Finite Group Databasebeta

← C2×#22612010 #33240368

Subgroups — C2×#22612010 #33240368

Order 18688.

686 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989027C211yesmaximal, characteristic
2C2×#17988965C211yesmaximal, characteristic, complemented
3C2×#17988704C211yesmaximal, characteristic
4#22612010C218yesmaximal, direct product factor
5C2×#17988407C211yesmaximal, characteristic, complemented
6C2×#17988404C211yesmaximal, characteristic, complemented
7C2×#17988403C211yesmaximal, characteristic, complemented
8C2×#510×C73C211yesmaximal, characteristic
9C22×Dic292C2211yescharacteristic
10C22×#11924018—21no—
11C2×#14556598—21no—
12C2×#14556589—21no—
13#17989027—22no—
14#17989027C2214yes—
15C2×#14556537—21no—
16C2×#14556535—21no—
17C2×#14556531C2211yescharacteristic
18#17988965—22no—
19#17988965C2214yescomplemented
20#17988704—22no—
21#17988704C2214yes—
22C2×#14556527C2211yescharacteristic
23C2×#14556518—21no—
24C2×C8×Dic73C2211yescharacteristic
25#17988407C2214yescomplemented
26#17988404C2214yescomplemented
27#17988403C2214yescomplemented
28C2×#135×C73C2211yescharacteristic
29C22×Q16×C73C2211yescharacteristic
30#510×C73—22no—
31#510×C73C2214yes—
32C2×Q32×C73—21no—
33C2×SD32×C73—21no—
34C2×M32×C73C2211yescharacteristic
35C22×Dic146—21no—
36C2×Dic292—21no—
37C2×Dic292—21no—
38C2×Dic292—21no—
39C2×Dic292—21no—
40C2×Dic292—21no—
41C2×Dic292C2312yes—
42C2×#11924018—24no—
43C2×#11924018—41no—
44C2×#11924018—41no—
45C2×#11924018—42no—
46#14556598—24no—
47#14556598—42no—
48C2×#11924012—21no—
49C2×#11924012—41no—
50C22×#10596831—41no—
51C22×#10596831D411yescharacteristic
52#14556589—24no—
53#14556589—42no—
54C2×#11924007—42no—
55C2×C4×Dic73D411yescharacteristic
56#14556537—24no—
57#14556535—24no—
58#14556531—21no—
59#14556531C2312yes—
60C2×#11924003—21no—
61#14556527—21no—
62#14556527C2312yes—
63#14556518—24no—
64C8×Dic73D412yes—
65C8×Dic73C2312yes—
66C2×#41×C73—21no—
67C22×Q8×C73—21no—
68#135×C73—21no—
69#135×C73—21no—
70#135×C73D412yes—
71#135×C73C2312yes—
72C2×Q16×C73—21no—
73C2×Q16×C73—21no—
74C2×Q16×C73—21no—
75C2×Q16×C73—21no—
76C2×Q16×C73—21no—
77C2×Q16×C73D411yescharacteristic
78C2×Q16×C73C2312yes—
79C2×SD16×C73—21no—
80C2×D8×C73D411yescharacteristic
81C22×C8×C73C2311yescharacteristic
82Q32×C73—24no—
83SD32×C73—24no—
84M32×C73—21no—
85M32×C73C2312yes—
86C2×C16×C73—21no—
87C2×Dic146—22no—
88C2×Dic146—41no—
89C2×Dic146—41no—
90C2×Dic146—41no—
91C2×Dic146—41no—
92C2×Dic146—41no—
93C22×Dic73—21no—
94C22×Dic73—41no—
95Dic292—22no—
96Dic292—22no—
97Dic292—41no—
98Dic292—41no—
99#11924018—44no—
100#11924018—44no—
101#11924012—22no—
102#11924012—41no—
103#11924012—44no—
104C2×#10596831—41no—
105C2×#10596831—44no—
106C2×#10596831D811yescharacteristic
107C2×#10596831D811yescharacteristic
108C2×#10596831D812yes—
109C2×#10596831C2×D412yes—
110#11924007—48no—
111C4×Dic73—21no—
112C4×Dic73C2×D412yes—
113#11924003—22no—
114#41×C73—22no—
115#41×C73—22no—
116#41×C73—41no—
117#41×C73—41no—
118C2×Q8×C73—21no—
119C2×Q8×C73—22no—
120C2×Q8×C73—41no—
121C2×Q8×C73—41no—
122C2×Q8×C73—41no—
123C2×Q8×C73—41no—
124C2×Q8×C73—41no—
125C2×D4×C73—21no—
126C2×D4×C73—41no—
127C22×C4×C73—41no—
128C22×C4×C73—41no—
129C22×C4×C73C2×D411yescharacteristic
130Q16×C73—21no—
131Q16×C73—22no—
132Q16×C73—22no—
133Q16×C73—41no—
134Q16×C73—41no—
135Q16×C73C2×D412yes—
136SD16×C73—22no—
137SD16×C73—22no—
138D8×C73—21no—
139D8×C73C2×D412yes—
140C2×C8×C73C2×D411yescharacteristic
141C2×C8×C73C2×D411yescharacteristic
142C2×C8×C73C2×D411yescharacteristic
143C2×C8×C73#4111yescharacteristic
144C2×C8×C73#4111yescharacteristic
145C2×C8×C73C2411yescharacteristic
146C16×C73—22no—
147C23×C73—41no—
148C23×C73AGL(1,ℤ/8)11yescharacteristic
149Q8×C73—22no—
150Q8×C73—41no—
151Q8×C73—42no—
152Q8×C73—42no—
153Q8×C73—81no—
154Q8×C73—81no—
155D4×C73—22no—
156D4×C73—42no—
157D4×C73—42no—
158D4×C73—41no—
159C2×C4×C73—41no—
160C2×C4×C73—42no—
161C2×C4×C73—42no—
162C2×C4×C73—42no—
163C2×C4×C73—81no—
164C2×C4×C73—81no—
165C2×C4×C73#12111yescharacteristic
166C2×C4×C73#12111yescharacteristic
167C2×C4×C73C2×D811yescharacteristic
168C2×C4×C73C2×D811yescharacteristic
169C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C73C22×D411yescharacteristic
171C2×Dic73—24no—
172C2×Dic73—22no—
173C2×Dic73—42no—
174C2×Dic73—81no—
175C2×Dic73—81no—
176Dic146—42no—
177Dic146—42no—
178Dic146—81no—
179Dic146—81no—
180C8×C73#12111yescharacteristic
181C8×C73#12111yescharacteristic
182C8×C73C22×D411yescharacteristic
183C8×C73C2×#4111yescharacteristic
184#10596831—42no—
185#10596831C2×D812yes—
186#10596831C2×D812yes—
187C22×C73—22no—
188C22×C73—42no—
189C22×C73—82no—
190C22×C73#45911yescharacteristic
191C22×C73#45911yescharacteristic
192C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
193C4×C73—42no—
194C4×C73—82no—
195C4×C73#45911yescharacteristic
196C4×C73#45911yescharacteristic
197C4×C73C2×#12111yescharacteristic
198C4×C73C22×D811yescharacteristic
199Dic73—24no—
200Dic73—82no—
201C2×#2214—731nomaximal, Sylow
202C2×C73—21no—
203C2×C73—21no—
204C2×C73—82no—
205C2×C73#221412yescomplemented
206C2×C73C2×#45911yescharacteristic
207C2×#510—731no—
208C2×#510D7311yescharacteristic
209C2×#494—731no—
210C2×#443—731no—
211#2214—738no—
212C2×#364—731no—
213C2×#362—731no—
214C2×#362—731no—
215C73C2×#221411yescharacteristic, complemented, Sylow
216C2×#135C2×D7311yescharacteristic
217C22×Q16—731no—
218C22×Q16—1461no—
219C22×Q16C2×D7311yescharacteristic
220C2×#131—1461no—
221C2×C4⋊Q8—1461no—
222#510—22no—
223#510—734no—
224#510—1462no—
225#510C2×D7314yes—
226C2×Q32—21no—
227C2×Q32—1461no—
228C2×SD32—21no—
229C2×SD32—1461no—
230C2×M32—731no—
231C2×M32C2×D7311yescharacteristic
232#494—734no—
233#494—1462no—
234#443—734no—
235#443—1462no—
236C2×#108—731no—
237C2×#104—1461no—
238C2×C4×C8—731no—
239#364—734no—
240#362—734no—
241#362—734no—
242C2×#41—21no—
243C22×Q8—21no—
244C22×Q8—1461no—
245#135—21no—
246#135—21no—
247#135C22⋊D7312yes—
248#135C22×D7312yes—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16—2921no—
255C2×Q16—2921no—
256C2×Q16—2922no—
257C2×Q16—732no—
258C2×Q16—1464no—
259C2×Q16—1461no—
260C2×Q16—1461no—
261C2×Q16—1461no—
262C2×Q16—1461no—
263C2×Q16—1461no—
264C2×Q16C22⋊D7311yescharacteristic
265C2×Q16C22×D7312yes—
266C2×SD16—21no—
267C2×D8C22⋊D7311yescharacteristic
268#131—2922no—
269#131—1464no—
270C2×M16—2921no—
271C2×M16—1461no—
272C22×C8—2921no—
273C22×C8—731no—
274C22×C8C22×D7311yescharacteristic
275C4⋊Q8—2922no—
276C4⋊Q8—1464no—
277C2×C4⋊C4—2922no—
278C2×C42—731no—
279Q32—24no—
280Q32—1464no—
281SD32—24no—
282SD32—1464no—
283M32—21no—
284M32—732no—
285M32—1461no—
286M32C22×D7312yes—
287C2×C16—21no—
288C2×C16—1461no—
289#108—732no—
290#108—1461no—
291#104—1464no—
292C4×C8—732no—
293C4×C8—732no—
294#41—22no—
295#41—22no—
296#41—41no—
297#41—41no—
298C2×Q8—21no—
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—2921no—
306C2×Q8—2921no—
307C2×Q8—2921no—
308C2×Q8—2921no—
309C2×Q8—2921no—
310C2×Q8—1462no—
311C2×D4—21no—
312C2×D4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—2921no—
316C22×C4—1461no—
317C22×C4D4×D7311yescharacteristic
318Q16—21no—
319Q16—22no—
320Q16—22no—
321Q16—41no—
322Q16—41no—
323Q16—2924no—
324Q16—2924no—
325Q16—2921no—
326Q16—2921no—
327Q16—1462no—
328Q16—1462no—
329Q16C2×C22⋊D7312yes—
330SD16—22no—
331SD16—22no—
332D8—21no—
333D8C2×C22⋊D7312yes—
334M16—2921no—
335M16—2924no—
336M16—1462no—
337C2×C8—2921no—
338C2×C8—2924no—
339C2×C8—731no—
340C2×C8—731no—
341C2×C8—732no—
342C2×C8—732no—
343C2×C8D4×D7311yescharacteristic
344C2×C8C2×C22⋊D7311yescharacteristic
345C2×C8C2×C22⋊D7311yescharacteristic
346C2×C8#1192402711yescharacteristic
347C2×C8#1192402711yescharacteristic
348C2×C8C23×D7311yescharacteristic
349C4⋊C4—2928no—
350C42—732no—
351C42—1461no—
352C16—22no—
353C16—1462no—
354C23—41no—
355C23#1455661511yescharacteristic
356Q8—22no—
357Q8—41no—
358Q8—42no—
359Q8—42no—
360Q8—81no—
361Q8—81no—
362Q8—2922no—
363Q8—2922no—
364Q8—5841no—
365Q8—5841no—
366D4—22no—
367D4—42no—
368D4—42no—
369D4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—2922no—
377C2×C4—5841no—
378C2×C4—5841no—
379C2×C4—1464no—
380C2×C4—1462no—
381C2×C4#1455656311yescharacteristic
382C2×C4#1455656311yescharacteristic
383C2×C4D8×D7311yescharacteristic
384C2×C4D8×D7311yescharacteristic
385C2×C4#1455661511yescharacteristic
386C2×C4C2×D4×D7311yescharacteristic
387C8—2922no—
388C8—732no—
389C8—732no—
390C8#1455656311yescharacteristic
391C8#1455656311yescharacteristic
392C8C22×C22⋊D7311yescharacteristic
393C8C2×#1192402711yescharacteristic
394C22—22no—
395C22—42no—
396C22—82no—
397C22#1798878011yescharacteristic
398C22#1798878011yescharacteristic
399C22C2×#1455661511yescharacteristic
400C4—42no—
401C4—82no—
402C4—5842no—
403C4—1464no—
404C4#1798878011yescharacteristic
405C4#1798878011yescharacteristic
406C4C2×#1455656311yescharacteristic
407C4C2×D8×D7311yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2#2261201012yesdirect product factor
412C2C2×#1798878011yescharacteristic
subgroupG/H
centerC22#17988780
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×#510×C73C2
socleC22×C73#459
prime radicalC2×#135×C73C22
hypercenterC2×#510D73
hypocenterC73C2×#2214
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C2×#17988965C2semidirect
4. #22612010C2direct (N × H)
5. C2×#17988407C2semidirect
6. C2×#17988404C2semidirect
7. C2×#17988403C2semidirect
19. #17988965C22semidirect
25. #17988407C22semidirect
26. #17988404C22semidirect
27. #17988403C22semidirect
205. C2×C73#2214semidirect
215. C73C2×#2214semidirect
411. C2#22612010direct (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×#179889652
C2×#179887042
#226120102
C2×#179884072
C2×#179884042
C2×#179884032
C2×#510×C732
C2×#221473