Finite Group Databasebeta

← C2×#22612061 #33240553

Subgroups — C2×#22612061 #33240553

Order 18688.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556536C211yesmaximal, characteristic, complemented
2C2×#17988862C211yesmaximal, characteristic, complemented
3C2×#17988857C211yesmaximal, characteristic
4#22612061C218yesmaximal, direct product factor
5C2×#17988417C211yesmaximal, characteristic, complemented
6C2×#17988404C211yesmaximal, characteristic, complemented
7C2×#17988401C211yesmaximal, characteristic, complemented
8C2×#504×C73C211yesmaximal, characteristic, complemented
9C2×#14556621—21no—
10C2×#14556616—21no—
11C22×Dic292C2211yescharacteristic
12C22×D584C2211yescharacteristic
13C2×#14556536—21no—
14C2×#14556536—21no—
15C2×#14556536—22no—
16C2×#14556536C2214yescomplemented
17#17988862—22no—
18#17988862C2214yescomplemented
19#17988857—22no—
20#17988857C2214yes—
21C2×#14556527C2211yescharacteristic
22C2×#14556527C2211yescharacteristic
23C2×#14556509—21no—
24C2×#14556507—21no—
25#17988417C2214yescomplemented
26#17988404C2214yescomplemented
27#17988401C2214yescomplemented
28C2×#131×C73C2211yescharacteristic
29#504×C73—22no—
30#504×C73C2214yescomplemented
31C2×M32×C73—21no—
32C2×M32×C73C2211yescharacteristic
33C22×C16×C73—21no—
34C22×C16×C73C2211yescharacteristic
35C22×Dic146—21no—
36C22×D292—21no—
37#14556621—24no—
38#14556621—42no—
39#14556616—24no—
40#14556616—42no—
41C2×Dic292—21no—
42C2×Dic292—21no—
43C2×Dic292—21no—
44C2×Dic292—21no—
45C2×Dic292—21no—
46C2×Dic292C2312yes—
47C2×#11924018—41no—
48C2×#11924016—41no—
49C2×#11924015—41no—
50C2×D584—21no—
51C2×D584—21no—
52C2×D584—21no—
53C2×D584—21no—
54C2×D584—21no—
55C2×D584C2312yes—
56C2×#11924013—41no—
57C2×#11924012—21no—
58C2×#11924012—21no—
59#14556536—24no—
60#14556536—24no—
61#14556527—21no—
62#14556527—21no—
63#14556527C2312yes—
64#14556527C2312yes—
65#14556509—24no—
66#14556507—24no—
67C2×#41×C73D411yescharacteristic
68#131×C73—21no—
69#131×C73—21no—
70#131×C73D412yes—
71#131×C73C2312yes—
72C2×M16×C73—21no—
73C2×M16×C73D411yescharacteristic
74C22×C8×C73—21no—
75C22×C8×C73C2311yescharacteristic
76M32×C73—21no—
77M32×C73—24no—
78M32×C73C2312yes—
79C2×C16×C73—21no—
80C2×C16×C73—24no—
81C2×C16×C73D411yescharacteristic
82C2×C16×C73D411yescharacteristic
83C2×C16×C73D412yes—
84C2×C16×C73C2312yes—
85C23×D73—41no—
86C2×Dic146—22no—
87C2×Dic146—41no—
88C2×Dic146—41no—
89C2×Dic146—41no—
90C2×Dic146—41no—
91C2×Dic146—41no—
92C2×D292—22no—
93C2×D292—41no—
94C2×D292—41no—
95C2×D292—41no—
96C2×D292—41no—
97C2×D292—41no—
98C22×Dic73—41no—
99Dic292—22no—
100Dic292—22no—
101Dic292—41no—
102Dic292—41no—
103#11924018—44no—
104#11924016—44no—
105#11924015—44no—
106D584—22no—
107D584—22no—
108D584—41no—
109D584—41no—
110#11924013—44no—
111#11924012—22no—
112#11924012—22no—
113#11924012—41no—
114#11924012—41no—
115C2×#10596831—41no—
116C2×#10596831—41no—
117#41×C73—21no—
118#41×C73—21no—
119#41×C73D812yes—
120#41×C73C2×D412yes—
121C2×Q8×C73D811yescharacteristic
122C2×D4×C73—21no—
123C2×D4×C73D811yescharacteristic
124C22×C4×C73—21no—
125C22×C4×C73C2×D411yescharacteristic
126M16×C73—21no—
127M16×C73—22no—
128M16×C73—22no—
129M16×C73C2×D412yes—
130C2×C8×C73—21no—
131C2×C8×C73—22no—
132C2×C8×C73—22no—
133C2×C8×C73C2×D411yescharacteristic
134C2×C8×C73C2×D411yescharacteristic
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73#4111yescharacteristic
137C2×C8×C73#4111yescharacteristic
138C2×C8×C73C2411yescharacteristic
139C16×C73—22no—
140C16×C73C2×D412yes—
141C16×C73C2×D412yes—
142C23×C73—21no—
143C23×C73#13511yescharacteristic
144C22×D73—42no—
145C22×D73—81no—
146C22×D73—81no—
147C22×D73—162no—
148Q8×C73—21no—
149Q8×C73C2×D812yes—
150D4×C73—22no—
151D4×C73—22no—
152D4×C73—21no—
153D4×C73C2×D812yes—
154C2×C4×C73—21no—
155C2×C4×C73—22no—
156C2×C4×C73—22no—
157C2×C4×C73#12111yescharacteristic
158C2×C4×C73#12111yescharacteristic
159C2×C4×C73C2×D811yescharacteristic
160C2×C4×C73C2×D811yescharacteristic
161C2×C4×C73#13511yescharacteristic
162C2×C4×C73C22×D411yescharacteristic
163C2×Dic73—42no—
164C2×Dic73—81no—
165C2×Dic73—81no—
166D292—42no—
167D292—42no—
168D292—81no—
169D292—81no—
170Dic146—42no—
171Dic146—42no—
172Dic146—81no—
173Dic146—81no—
174C8×C73—22no—
175C8×C73#12111yescharacteristic
176C8×C73#12111yescharacteristic
177C8×C73C22×D411yescharacteristic
178C8×C73C2×#4111yescharacteristic
179#10596831—42no—
180#10596831—42no—
181C22×C73—22no—
182C22×C73—22no—
183C22×C73—42no—
184C22×C73#46611yescharacteristic
185C22×C73#46611yescharacteristic
186C22×C73C2×#13511yescharacteristic
187C2×D73—82no—
188C2×D73—162no—
189C2×D73—162no—
190C2×D73—162no—
191C4×C73—22no—
192C4×C73#46611yescharacteristic
193C4×C73#46611yescharacteristic
194C4×C73C2×#12111yescharacteristic
195C4×C73C22×D811yescharacteristic
196Dic73—82no—
197C2×#2223—731nomaximal, Sylow
198C2×C73—21no—
199C2×C73—21no—
200C2×C73—42no—
201C2×C73#222312yescomplemented
202C2×C73C2×#46611yescharacteristic
203D73—162no—
204C22×SD32—731no—
205C2×#504D7311yescharacteristic, complemented
206C2×#473—731no—
207C2×#472—731no—
208#2223—738no—
209C2×#368—731no—
210C2×#362—731no—
211C2×#361—731no—
212C73C2×#222311yescharacteristic, complemented, Sylow
213C2×#137—1461no—
214C2×AGL(1,ℤ/8)—1461no—
215C22×Q16—731no—
216C22×D8—731no—
217C2×#131C2×D7311yescharacteristic
218C2×SD32—734no—
219C2×SD32—1461no—
220C2×SD32—1461no—
221C2×SD32—1462no—
222#504—22no—
223#504C2×D7314yescomplemented
224C2×M32—21no—
225C2×M32C2×D7311yescharacteristic
226C22×C16—21no—
227C22×C16C2×D7311yescharacteristic
228#473—734no—
229#473—1462no—
230#472—734no—
231#472—1462no—
232C2×#108—731no—
233C2×#108—731no—
234C2×#101—1461no—
235C2×#100—1461no—
236#368—734no—
237#362—734no—
238#361—734no—
239C2×#41D29211yescharacteristic
240C22×Q8—1461no—
241C22×D4—1461no—
242#137—2922no—
243#137—1464no—
244AGL(1,ℤ/8)—2922no—
245AGL(1,ℤ/8)—1464no—
246C2×Q16—2921no—
247C2×Q16—732no—
248C2×Q16—1461no—
249C2×Q16—1461no—
250C2×Q16—1461no—
251C2×Q16—1461no—
252C2×Q16—1461no—
253C2×SD16—2921no—
254C2×SD16—2921no—
255C2×D8—2921no—
256C2×D8—732no—
257C2×D8—1461no—
258C2×D8—1461no—
259C2×D8—1461no—
260C2×D8—1461no—
261C2×D8—1461no—
262#131—21no—
263#131—21no—
264#131D29212yes—
265#131C22×D7312yes—
266C2×M16—21no—
267C2×M16—1461no—
268C2×M16—1461no—
269C2×M16D29211yescharacteristic
270C22×C8—21no—
271C22×C8C22×D7311yescharacteristic
272SD32—1464no—
273SD32—1464no—
274M32—21no—
275M32—24no—
276M32C22×D7312yes—
277C2×C16—21no—
278C2×C16—24no—
279C2×C16C22⋊D7311yescharacteristic
280C2×C16C22⋊D7311yescharacteristic
281C2×C16C22⋊D7312yes—
282C2×C16C22×D7312yes—
283#108—732no—
284#108—732no—
285#108—1461no—
286#108—1461no—
287#101—1464no—
288#100—1464no—
289C24—2921no—
290#41—21no—
291#41—21no—
292#41D58412yes—
293#41C2×D29212yes—
294C2×Q8—2921no—
295C2×Q8—2921no—
296C2×Q8—2921no—
297C2×Q8—2921no—
298C2×Q8—2921no—
299C2×Q8—1462no—
300C2×Q8D58411yescharacteristic
301C2×D4—21no—
302C2×D4—2921no—
303C2×D4—2921no—
304C2×D4—2921no—
305C2×D4—2921no—
306C2×D4—2921no—
307C2×D4—1462no—
308C2×D4D58411yescharacteristic
309C22×C4—21no—
310C22×C4—2921no—
311C22×C4C2×D29211yescharacteristic
312Q16—2924no—
313Q16—2921no—
314Q16—2921no—
315Q16—1462no—
316Q16—1462no—
317SD16—2924no—
318SD16—2924no—
319D8—2924no—
320D8—2921no—
321D8—2921no—
322D8—1462no—
323D8—1462no—
324M16—21no—
325M16—22no—
326M16—22no—
327M16—2921no—
328M16—2921no—
329M16—1462no—
330M16—1462no—
331M16C2×D29212yes—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—2921no—
336C2×C8—2921no—
337C2×C8C2×C22⋊D7311yescharacteristic
338C2×C8C2×C22⋊D7311yescharacteristic
339C2×C8C2×D29211yescharacteristic
340C2×C8#1192402811yescharacteristic
341C2×C8#1192402811yescharacteristic
342C2×C8C23×D7311yescharacteristic
343C16—22no—
344C16C2×C22⋊D7312yes—
345C16C2×C22⋊D7312yes—
346C23—21no—
347C23—2922no—
348C23—5841no—
349C23—5841no—
350C23—11682no—
351C23#1455661311yescharacteristic
352Q8—21no—
353Q8—2922no—
354Q8—2922no—
355Q8—5841no—
356Q8—5841no—
357Q8C2×D58412yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—2922no—
362D4—2922no—
363D4—5841no—
364D4—5841no—
365D4C2×D58412yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—2922no—
370C2×C4—5841no—
371C2×C4—5841no—
372C2×C4#1455656511yescharacteristic
373C2×C4#1455656511yescharacteristic
374C2×C4C2×D58411yescharacteristic
375C2×C4C2×D58411yescharacteristic
376C2×C4#1455661311yescharacteristic
377C2×C4C22×D29211yescharacteristic
378C8—22no—
379C8—2922no—
380C8—2922no—
381C8#1455656511yescharacteristic
382C8#1455656511yescharacteristic
383C8C22×C22⋊D7311yescharacteristic
384C8C2×#1192402811yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—5842no—
389C22—11682no—
390C22—11682no—
391C22—11682no—
392C22#1798882311yescharacteristic
393C22#1798882311yescharacteristic
394C22C2×#1455661311yescharacteristic
395C4—22no—
396C4—5842no—
397C4#1798882311yescharacteristic
398C4#1798882311yescharacteristic
399C4C2×#1455656511yescharacteristic
400C4C22×D58411yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—11682no—
405C2#2261206112yesdirect product factor
406C2C2×#1798882311yescharacteristic
subgroupG/H
centerC22#17988823
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×#504×C73C2
socleC22×C73#466
prime radicalC2×#17988857C2
hypercenterC2×#504D73
hypocenterC73C2×#2223
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C22×#14556536C2semidirect
2. C2×#17988862C2semidirect
4. #22612061C2direct (N × H)
5. C2×#17988417C2semidirect
6. C2×#17988404C2semidirect
7. C2×#17988401C2semidirect
8. C2×#504×C73C2semidirect
16. C2×#14556536C22semidirect
18. #17988862C22semidirect
25. #17988417C22semidirect
26. #17988404C22semidirect
27. #17988401C22semidirect
30. #504×C73C22semidirect
201. C2×C73#2223semidirect
205. C2×#504D73semidirect
212. C73C2×#2223semidirect
223. #504C2×D73semidirect
405. C2#22612061direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565362
C2×#179888622
C2×#179888572
#226120612
C2×#179884172
C2×#179884042
C2×#179884012
C2×#504×C732
C2×#222373