—1462no—
342C2×C8—2921no—
343C2×C8—2924no—
344C2×C8#1192401311yescharacteristic
345C2×C8#1192401311yescharacteristic
346C2×C8#1192401312yes—
347C2×C8D4×D7311yescharacteristic
348C2×C8D4×D7311yescharacteristic
349C2×C8C2×C22⋊D7311yescharacteristic
350C2×C8C2×C22⋊D7312yes—
351C2×C8#1192402711yescharacteristic
352C2×C8#1192402711yescharacteristic
353C2×C8C23×D7311yescharacteristic
354C22⋊C4—48no—
355C42—21no—
356C42C2×C22⋊D7312yes—
357C16—1462no—
358C16—1462no—
359C23—42no—
360C23—84no—
361C23—81no—
362C23—81no—
363C23—2921no—
364C23#1455661711yescharacteristic
365Q8—42no—
366Q8—42no—
367Q8—81no—
368Q8—81no—
369Q8—2921no—
370Q8—1462no—
371D4—42no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—2922no—
376D4—2922no—
377D4—2921no—
378D4—1462no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—2921no—
385C2×C4—2922no—
386C2×C4—2922no—
387C2×C4#1455656211yescharacteristic
388C2×C4#1455656211yescharacteristic
389C2×C4C2×#1192401311yescharacteristic
390C2×C4C2×#1192401311yescharacteristic
391C2×C4#1455661711yescharacteristic
392C2×C4C22×C22⋊D7311yescharacteristic
393C8—2922no—
394C8#1455656211yescharacteristic
395C8#1455656211yescharacteristic
396C8C2×#1192401312yes—
397C8C2×#1192401312yes—
398C8C2×D4×D7311yescharacteristic
399C8C2×#1192402711yescharacteristic
400C22—22no—
401C22—84no—
402C22—82no—
403C22—162no—
404C22—162no—
405C22—2922no—
406C22—5842no—
407C22#1798877911yescharacteristic
408C22#1798877911yescharacteristic
409C22C2×#1455661711yescharacteristic
410C4—42no—
411C4—82no—
412C4—2922no—
413C4#1798877911yescharacteristic
414C4#1798877911yescharacteristic
415C4C2×#1455656211yescharacteristic
416C4C22×#1192401311yescharacteristic
417C2—21no—
418C2—21no—
419C2—162no—
420C2—5842no—
421C2#2261199712yesdirect product factor
422C2C2×#1798877911yescharacteristic
subgroupG/H
centerC22#17988779
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×#495×C73C2
socleC22×C73#459
prime radicalC2×#17989023C2
hypercenterC2×#495D73
hypocenterC73C2×#2212
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#17989028C2semidirect
3. C2×#17988705C2semidirect
4. #22611997C2direct (N × H)
5. C2×#17988408C2semidirect
6. C2×#17988403C2semidirect
7. C2×#17988400C2semidirect
8. C2×#495×C73C2semidirect
12. #17989028C22semidirect
22. #17988705C22semidirect
25. #17988408C22semidirect
26. #17988403C22semidirect
27. #17988400C22semidirect
33. #495×C73C22semidirect
209. C2×C73#2212semidirect
214. C2×#495D73semidirect
220. C73C2×#2212semidirect
238. #495C2×D73semidirect
421. C2#22611997direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890282
C2×#179890232
C2×#179887052
#226119972
C2×#179884082
C2×#179884032
C2×#179884002
C2×#495×C732
C2×#221273