Finite Group Databasebeta

← C2×#22612054 #33240545

Subgroups — C2×#22612054 #33240545

Order 18688.

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×#14556537C211yesmaximal, characteristic, complemented
2C2×#17989004C211yesmaximal, characteristic
3C2×#17988862C211yesmaximal, characteristic
4#22612054C218yesmaximal, direct product factor
5C2×#17988416C211yesmaximal, characteristic, complemented
6C2×#17988403C211yesmaximal, characteristic, complemented
7C2×#17988402C211yesmaximal, characteristic, complemented
8C2×#473×C73C211yesmaximal, characteristic
9C2×#14556621—21no—
10C22×Dic292C2211yescharacteristic
11C2×#14556537—21no—
12C2×#14556537—21no—
13C2×#14556537—22no—
14C2×#14556537C2214yescomplemented
15#17989004—22no—
16#17989004C2214yes—
17C2×#14556531—21no—
18C2×#14556531C2211yescharacteristic
19C22×#11924003—21no—
20C22×#11924003C2211yescharacteristic
21#17988862—22no—
22#17988862C2214yes—
23C2×#14556527C2211yescharacteristic
24C2×#14556509—21no—
25#17988416C2214yescomplemented
26#17988403C2214yescomplemented
27#17988402C2214yescomplemented
28C2×#137×C73—21no—
29C22×Q16×C73C2211yescharacteristic
30C2×#131×C73C2211yescharacteristic
31#473×C73—22no—
32#473×C73C2214yes—
33C2×#108×C73C2211yescharacteristic
34C2×#101×C73—21no—
35C22×Dic146—21no—
36#14556621—24no—
37#14556621—42no—
38C2×Dic292—21no—
39C2×Dic292—21no—
40C2×Dic292—21no—
41C2×Dic292—21no—
42C2×Dic292—21no—
43C2×Dic292C2312yes—
44C2×#11924018—41no—
45C2×#11924016—41no—
46C2×#11924012—21no—
47#14556537—24no—
48#14556537—24no—
49#14556531—24no—
50#14556531—21no—
51#14556531C2312yes—
52C2×#11924003—24no—
53C2×#11924003—21no—
54C2×#11924003D411yescharacteristic
55C2×#11924003D411yescharacteristic
56C2×#11924003D412yes—
57C2×#11924003C2312yes—
58#14556527—21no—
59#14556527C2312yes—
60#14556509—24no—
61C2×#41×C73D411yescharacteristic
62C22×Q8×C73—21no—
63#137×C73—24no—
64#137×C73—42no—
65C2×Q16×C73—21no—
66C2×Q16×C73—21no—
67C2×Q16×C73—21no—
68C2×Q16×C73—21no—
69C2×Q16×C73—21no—
70C2×Q16×C73—41no—
71C2×Q16×C73C2312yes—
72C2×SD16×C73—41no—
73#131×C73—21no—
74#131×C73—21no—
75#131×C73D412yes—
76#131×C73C2312yes—
77C2×M16×C73—21no—
78C2×M16×C73—21no—
79C2×M16×C73D411yescharacteristic
80C22×C8×C73—21no—
81C22×C8×C73C2311yescharacteristic
82#108×C73—21no—
83#108×C73C2312yes—
84#101×C73—24no—
85C2×Dic146—22no—
86C2×Dic146—41no—
87C2×Dic146—41no—
88C2×Dic146—41no—
89C2×Dic146—41no—
90C2×Dic146—41no—
91C22×Dic73—41no—
92Dic292—22no—
93Dic292—22no—
94Dic292—41no—
95Dic292—41no—
96#11924018—44no—
97#11924016—44no—
98#11924012—22no—
99#11924012—41no—
100C2×#10596831—41no—
101#11924003—22no—
102#11924003C2×D412yes—
103#11924003C2×D412yes—
104#41×C73—21no—
105#41×C73—21no—
106#41×C73D812yes—
107#41×C73C2×D412yes—
108C2×Q8×C73—22no—
109C2×Q8×C73—41no—
110C2×Q8×C73—41no—
111C2×Q8×C73—41no—
112C2×Q8×C73—41no—
113C2×Q8×C73—41no—
114C2×Q8×C73D811yescharacteristic
115C2×D4×C73—21no—
116C2×D4×C73D811yescharacteristic
117C22×C4×C73—21no—
118C22×C4×C73—41no—
119C22×C4×C73C2×D411yescharacteristic
120Q16×C73—22no—
121Q16×C73—22no—
122Q16×C73—44no—
123Q16×C73—41no—
124Q16×C73—41no—
125SD16×C73—44no—
126M16×C73—21no—
127M16×C73—22no—
128M16×C73—22no—
129M16×C73—22no—
130M16×C73—41no—
131M16×C73C2×D412yes—
132C2×C8×C73—21no—
133C2×C8×C73—22no—
134C2×C8×C73—22no—
135C2×C8×C73—41no—
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73#4111yescharacteristic
140C2×C8×C73#4111yescharacteristic
141C2×C8×C73C2411yescharacteristic
142C23×C73—21no—
143C23×C73#13511yescharacteristic
144Q8×C73—21no—
145Q8×C73—42no—
146Q8×C73—42no—
147Q8×C73—81no—
148Q8×C73—81no—
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—42no—
158C2×C4×C73—81no—
159C2×C4×C73—81no—
160C2×C4×C73#12111yescharacteristic
161C2×C4×C73#12111yescharacteristic
162C2×C4×C73C2×D811yescharacteristic
163C2×C4×C73C2×D811yescharacteristic
164C2×C4×C73#13511yescharacteristic
165C2×C4×C73C22×D411yescharacteristic
166C2×Dic73—42no—
167C2×Dic73—81no—
168C2×Dic73—81no—
169Dic146—42no—
170Dic146—42no—
171Dic146—81no—
172Dic146—81no—
173C8×C73—22no—
174C8×C73—42no—
175C8×C73#12111yescharacteristic
176C8×C73#12111yescharacteristic
177C8×C73C22×D411yescharacteristic
178C8×C73C2×#4111yescharacteristic
179#10596831—42no—
180C22×C73—22no—
181C22×C73—22no—
182C22×C73—42no—
183C22×C73#46611yescharacteristic
184C22×C73#46611yescharacteristic
185C22×C73C2×#13511yescharacteristic
186C4×C73—22no—
187C4×C73—82no—
188C4×C73#46611yescharacteristic
189C4×C73#46611yescharacteristic
190C4×C73C2×#12111yescharacteristic
191C4×C73C22×D811yescharacteristic
192Dic73—82no—
193C2×#2222—731nomaximal, Sylow
194C2×C73—21no—
195C2×C73—21no—
196C2×C73—42no—
197C2×C73#222212yescomplemented
198C2×C73C2×#46611yescharacteristic
199C22×Q32—731no—
200C2×#504—731no—
201C2×#473—731no—
202C2×#473D7311yescharacteristic
203#2222—738no—
204C2×#368—731no—
205C2×#362—731no—
206C2×#362—731no—
207C73C2×#222211yescharacteristic, complemented, Sylow
208C2×#137—21no—
209C2×#137—1461no—
210C22×Q16—731no—
211C22×Q16C2×D7311yescharacteristic
212C2×#131C2×D7311yescharacteristic
213C2×Q32—734no—
214C2×Q32—1461no—
215C2×Q32—1461no—
216C2×Q32—1462no—
217#504—734no—
218#504—1462no—
219C2×M32—731no—
220C2×M32—1461no—
221C22×C16—731no—
222C22×C16—1461no—
223#473—22no—
224#473—734no—
225#473—1462no—
226#473C2×D7314yes—
227C2×#108—731no—
228C2×#108C2×D7311yescharacteristic
229C2×#101—21no—
230C2×#101—1461no—
231#368—734no—
232#362—734no—
233#362—734no—
234C2×#41C22⋊D7311yescharacteristic
235C22×Q8—21no—
236C22×Q8—1461no—
237#137—24no—
238#137—42no—
239#137—2922no—
240#137—1464no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—41no—
247C2×Q16—2921no—
248C2×Q16—732no—
249C2×Q16—1461no—
250C2×Q16—1461no—
251C2×Q16—1461no—
252C2×Q16—1461no—
253C2×Q16—1461no—
254C2×Q16C22×D7312yes—
255C2×SD16—41no—
256C2×SD16—2921no—
257#131—21no—
258#131—21no—
259#131C22⋊D7312yes—
260#131C22×D7312yes—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—1461no—
264C2×M16C22⋊D7311yescharacteristic
265C22×C8—21no—
266C22×C8C22×D7311yescharacteristic
267Q32—1464no—
268Q32—1464no—
269M32—732no—
270M32—1464no—
271M32—1461no—
272C2×C16—731no—
273C2×C16—731no—
274C2×C16—732no—
275C2×C16—732no—
276C2×C16—1464no—
277C2×C16—1461no—
278#108—21no—
279#108—732no—
280#108—1461no—
281#108C22×D7312yes—
282#101—24no—
283#101—1464no—
284#41—21no—
285#41—21no—
286#41#1192401312yes—
287#41C2×C22⋊D7312yes—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—2921no—
295C2×Q8—2921no—
296C2×Q8—2921no—
297C2×Q8—2921no—
298C2×Q8—2921no—
299C2×Q8—1462no—
300C2×Q8#1192401311yescharacteristic
301C2×D4—21no—
302C2×D4#1192401311yescharacteristic
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—2921no—
306C22×C4C2×C22⋊D7311yescharacteristic
307Q16—22no—
308Q16—22no—
309Q16—44no—
310Q16—41no—
311Q16—41no—
312Q16—2924no—
313Q16—2921no—
314Q16—2921no—
315Q16—1462no—
316Q16—1462no—
317SD16—44no—
318SD16—2924no—
319M16—21no—
320M16—22no—
321M16—22no—
322M16—22no—
323M16—41no—
324M16—2921no—
325M16—1462no—
326M16C2×C22⋊D7312yes—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—2921no—
332C2×C8D4×D7311yescharacteristic
333C2×C8D4×D7311yescharacteristic
334C2×C8C2×C22⋊D7311yescharacteristic
335C2×C8#1192402711yescharacteristic
336C2×C8#1192402711yescharacteristic
337C2×C8C23×D7311yescharacteristic
338C16—732no—
339C16—732no—
340C16—1462no—
341C23—21no—
342C23#1455661111yescharacteristic
343Q8—21no—
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348Q8—2922no—
349Q8—2922no—
350Q8—5841no—
351Q8—5841no—
352Q8C2×#1192401312yes—
353D4—22no—
354D4—22no—
355D4—21no—
356D4C2×#1192401312yes—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—2922no—
364C2×C4—5841no—
365C2×C4—5841no—
366C2×C4#1455656311yescharacteristic
367C2×C4#1455656311yescharacteristic
368C2×C4C2×#1192401311yescharacteristic
369C2×C4C2×#1192401311yescharacteristic
370C2×C4#1455661111yescharacteristic
371C2×C4C22×C22⋊D7311yescharacteristic
372C8—22no—
373C8—42no—
374C8—2922no—
375C8#1455656311yescharacteristic
376C8#1455656311yescharacteristic
377C8C2×D4×D7311yescharacteristic
378C8C2×#1192402711yescharacteristic
379C22—22no—
380C22—22no—
381C22—42no—
382C22#1798882111yescharacteristic
383C22#1798882111yescharacteristic
384C22C2×#1455661111yescharacteristic
385C4—22no—
386C4—82no—
387C4—5842no—
388C4#1798882111yescharacteristic
389C4#1798882111yescharacteristic
390C4C2×#1455656311yescharacteristic
391C4C22×#1192401311yescharacteristic
392C2—21no—
393C2—21no—
394C2—42no—
395C2#2261205412yesdirect product factor
396C2C2×#1798882111yescharacteristic
subgroupG/H
centerC22#17988821
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×#473×C73C2
socleC22×C73#466
prime radicalC2×#41×C73D4
hypercenterC2×#473D73
hypocenterC73C2×#2222
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#473

Complements

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

NH ≅ G/Ntype
1. C22×#14556537C2semidirect
4. #22612054C2direct (N × H)
5. C2×#17988416C2semidirect
6. C2×#17988403C2semidirect
7. C2×#17988402C2semidirect
14. C2×#14556537C22semidirect
25. #17988416C22semidirect
26. #17988403C22semidirect
27. #17988402C22semidirect
197. C2×C73#2222semidirect
207. C73C2×#2222semidirect
395. C2#22612054direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565372
C2×#179890042
C2×#179888622
#226120542
C2×#179884162
C2×#179884032
C2×#179884022
C2×#473×C732
C2×#222273