Finite Group Databasebeta

← C2×#21447942 #29834574

Subgroups — C2×#21447942 #29834574

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519723C211yesmaximal, characteristic, complemented
2C2×#16840179C211yesmaximal, characteristic
3C2×#16840037C211yesmaximal, characteristic
4#21447942C218yesmaximal, direct product factor
5C2×#16839591C211yesmaximal, characteristic, complemented
6C2×#16839578C211yesmaximal, characteristic, complemented
7C2×#16839577C211yesmaximal, characteristic, complemented
8C2×C61×#473C211yesmaximal, characteristic
9C2×#14519807—21no—
10C22×Dic244C2211yescharacteristic
11C2×#14519723—21no—
12C2×#14519723—21no—
13C2×#14519723—22no—
14C2×#14519723C2214yescomplemented
15#16840179—22no—
16#16840179C2214yes—
17C2×#14519717—21no—
18C2×#14519717C2211yescharacteristic
19C22×#11758185—21no—
20C22×#11758185C2211yescharacteristic
21#16840037—22no—
22#16840037C2214yes—
23C2×#14519713C2211yescharacteristic
24C2×#14519695—21no—
25#16839591C2214yescomplemented
26#16839578C2214yescomplemented
27#16839577C2214yescomplemented
28C2×#137×C61—21no—
29C22×Q16×C61C2211yescharacteristic
30C2×#131×C61C2211yescharacteristic
31C61×#473—22no—
32C61×#473C2214yes—
33C2×#108×C61C2211yescharacteristic
34C2×#101×C61—21no—
35C22×Dic122—21no—
36#14519807—24no—
37#14519807—42no—
38C2×Dic244—21no—
39C2×Dic244—21no—
40C2×Dic244—21no—
41C2×Dic244—21no—
42C2×Dic244—21no—
43C2×Dic244C2312yes—
44C2×#11758202—41no—
45C2×#11758200—41no—
46C2×#11758194—21no—
47#14519723—24no—
48#14519723—24no—
49#14519717—21no—
50#14519717—24no—
51#14519717C2312yes—
52C2×#11758185—21no—
53C2×#11758185—24no—
54C2×#11758185D411yescharacteristic
55C2×#11758185D411yescharacteristic
56C2×#11758185D412yes—
57C2×#11758185C2312yes—
58#14519713—21no—
59#14519713C2312yes—
60#14519695—24no—
61C2×#41×C61D411yescharacteristic
62C22×Q8×C61—21no—
63#137×C61—24no—
64#137×C61—42no—
65C2×Q16×C61—21no—
66C2×Q16×C61—21no—
67C2×Q16×C61—21no—
68C2×Q16×C61—21no—
69C2×Q16×C61—21no—
70C2×Q16×C61—41no—
71C2×Q16×C61C2312yes—
72C2×SD16×C61—41no—
73#131×C61—21no—
74#131×C61—21no—
75#131×C61D412yes—
76#131×C61C2312yes—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61D411yescharacteristic
80C22×C8×C61—21no—
81C22×C8×C61C2311yescharacteristic
82#108×C61—21no—
83#108×C61C2312yes—
84#101×C61—24no—
85#41×C61—21no—
86#41×C61—21no—
87#41×C61D812yes—
88#41×C61C2×D412yes—
89C2×Q8×C61—22no—
90C2×Q8×C61—41no—
91C2×Q8×C61—41no—
92C2×Q8×C61—41no—
93C2×Q8×C61—41no—
94C2×Q8×C61—41no—
95C2×Q8×C61D811yescharacteristic
96C2×D4×C61—21no—
97C2×D4×C61D811yescharacteristic
98C22×C4×C61—21no—
99C22×C4×C61—41no—
100C22×C4×C61C2×D411yescharacteristic
101C22×Dic61—41no—
102C2×Dic122—22no—
103C2×Dic122—41no—
104C2×Dic122—41no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108Q16×C61—22no—
109Q16×C61—22no—
110Q16×C61—44no—
111Q16×C61—41no—
112Q16×C61—41no—
113SD16×C61—44no—
114M16×C61—21no—
115M16×C61—22no—
116M16×C61—22no—
117M16×C61—22no—
118M16×C61—41no—
119M16×C61C2×D412yes—
120C2×C8×C61—21no—
121C2×C8×C61—22no—
122C2×C8×C61—22no—
123C2×C8×C61—41no—
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61#4111yescharacteristic
128C2×C8×C61#4111yescharacteristic
129C2×C8×C61C2411yescharacteristic
130#11758202—44no—
131#11758200—44no—
132#11758194—22no—
133#11758194—41no—
134C2×#92418—41no—
135Dic244—22no—
136Dic244—22no—
137Dic244—41no—
138Dic244—41no—
139#11758185—22no—
140#11758185C2×D412yes—
141#11758185C2×D412yes—
142C23×C61—21no—
143C23×C61#13511yescharacteristic
144Q8×C61—21no—
145Q8×C61—42no—
146Q8×C61—42no—
147Q8×C61—81no—
148Q8×C61—81no—
149Q8×C61C2×D812yes—
150D4×C61—22no—
151D4×C61—22no—
152D4×C61—21no—
153D4×C61C2×D812yes—
154C2×C4×C61—21no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—42no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61C2×D811yescharacteristic
163C2×C4×C61C2×D811yescharacteristic
164C2×C4×C61#13511yescharacteristic
165C2×C4×C61C22×D411yescharacteristic
166C2×Dic61—42no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169Dic122—42no—
170Dic122—42no—
171Dic122—81no—
172Dic122—81no—
173C8×C61—22no—
174C8×C61—42no—
175C8×C61#12111yescharacteristic
176C8×C61#12111yescharacteristic
177C8×C61C22×D411yescharacteristic
178C8×C61C2×#4111yescharacteristic
179#92418—42no—
180C2×#2222—611nomaximal, Sylow
181C22×C61—22no—
182C22×C61—22no—
183C22×C61—42no—
184C22×C61#46611yescharacteristic
185C22×C61#46611yescharacteristic
186C22×C61C2×#13511yescharacteristic
187C4×C61—22no—
188C4×C61—82no—
189C4×C61#46611yescharacteristic
190C4×C61#46611yescharacteristic
191C4×C61C2×#12111yescharacteristic
192C4×C61C22×D811yescharacteristic
193Dic61—82no—
194C22×Q32—611no—
195C2×#504—611no—
196C2×#473—611no—
197C2×#473D6111yescharacteristic
198#2222—618no—
199C2×#368—611no—
200C2×#362—611no—
201C2×#362—611no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61—42no—
205C2×C61#222212yescomplemented
206C2×C61C2×#46611yescharacteristic
207C2×#137—21no—
208C2×#137—1221no—
209C22×Q16—611no—
210C22×Q16C2×D6111yescharacteristic
211C2×#131C2×D6111yescharacteristic
212C2×Q32—614no—
213C2×Q32—1221no—
214C2×Q32—1221no—
215C2×Q32—1222no—
216#504—614no—
217#504—1222no—
218C2×M32—611no—
219C2×M32—1221no—
220C22×C16—611no—
221C22×C16—1221no—
222#473—22no—
223#473—614no—
224#473—1222no—
225#473C2×D6114yes—
226C2×#108—611no—
227C2×#108C2×D6111yescharacteristic
228C2×#101—21no—
229C2×#101—1221no—
230#368—614no—
231#362—614no—
232#362—614no—
233C61C2×#222211yescharacteristic, complemented, Sylow
234C2×#41C22⋊D6111yescharacteristic
235C22×Q8—21no—
236C22×Q8—1221no—
237#137—24no—
238#137—42no—
239#137—1224no—
240#137—2442no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—41no—
247C2×Q16—612no—
248C2×Q16—1221no—
249C2×Q16—1221no—
250C2×Q16—1221no—
251C2×Q16—1221no—
252C2×Q16—1221no—
253C2×Q16—2441no—
254C2×Q16C22×D6112yes—
255C2×SD16—41no—
256C2×SD16—2441no—
257#131—21no—
258#131—21no—
259#131C22⋊D6112yes—
260#131C22×D6112yes—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—1221no—
264C2×M16C22⋊D6111yescharacteristic
265C22×C8—21no—
266C22×C8C22×D6111yescharacteristic
267Q32—1224no—
268Q32—1224no—
269M32—612no—
270M32—1224no—
271M32—1221no—
272C2×C16—611no—
273C2×C16—611no—
274C2×C16—612no—
275C2×C16—612no—
276C2×C16—1224no—
277C2×C16—1221no—
278#108—21no—
279#108—612no—
280#108—1221no—
281#108C22×D6112yes—
282#101—24no—
283#101—1224no—
284#41—21no—
285#41—21no—
286#41#1175819912yes—
287#41C2×C22⋊D6112yes—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—1222no—
295C2×Q8—2441no—
296C2×Q8—2441no—
297C2×Q8—2441no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C2×Q8#1175819911yescharacteristic
301C2×D4—21no—
302C2×D4#1175819911yescharacteristic
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—2441no—
306C22×C4C2×C22⋊D6111yescharacteristic
307Q16—22no—
308Q16—22no—
309Q16—44no—
310Q16—41no—
311Q16—41no—
312Q16—1222no—
313Q16—1222no—
314Q16—2444no—
315Q16—2441no—
316Q16—2441no—
317SD16—44no—
318SD16—2444no—
319M16—21no—
320M16—22no—
321M16—22no—
322M16—22no—
323M16—41no—
324M16—1222no—
325M16—2441no—
326M16C2×C22⋊D6112yes—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—2441no—
332C2×C8D4×D6111yescharacteristic
333C2×C8D4×D6111yescharacteristic
334C2×C8#1175822411yescharacteristic
335C2×C8#1175822411yescharacteristic
336C2×C8C2×C22⋊D6111yescharacteristic
337C2×C8C23×D6111yescharacteristic
338C16—612no—
339C16—612no—
340C16—1222no—
341C23—21no—
342C23#1451979711yescharacteristic
343Q8—21no—
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348Q8—4881no—
349Q8—4881no—
350Q8—2442no—
351Q8—2442no—
352Q8C2×#1175819912yes—
353D4—22no—
354D4—22no—
355D4—21no—
356D4C2×#1175819912yes—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—4881no—
364C2×C4—4881no—
365C2×C4—2442no—
366C2×C4#1451974911yescharacteristic
367C2×C4#1451974911yescharacteristic
368C2×C4C2×#1175819911yescharacteristic
369C2×C4C2×#1175819911yescharacteristic
370C2×C4#1451979711yescharacteristic
371C2×C4C22×C22⋊D6111yescharacteristic
372C8—22no—
373C8—42no—
374C8—2442no—
375C8#1451974911yescharacteristic
376C8#1451974911yescharacteristic
377C8C2×D4×D6111yescharacteristic
378C8C2×#1175822411yescharacteristic
379C22—22no—
380C22—22no—
381C22—42no—
382C22#1683999611yescharacteristic
383C22#1683999611yescharacteristic
384C22C2×#1451979711yescharacteristic
385C4—22no—
386C4—82no—
387C4—4882no—
388C4#1683999611yescharacteristic
389C4#1683999611yescharacteristic
390C4C2×#1451974911yescharacteristic
391C4C22×#1175819911yescharacteristic
392C2—21no—
393C2—21no—
394C2—42no—
395C2#2144794212yesdirect product factor
396C2C2×#1683999611yescharacteristic
subgroupG/H
centerC22#16839996
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#473C2
socleC22×C61#466
prime radicalC2×#41×C61D4
hypercenterC2×#473D61
hypocenterC61C2×#2222
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
1. C22×#14519723C2semidirect
4. #21447942C2direct (N × H)
5. C2×#16839591C2semidirect
6. C2×#16839578C2semidirect
7. C2×#16839577C2semidirect
14. C2×#14519723C22semidirect
25. #16839591C22semidirect
26. #16839578C22semidirect
27. #16839577C22semidirect
205. C2×C61#2222semidirect
233. C61C2×#2222semidirect
395. C2#21447942direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197232
C2×#168401792
C2×#168400372
#214479422
C2×#168395912
C2×#168395782
C2×#168395772
C2×C61×#4732
C2×#222261