Finite Group Databasebeta

← C2×#21447943 #29834575

Subgroups — C2×#21447943 #29834575

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×#16840180C211yesmaximal, characteristic
3C2×#16840038C211yesmaximal, characteristic
4C2×#16840034C211yesmaximal, characteristic
5#21447943C218yesmaximal, direct product factor
6C2×#16839591C211yesmaximal, characteristic, complemented
7C2×#16839579C211yesmaximal, characteristic, complemented
8C2×C61×#362C211yesmaximal, characteristic, complemented
9C2×#14519810—21no—
10C2×#14519808—21no—
11C22×Dic244C2211yescharacteristic
12C2×#14519783C2211yescharacteristic
13C2×#14519723—21no—
14C2×#14519723—21no—
15C2×#14519723—22no—
16C2×#14519723C2214yescomplemented
17#16840180—22no—
18#16840180C2214yes—
19C2×#14519716—21no—
20C22×#11758185C2211yescharacteristic
21C2×C16×D61—21no—
22#16840038—22no—
23#16840038C2214yes—
24#16840034—22no—
25#16840034C2214yes—
26C2×#14519713C2211yescharacteristic
27C2×#14519696—21no—
28C2×#14519695—21no—
29#16839591C2214yescomplemented
30#16839579C2214yescomplemented
31C22×Q16×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic
33C2×#108×C61C2211yescharacteristic
34C61×#362C2214yescomplemented
35C2×#11758222D411yescharacteristic
36C22×Dic122—21no—
37#14519810—24no—
38#14519810—42no—
39#14519808—24no—
40#14519808—42no—
41C2×Dic244—21no—
42C2×Dic244—21no—
43C2×Dic244—21no—
44C2×Dic244—21no—
45C2×Dic244—21no—
46C2×Dic244—41no—
47C2×Dic244C2312yes—
48C2×#11758202—41no—
49C2×#11758190—41no—
50C2×#11758201—41no—
51#14519783—21no—
52#14519783—21no—
53#14519783D412yes—
54#14519783C2312yes—
55C2×#11758194—21no—
56C2×#11758194D411yescharacteristic
57C2×#11758189—21no—
58C2×C8×D61—21no—
59#14519723—24no—
60#14519723—24no—
61#14519716—24no—
62C2×#11758185D411yescharacteristic
63C2×#11758185D411yescharacteristic
64C2×#11758185D412yes—
65C2×#11758185C2312yes—
66C16×D61—24no—
67#14519713—21no—
68#14519713C2312yes—
69#14519696—24no—
70#14519695—24no—
71C22×Q8×C61—21no—
72C2×Q16×C61—21no—
73C2×Q16×C61—21no—
74C2×Q16×C61—21no—
75C2×Q16×C61—21no—
76C2×Q16×C61—21no—
77C2×Q16×C61C2312yes—
78C2×M16×C61—21no—
79C22×C8×C61C2311yescharacteristic
80M32×C61—21no—
81M32×C61C2312yes—
82C2×C16×C61—21no—
83#108×C61—21no—
84#108×C61C2312yes—
85C2×Q8×C61—22no—
86C2×Q8×C61—41no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C2×Q8×C61—41no—
90C2×Q8×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C2×D411yescharacteristic
93C2×C22⋊D61—21no—
94C22×Dic61—41no—
95#11758222—21no—
96#11758222—21no—
97#11758222D812yes—
98#11758222C2×D412yes—
99C2×D244D811yescharacteristic
100C2×C4×D61—21no—
101C2×Dic122—22no—
102C2×Dic122—41no—
103C2×Dic122—41no—
104C2×Dic122—41no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107C2×Dic122D811yescharacteristic
108Q16×C61—22no—
109Q16×C61—22no—
110Q16×C61—41no—
111Q16×C61—41no—
112M16×C61—22no—
113M16×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61#4111yescharacteristic
119C2×C8×C61#4111yescharacteristic
120C2×C8×C61C2411yescharacteristic
121#11758202—44no—
122#11758201—44no—
123#11758194—21no—
124#11758194—22no—
125#11758194—41no—
126#11758194C2×D412yes—
127C2×#92418—21no—
128C2×#92418—41no—
129Dic244—22no—
130Dic244—22no—
131Dic244—44no—
132Dic244—41no—
133Dic244—41no—
134#11758190—44no—
135#11758189—22no—
136#11758189—22no—
137C8×D61—22no—
138C8×D61—22no—
139C16×C61—22no—
140#11758185C2×D412yes—
141#11758185C2×D412yes—
142C23×C61#13511yescharacteristic
143C22×D61—21no—
144Q8×C61—42no—
145Q8×C61—42no—
146Q8×C61—81no—
147Q8×C61—81no—
148C2×C4×C61—42no—
149C2×C4×C61—81no—
150C2×C4×C61—81no—
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C2×D811yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61C22×D411yescharacteristic
157C22⋊D61—22no—
158C22⋊D61—22no—
159C2×Dic61—21no—
160C2×Dic61—42no—
161C2×Dic61—81no—
162C2×Dic61—81no—
163D244—21no—
164D244C2×D812yes—
165C4×D61—22no—
166C4×D61—22no—
167Dic122—21no—
168Dic122—42no—
169Dic122—42no—
170Dic122—81no—
171Dic122—81no—
172Dic122C2×D812yes—
173C8×C61—42no—
174C8×C61#12111yescharacteristic
175C8×C61#12111yescharacteristic
176C8×C61C22×D411yescharacteristic
177C8×C61C2×#4111yescharacteristic
178#92418—22no—
179#92418—42no—
180C2×#2222—611nomaximal, Sylow
181C22×C61—22no—
182C22×C61#46611yescharacteristic
183C22×C61#46611yescharacteristic
184C22×C61C2×#13511yescharacteristic
185C2×D61—22no—
186C2×D61—42no—
187C4×C61—82no—
188C4×C61#46611yescharacteristic
189C4×C61#46611yescharacteristic
190C4×C61C2×#12111yescharacteristic
191C4×C61C22×D811yescharacteristic
192Dic61—22no—
193Dic61—82no—
194C22×Q32—611no—
195C2×#504—611no—
196C2×#473—611no—
197C2×#473—611no—
198#2222—618no—
199C2×#368—611no—
200C2×#362—611no—
201C2×#362D6111yescharacteristic, complemented
202C2×C61—21no—
203C2×C61—21no—
204C2×C61#222212yescomplemented
205C2×C61C2×#46611yescharacteristic
206D61—42no—
207C2×#137—1221no—
208C2×#137—1221no—
209C22×Q16—611no—
210C22×Q16C2×D6111yescharacteristic
211C2×#131—611no—
212C2×Q32—614no—
213C2×Q32—1221no—
214C2×Q32—1221no—
215C2×Q32—1222no—
216#504—614no—
217#504—1222no—
218C2×M32—1221no—
219C2×M32C2×D6111yescharacteristic
220C22×C16—611no—
221C22×C16—1221no—
222#473—614no—
223#473—614no—
224#473—1222no—
225#473—1222no—
226C2×#108—611no—
227C2×#108C2×D6111yescharacteristic
228C2×#101—1221no—
229C2×#101—1221no—
230#368—614no—
231#362—614no—
232#362C2×D6114yescomplemented
233C61C2×#222211yescharacteristic, complemented, Sylow
234C2×#41—611no—
235C22×Q8—21no—
236C22×Q8—1221no—
237#137—1224no—
238#137—1224no—
239#137—2442no—
240#137—2442no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—612no—
247C2×Q16—1221no—
248C2×Q16—1221no—
249C2×Q16—1221no—
250C2×Q16—1221no—
251C2×Q16—1221no—
252C2×Q16—2441no—
253C2×Q16—2441no—
254C2×Q16C22×D6112yes—
255C2×SD16—2441no—
256C2×SD16—2441no—
257#131—612no—
258#131—612no—
259#131—1221no—
260#131—1221no—
261C2×M16—21no—
262C2×M16—611no—
263C2×M16—1221no—
264C2×M16—1221no—
265C22×C8—1221no—
266C22×C8C22×D6111yescharacteristic
267Q32—1224no—
268Q32—1224no—
269M32—21no—
270M32—1224no—
271M32C22×D6112yes—
272C2×C16—21no—
273C2×C16—611no—
274C2×C16—611no—
275C2×C16—612no—
276C2×C16—612no—
277C2×C16—1224no—
278#108—21no—
279#108—612no—
280#108—1221no—
281#108C22×D6112yes—
282#101—1224no—
283#101—1224no—
284#41—612no—
285#41—612no—
286#41—1221no—
287#41—1221no—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—611no—
295C2×Q8—1222no—
296C2×Q8—2441no—
297C2×Q8—2441no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C2×Q8—2441no—
301C2×D4—611no—
302C2×D4—1221no—
303C22×C4—41no—
304C22×C4—1221no—
305C22×C4—2441no—
306C22×C4D4×D6111yescharacteristic
307Q16—22no—
308Q16—22no—
309Q16—41no—
310Q16—41no—
311Q16—1222no—
312Q16—1222no—
313Q16—2444no—
314Q16—2444no—
315Q16—2441no—
316Q16—2441no—
317SD16—2444no—
318SD16—2444no—
319M16—22no—
320M16—41no—
321M16—612no—
322M16—1221no—
323M16—1222no—
324M16—1222no—
325M16—1222no—
326M16—2441no—
327C2×C8—41no—
328C2×C8—1221no—
329C2×C8—1222no—
330C2×C8—1222no—
331C2×C8—2441no—
332C2×C8#1175822211yescharacteristic
333C2×C8#1175822211yescharacteristic
334C2×C8D4×D6111yescharacteristic
335C2×C8D4×D6111yescharacteristic
336C2×C8D4×D6111yescharacteristic
337C2×C8C23×D6111yescharacteristic
338C16—22no—
339C16—612no—
340C16—612no—
341C23—1221no—
342C23#1451979811yescharacteristic
343Q8—42no—
344Q8—42no—
345Q8—81no—
346Q8—81no—
347Q8—612no—
348Q8—1221no—
349Q8—4881no—
350Q8—4881no—
351Q8—2442no—
352Q8—2442no—
353D4—612no—
354D4—1222no—
355D4—1222no—
356D4—1221no—
357C2×C4—42no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—1221no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—4881no—
364C2×C4—4881no—
365C2×C4—2442no—
366C2×C4#1451975011yescharacteristic
367C2×C4#1451975011yescharacteristic
368C2×C4D8×D6111yescharacteristic
369C2×C4D8×D6111yescharacteristic
370C2×C4#1451979811yescharacteristic
371C2×C4C2×D4×D6111yescharacteristic
372C8—42no—
373C8—1222no—
374C8—2442no—
375C8#1451975011yescharacteristic
376C8#1451975011yescharacteristic
377C8C2×D4×D6111yescharacteristic
378C8C2×#1175822211yescharacteristic
379C22—22no—
380C22—1222no—
381C22—2442no—
382C22#1683999711yescharacteristic
383C22#1683999711yescharacteristic
384C22C2×#1451979811yescharacteristic
385C4—82no—
386C4—1222no—
387C4—4882no—
388C4#1683999711yescharacteristic
389C4#1683999711yescharacteristic
390C4C2×#1451975011yescharacteristic
391C4C2×D8×D6111yescharacteristic
392C2—21no—
393C2—21no—
394C2—2442no—
395C2#2144794312yesdirect product factor
396C2C2×#1683999711yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#362C2
socleC22×C61#466
prime radicalC2×#11758222D4
hypercenterC2×#362D61
hypocenterC61C2×#2222
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
1. C22×#14519723C2semidirect
5. #21447943C2direct (N × H)
6. C2×#16839591C2semidirect
7. C2×#16839579C2semidirect
8. C2×C61×#362C2semidirect
16. C2×#14519723C22semidirect
29. #16839591C22semidirect
30. #16839579C22semidirect
34. C61×#362C22semidirect
201. C2×#362D61semidirect
204. C2×C61#2222semidirect
232. #362C2×D61semidirect
233. C61C2×#2222semidirect
395. C2#21447943direct (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×#168401802
C2×#168400382
C2×#168400342
#214479432
C2×#168395912
C2×#168395792
C2×C61×#3622
C2×#222261