Finite Group Databasebeta

← C2×#22612000 #33240356

Subgroups — C2×#22612000 #33240356

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×#17989027C211yesmaximal, characteristic, complemented
2C2×#17989022C211yesmaximal, characteristic
3C2×#17988971C211yesmaximal, characteristic, complemented
4#22612000C218yesmaximal, direct product factor
5C2×#17988408C211yesmaximal, characteristic, complemented
6C2×#17988402C211yesmaximal, characteristic, complemented
7C2×#17988399C211yesmaximal, characteristic, complemented
8C2×#443×C73C211yesmaximal, characteristic, complemented
9C22×Dic292C2211yescharacteristic
10C22×#11924017—21no—
11C22×D584C2211yescharacteristic
12C2×#14556579—21no—
13#17989027—22no—
14#17989027C2214yescomplemented
15#17989022—22no—
16#17989022C2214yes—
17C2×#14556537—21no—
18C2×#14556535—21no—
19C2×#14556534—21no—
20C2×#14556532—21no—
21C2×#14556531C2211yescharacteristic
22C2×#14556531C2211yescharacteristic
23#17988971—22no—
24#17988971C2214yescomplemented
25#17988408C2214yescomplemented
26#17988402C2214yescomplemented
27#17988399C2214yescomplemented
28C2×#135×C73C2211yescharacteristic
29C2×#131×C73—21no—
30#443×C73—22no—
31#443×C73C2214yescomplemented
32C2×#108×C73C2211yescharacteristic
33C2×#104×C73—21no—
34C2×C4×C8×C73C2211yescharacteristic
35C22×Dic146—21no—
36C22×D292—21no—
37C2×Dic292—21no—
38C2×Dic292—21no—
39C2×Dic292—21no—
40C2×Dic292—21no—
41C2×Dic292—21no—
42C2×Dic292C2312yes—
43C2×#11924017—24no—
44C2×#11924017—41no—
45C2×#11924017—41no—
46C2×#11924017—42no—
47C2×D584—21no—
48C2×D584—21no—
49C2×D584—21no—
50C2×D584—21no—
51C2×D584—21no—
52C2×D584C2312yes—
53#14556579—24no—
54#14556579—42no—
55C2×#11924005—42no—
56#14556537—24no—
57#14556535—24no—
58#14556534—24no—
59#14556532—24no—
60#14556531—21no—
61#14556531—21no—
62#14556531C2312yes—
63#14556531C2312yes—
64C2×#11924003—21no—
65C2×#11924003—21no—
66C2×#41×C73—21no—
67#135×C73—21no—
68#135×C73—21no—
69#135×C73D412yes—
70#135×C73C2312yes—
71C2×Q16×C73D411yescharacteristic
72C2×SD16×C73—21no—
73C2×D8×C73D411yescharacteristic
74#131×C73—24no—
75#131×C73—42no—
76C2×M16×C73—21no—
77C2×M16×C73—41no—
78C22×C8×C73—41no—
79C22×C8×C73D411yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C2×C42×C73D411yescharacteristic
82#108×C73—21no—
83#108×C73C2312yes—
84#104×C73—24no—
85C4×C8×C73D412yes—
86C4×C8×C73C2312yes—
87C23×D73—41no—
88C2×Dic146—22no—
89C2×Dic146—41no—
90C2×Dic146—41no—
91C2×Dic146—41no—
92C2×Dic146—41no—
93C2×Dic146—41no—
94C2×D292—22no—
95C2×D292—41no—
96C2×D292—41no—
97C2×D292—41no—
98C2×D292—41no—
99C2×D292—41no—
100C22×Dic73—41no—
101Dic292—22no—
102Dic292—22no—
103Dic292—41no—
104Dic292—41no—
105#11924017—44no—
106#11924017—44no—
107D584—22no—
108D584—22no—
109D584—41no—
110D584—41no—
111#11924005—48no—
112#11924003—22no—
113#11924003—22no—
114#41×C73—22no—
115#41×C73—22no—
116#41×C73—41no—
117#41×C73—41no—
118C2×Q8×C73—21no—
119C2×D4×C73—21no—
120C2×D4×C73—41no—
121C22×C4×C73—21no—
122C22×C4×C73—41no—
123C22×C4×C73C2×D411yescharacteristic
124Q16×C73—21no—
125Q16×C73C2×D412yes—
126SD16×C73—22no—
127SD16×C73—22no—
128D8×C73—21no—
129D8×C73C2×D412yes—
130M16×C73—22no—
131M16×C73—41no—
132M16×C73—44no—
133C2×C8×C73—41no—
134C2×C8×C73—44no—
135C2×C8×C73D811yescharacteristic
136C2×C8×C73D811yescharacteristic
137C2×C8×C73D812yes—
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D412yes—
140C2×C8×C73C2×D411yescharacteristic
141C2×C8×C73C2×D411yescharacteristic
142C2×C8×C73#4111yescharacteristic
143C2×C8×C73#4111yescharacteristic
144C2×C8×C73C2411yescharacteristic
145C42×C73—21no—
146C42×C73C2×D412yes—
147C23×C73—41no—
148C23×C73AGL(1,ℤ/8)11yescharacteristic
149C22×D73—42no—
150C22×D73—84no—
151C22×D73—81no—
152C22×D73—81no—
153Q8×C73—22no—
154Q8×C73—41no—
155D4×C73—22no—
156D4×C73—42no—
157D4×C73—42no—
158D4×C73—41no—
159C2×C4×C73—22no—
160C2×C4×C73—42no—
161C2×C4×C73—41no—
162C2×C4×C73—42no—
163C2×C4×C73—42no—
164C2×C4×C73#12111yescharacteristic
165C2×C4×C73#12111yescharacteristic
166C2×C4×C73C2×D811yescharacteristic
167C2×C4×C73C2×D811yescharacteristic
168C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C73C22×D411yescharacteristic
170C2×Dic73—42no—
171C2×Dic73—81no—
172C2×Dic73—81no—
173D292—42no—
174D292—42no—
175D292—81no—
176D292—81no—
177Dic146—42no—
178Dic146—42no—
179Dic146—81no—
180Dic146—81no—
181C8×C73—42no—
182C8×C73#12111yescharacteristic
183C8×C73#12111yescharacteristic
184C8×C73C2×D812yes—
185C8×C73C2×D812yes—
186C8×C73C22×D411yescharacteristic
187C8×C73C2×#4111yescharacteristic
188C22×C73—22no—
189C22×C73—42no—
190C22×C73—82no—
191C22×C73#45911yescharacteristic
192C22×C73#45911yescharacteristic
193C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
194C2×D73—84no—
195C2×D73—82no—
196C2×D73—162no—
197C2×D73—162no—
198C4×C73—42no—
199C4×C73—42no—
200C4×C73#45911yescharacteristic
201C4×C73#45911yescharacteristic
202C4×C73C2×#12111yescharacteristic
203C4×C73C22×D811yescharacteristic
204Dic73—82no—
205C2×#2212—731nomaximal, Sylow
206C2×C73—21no—
207C2×C73—21no—
208C2×C73—82no—
209C2×C73#221212yescomplemented
210C2×C73C2×#45911yescharacteristic
211D73—162no—
212C2×#510—731no—
213C2×#509—731no—
214C2×#495—731no—
215C2×#443D7311yescharacteristic, complemented
216#2212—738no—
217C2×#364—731no—
218C2×#362—731no—
219C2×#361—731no—
220C73C2×#221211yescharacteristic, complemented, Sylow
221C2×#135C2×D7311yescharacteristic
222C22×Q16—731no—
223C22×SD16—1461no—
224C22×D8—731no—
225C2×#131—21no—
226C2×#124—1461no—
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—734no—
238#495—1462no—
239#443—22no—
240#443C2×D7314yescomplemented
241C2×#108C2×D7311yescharacteristic
242C2×#104—21no—
243C2×C4×C8C2×D7311yescharacteristic
244#364—734no—
245#362—734no—
246#361—734no—
247C2×#41—21no—
248C22×Q8—1461no—
249C22×D4—1461no—
250#135—21no—
251#135—21no—
252#135D29212yes—
253#135C22×D7312yes—
254C2×Q16—732no—
255C2×Q16—1461no—
256C2×Q16—1461no—
257C2×Q16—1461no—
258C2×Q16—1461no—
259C2×Q16—1461no—
260C2×Q16D29211yescharacteristic
261C2×SD16—21no—
262C2×SD16—2921no—
263C2×SD16—2921no—
264C2×SD16—2922no—
265C2×SD16—1464no—
266C2×D8—732no—
267C2×D8—1461no—
268C2×D8—1461no—
269C2×D8—1461no—
270C2×D8—1461no—
271C2×D8—1461no—
272C2×D8D29211yescharacteristic
273#131—24no—
274#131—42no—
275C2×M16—21no—
276C2×M16—41no—
277C22×C8—41no—
278C22×C8C22⋊D7311yescharacteristic
279C22×C8C22×D7311yescharacteristic
280#124—2922no—
281#124—1464no—
282C2×C22⋊C4—2922no—
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—21no—
295#108C22×D7312yes—
296#104—24no—
297C4×C8C22⋊D7312yes—
298C4×C8C22×D7312yes—
299C24—2921no—
300#41—22no—
301#41—22no—
302#41—41no—
303#41—41no—
304C2×Q8—21no—
305C2×Q8—2921no—
306C2×Q8—2921no—
307C2×Q8—2921no—
308C2×Q8—2921no—
309C2×Q8—2921no—
310C2×Q8—1462no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—2921no—
314C2×D4—2921no—
315C2×D4—2921no—
316C2×D4—2921no—
317C2×D4—2921no—
318C2×D4—1462no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—2921no—
322C22×C4C2×C22⋊D7311yescharacteristic
323Q16—21no—
324Q16—2921no—
325Q16—2921no—
326Q16—1462no—
327Q16—1462no—
328Q16C2×D29212yes—
329SD16—22no—
330SD16—22no—
331SD16—2924no—
332SD16—2924no—
333D8—21no—
334D8—2921no—
335D8—2921no—
336D8—1462no—
337D8—1462no—
338D8C2×D29212yes—
339M16—22no—
340M16—41no—
341M16—44no—
342C2×C8—41no—
343C2×C8—44no—
344C2×C8#1192401311yescharacteristic
345C2×C8#1192401311yescharacteristic
346C2×C8#1192401312yes—
347C2×C8C2×C22⋊D7311yescharacteristic
348C2×C8C2×C22⋊D7312yes—
349C2×C8C2×D29211yescharacteristic
350C2×C8C2×D29211yescharacteristic
351C2×C8#1192402811yescharacteristic
352C2×C8#1192402811yescharacteristic
353C2×C8C23×D7311yescharacteristic
354C22⋊C4—2928no—
355C42—21no—
356C42C2×C22⋊D7312yes—
357C16—1462no—
358C16—1462no—
359C23—41no—
360C23—2922no—
361C23—5844no—
362C23—5841no—
363C23—5841no—
364C23#1455661611yescharacteristic
365Q8—22no—
366Q8—41no—
367Q8—2922no—
368Q8—2922no—
369Q8—5841no—
370Q8—5841no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—41no—
375D4—2922no—
376D4—2922no—
377D4—5841no—
378D4—5841no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—2922no—
385C2×C4—5841no—
386C2×C4—5841no—
387C2×C4#1455656511yescharacteristic
388C2×C4#1455656511yescharacteristic
389C2×C4C2×#1192401311yescharacteristic
390C2×C4C2×#1192401311yescharacteristic
391C2×C4#1455661611yescharacteristic
392C2×C4C22×C22⋊D7311yescharacteristic
393C8—42no—
394C8#1455656511yescharacteristic
395C8#1455656511yescharacteristic
396C8C2×#1192401312yes—
397C8C2×#1192401312yes—
398C8C22×D29211yescharacteristic
399C8C2×#1192402811yescharacteristic
400C22—22no—
401C22—42no—
402C22—82no—
403C22—5844no—
404C22—5842no—
405C22—11682no—
406C22—11682no—
407C22#1798878211yescharacteristic
408C22#1798878211yescharacteristic
409C22C2×#1455661611yescharacteristic
410C4—42no—
411C4—42no—
412C4—5842no—
413C4#1798878211yescharacteristic
414C4#1798878211yescharacteristic
415C4C2×#1455656511yescharacteristic
416C4C22×#1192401311yescharacteristic
417C2—21no—
418C2—21no—
419C2—82no—
420C2—11682no—
421C2#2261200012yesdirect product factor
422C2C2×#1798878211yescharacteristic
subgroupG/H
centerC22#17988782
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×#443×C73C2
socleC22×C73#459
prime radicalC2×#17989022C2
hypercenterC2×#443D73
hypocenterC73C2×#2212
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
1. C2×#17989027C2semidirect
3. C2×#17988971C2semidirect
4. #22612000C2direct (N × H)
5. C2×#17988408C2semidirect
6. C2×#17988402C2semidirect
7. C2×#17988399C2semidirect
8. C2×#443×C73C2semidirect
14. #17989027C22semidirect
24. #17988971C22semidirect
25. #17988408C22semidirect
26. #17988402C22semidirect
27. #17988399C22semidirect
31. #443×C73C22semidirect
209. C2×C73#2212semidirect
215. C2×#443D73semidirect
220. C73C2×#2212semidirect
240. #443C2×D73semidirect
421. C2#22612000direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890272
C2×#179890222
C2×#179889712
#226120002
C2×#179884082
C2×#179884022
C2×#179883992
C2×#443×C732
C2×#221273