Finite Group Databasebeta

← C2×#34036803 #49172280

Subgroups — C2×#34036803 #49172280

Order 37504.

1328 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036803C2116yesmaximal, direct product factor
2C2×#22627619C211yesmaximal, characteristic, complemented
3C2×#22627618C211yesmaximal, characteristic, complemented
4C2×#22627612C211yesmaximal, characteristic, complemented
5C2×#22627609C211yesmaximal, characteristic, complemented
6C2×#22627609C211yesmaximal, characteristic, complemented
7C2×#22627607C211yesmaximal, characteristic, complemented
8C2×#22627602C211yesmaximal, characteristic, complemented
9C2×#22627601C211yesmaximal, characteristic, complemented
10C2×#22627594C211yesmaximal, characteristic
11C2×C4×D1172C211yesmaximal, characteristic, complemented
12C2×#22627584C211yesmaximal, characteristic, complemented
13C2×#22627581C211yesmaximal, characteristic, complemented
14C22×#17989779C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×D293C211yesmaximal, characteristic, complemented
16C2×#117×C293C211yesmaximal, characteristic, complemented
17C24×D293C2211yescharacteristic
18C22×Dic586C2211yescharacteristic, complemented
19C22×D1172C2211yescharacteristic
20C22×D1172C2211yescharacteristic
21C22×C22⋊D293C2211yescharacteristic
22C23×Dic293C2211yescharacteristic
23C22×C4×D293C2211yescharacteristic
24C22×C4×D293C2211yescharacteristic
25C22×C4×D293C2211yescharacteristic, complemented
26#22627619C2218yescomplemented
27#22627618C2218yescomplemented
28#22627612C2218yescomplemented
29#22627609C2218yescomplemented
30#22627609C2218yescomplemented
31#22627607C2218yescomplemented
32#22627602C2218yescomplemented
33#22627601C2218yescomplemented
34#22627594C2218yes—
35C4×D1172C2218yescomplemented
36#22627584C2218yescomplemented
37#22627581C2218yescomplemented
38C2×C4⋊Dic293C2211yescharacteristic, complemented
39C2×#17989781C2211yescharacteristic, complemented
40C2×#17989781C2211yescharacteristic, complemented
41C2×#17989781C2211yescharacteristic, complemented
42C2×#17989781C2211yescharacteristic, complemented
43C2×#17989781C2211yescharacteristic, complemented
44C2×C22⋊Dic293C2211yescharacteristic
45C2×#17989779C2211yescharacteristic
46C2×#17989779C2211yescharacteristic
47C2×#17989779C2211yescharacteristic
48C2×#17989779C2211yescharacteristic
49C2×#17989779C2211yescharacteristic
50C2×#17989779C2211yescharacteristic
51C2×#17989779C2211yescharacteristic
52C2×#17989779C2211yescharacteristic
53C2×#17989779C2218yescomplemented
54C2×#17989779C2211yescharacteristic, complemented
55C2×#17989779C2211yescharacteristic, complemented
56C2×#17989779C2211yescharacteristic, complemented
57C22⋊C4×D293C2218yescomplemented
58C2×C4×Dic293C2211yescharacteristic, complemented
59C23×C4×C293C2211yescharacteristic
60#117×C293C2218yescomplemented
61C2×C4⋊C4×C293C2211yescharacteristic, complemented
62C2×C4⋊C4×C293C2211yescharacteristic, complemented
63C2×C22⋊C4×C293C2211yescharacteristic
64C2×C22⋊C4×C293C2211yescharacteristic
65C2×C42×C293C2211yescharacteristic, complemented
66C2×C42×C293C2211yescharacteristic, complemented
67C23×D293—24no—
68C23×D293—24no—
69C23×D293—42no—
70C23×D293C2311yescharacteristic
71C23×D293C2311yescharacteristic
72C23×D293C2314yes—
73C23×D293C2311yescharacteristic
74C2×Dic586—42no—
75C2×Dic586C2314yescomplemented
76C2×D1172—24no—
77C2×D1172—42no—
78C2×D1172C2314yes—
79C2×D1172C2314yes—
80C2×C22⋊D293—24no—
81C2×C22⋊D293C2314yes—
82C22×Dic293—42no—
83C22×Dic293C2311yescharacteristic
84C22×Dic293C2311yescharacteristic
85C22×Dic293C2311yescharacteristic
86C22×Dic293C2311yescharacteristic
87C22×Dic293C2311yescharacteristic
88C22×Dic293C2314yes—
89C2×C4×D293—24no—
90C2×C4×D293—42no—
91C2×C4×D293—42no—
92C2×C4×D293C2314yes—
93C2×C4×D293C2314yes—
94C2×C4×D293C2314yescomplemented
95C4⋊Dic293C2314yescomplemented
96#17989781C2314yescomplemented
97#17989781C2314yescomplemented
98#17989781C2314yescomplemented
99#17989781C2314yescomplemented
100#17989781C2314yescomplemented
101C22⋊Dic293C2314yes—
102#17989779C2314yes—
103#17989779C2314yes—
104#17989779C2314yes—
105#17989779C2314yes—
106#17989779C2314yes—
107#17989779C2314yes—
108#17989779C2314yes—
109#17989779C2314yes—
110#17989779C2314yescomplemented
111#17989779C2314yescomplemented
112#17989779C2314yescomplemented
113C4×Dic293C2314yescomplemented
114C24×C293C2311yescharacteristic
115C22×C4×C293—24no—
116C22×C4×C293C2314yes—
117C22×C4×C293C2311yescharacteristic
118C22×C4×C293C2311yescharacteristic
119C22×C4×C293C2311yescharacteristic
120C22×C4×C293C2311yescharacteristic
121C22×C4×C293C2311yescharacteristic
122C22×C4×C293C2311yescharacteristic
123C4⋊C4×C293C2314yescomplemented
124C4⋊C4×C293C2314yescomplemented
125C22⋊C4×C293C2314yes—
126C22⋊C4×C293C2314yes—
127C42×C293C2314yescomplemented
128C42×C293C2314yescomplemented
129C22×D293—22no—
130C22×D293—22no—
131C22×D293—22no—
132C22×D293—22no—
133C22×D293—22no—
134C22×D293—28no—
135C22×D293—22no—
136C22×D293—22no—
137C22×D293—22no—
138C22×D293—28no—
139C22×D293—44no—
140C22×D293—416no—
141C22×D293#4114yes—
142C22×D293C2412yes—
143C22×D293C2412yes—
144C22×D293C2412yes—
145Dic586—44no—
146D1172—28no—
147D1172—44no—
148C22⋊D293—28no—
149C2×Dic293—22no—
150C2×Dic293—22no—
151C2×Dic293—22no—
152C2×Dic293—22no—
153C2×Dic293—22no—
154C2×Dic293—44no—
155C2×Dic293C2412yes—
156C2×Dic293C2412yes—
157C2×Dic293C2412yes—
158C2×Dic293C2412yes—
159C2×Dic293C2412yes—
160C4×D293—28no—
161C4×D293—44no—
162C4×D293—44no—
163C23×C293—22no—
164C23×C293—22no—
165C23×C293#4114yes—
166C23×C293C2412yes—
167C23×C293C2411yescharacteristic
168C2×C4×C293—28no—
169C2×C4×C293—22no—
170C2×C4×C293—22no—
171C2×C4×C293—22no—
172C2×C4×C293—22no—
173C2×C4×C293—22no—
174C2×C4×C293—22no—
175C2×C4×C293C2412yes—
176C2×C4×C293C2412yes—
177C2×C4×C293C2412yes—
178C2×C4×C293C2412yes—
179C2×C4×C293C2412yes—
180C2×C4×C293C2412yes—
181C22×C293—28no—
182C22×C293—22no—
183C22×C293—22no—
184C22×C293C2×#4112yes—
185C22×C293C2×#4114yes—
186C22×C293C2×#4112yes—
187C22×C293H(5,𝔽2)12yes—
188C22×C293C2511yescharacteristic
189C2×D293—28no—
190C2×D293—22no—
191C2×D293—22no—
192C2×D293—22no—
193C2×D293—22no—
194C2×D293—22no—
195C2×D293—22no—
196C2×D293—22no—
197C2×D293—22no—
198C2×D293—416no—
199C2×D293—44no—
200C2×D293—44no—
201C2×D293C2×#4114yes—
202C4×C293—22no—
203C4×C293—22no—
204C4×C293—22no—
205C4×C293—22no—
206C4×C293—22no—
207C4×C293—22no—
208Dic293—22no—
209Dic293—22no—
210Dic293—22no—
211Dic293—22no—
212Dic293—22no—
213C2×C293—24no—
214C2×C293#55114yescomplemented
215C2×C293C22×#4111yescharacteristic
216C2×C293C22×#4111yescharacteristic
217C2×C293C2×H(5,𝔽2)11yescharacteristic
218D293—24no—
219D293—42no—
220D293—42no—
221C293C2×#55111yescharacteristic, complemented, Sylow
222C2×#551—2931nomaximal, Sylow
223#551—29316no—
224C2×#126—2931no—
225C2×#126—2931no—
226C2×#124—2931no—
227C2×#123—2931no—
228C2×#123—2931no—
229C2×#123—2931no—
230C2×C22⋊Q8—2931no—
231C2×C22⋊Q8—2931no—
232C2×#120—2931no—
233C2×C4×D4—2931no—
234C2×C4×D4—2931no—
235C2×#117—2931no—
236C2×#117D29311yescharacteristic, complemented
237C22×C22⋊C4—2931no—
238C22×C22⋊C4—2931no—
239C25—2931no—
240C22×Q8—2931no—
241C22×D4—2931no—
242C22×D4—2931no—
243C22×D4—2931no—
244C23×C4—2931no—
245C23×C4—2931no—
246C23×C4—2931no—
247C23×C4—2931no—
248C23×C4C2×D29311yescharacteristic
249#126—2938no—
250#126—2938no—
251#124—2938no—
252#123—2938no—
253#123—2938no—
254#123—2938no—
255C22⋊Q8—2938no—
256C22⋊Q8—2938no—
257#120—2938no—
258C4×D4—2938no—
259C4×D4—2938no—
260#117—2938no—
261#117C2×D29318yescomplemented
262C2×C4⋊C4—2931no—
263C2×C4⋊C4—2931no—
264C2×C4⋊C4—2931no—
265C2×C4⋊C4—2931no—
266C2×C4⋊C4—2931no—
267C2×C4⋊C4—2931no—
268C2×C4⋊C4C2×D29311yescharacteristic, complemented
269C2×C4⋊C4C2×D29311yescharacteristic, complemented
270C2×C22⋊C4—2931no—
271C2×C22⋊C4—2931no—
272C2×C22⋊C4—2931no—
273C2×C22⋊C4—2931no—
274C2×C22⋊C4—2931no—
275C2×C22⋊C4—2931no—
276C2×C22⋊C4—2931no—
277C2×C22⋊C4—2938no—
278C2×C22⋊C4—2931no—
279C2×C22⋊C4—2931no—
280C2×C22⋊C4—2931no—
281C2×C22⋊C4—2931no—
282C2×C22⋊C4—2931no—
283C2×C22⋊C4—2938no—
284C2×C22⋊C4C2×D29311yescharacteristic
285C2×C22⋊C4C2×D29311yescharacteristic
286C2×C42—2931no—
287C2×C42C2×D29311yescharacteristic, complemented
288C2×C42C2×D29311yescharacteristic, complemented
289C24—2931no—
290C24—2931no—
291C24—2931no—
292C24—2934no—
293C24—5864no—
294C24—5864no—
295C24—11722no—
296C24C22×D29311yescharacteristic
297C2×Q8—2934no—
298C2×Q8—11722no—
299C2×D4—2934no—
300C2×D4—2934no—
301C2×D4—2934no—
302C2×D4—5864no—
303C2×D4—5864no—
304C2×D4—11722no—
305C22×C4—24no—
306C22×C4—2931no—
307C22×C4—2931no—
308C22×C4—2931no—
309C22×C4—2931no—
310C22×C4—2931no—
311C22×C4—2934no—
312C22×C4—2934no—
313C22×C4—2934no—
314C22×C4—2934no—
315C22×C4—5864no—
316C22×C4—11722no—
317C22×C4—11722no—
318C22×C4—11722no—
319C22×C4C22×D29314yes—
320C22×C4C22×D29311yescharacteristic
321C22×C4C22×D29311yescharacteristic
322C22×C4C22×D29311yescharacteristic
323C22×C4C22×D29311yescharacteristic
324C22×C4C22×D29311yescharacteristic
325C22×C4C22×D29311yescharacteristic
326C4⋊C4—2934no—
327C4⋊C4—2934no—
328C4⋊C4—2934no—
329C4⋊C4—2934no—
330C4⋊C4—2934no—
331C4⋊C4—2934no—
332C4⋊C4C22×D29314yescomplemented
333C4⋊C4C22×D29314yescomplemented
334C22⋊C4—2934no—
335C22⋊C4—2934no—
336C22⋊C4—2934no—
337C22⋊C4—2934no—
338C22⋊C4—2934no—
339C22⋊C4—2934no—
340C22⋊C4—2934no—
341C22⋊C4—2934no—
342C22⋊C4—2934no—
343C22⋊C4—2934no—
344C22⋊C4—2934no—
345C22⋊C4—2934no—
346C22⋊C4C22×D29314yes—
347C22⋊C4C22×D29314yes—
348C42—2934no—
349C42C22×D29314yescomplemented
350C42C22×D29314yescomplemented
351C23—22no—
352C23—22no—
353C23—2934no—
354C23—2932no—
355C23—2932no—
356C23—2932no—
357C23—5868no—
358C23—5862no—
359C23—5862no—
360C23—5862no—
361C23—5862no—
362C23—5862no—
363C23—5868no—
364C23—5862no—
365C23—5862no—
366C23—5862no—
367C23—11724no—
368C23—117216no—
369C23#1798980214yes—
370C23C23×D29312yes—
371C23C23×D29311yescharacteristic
372Q8—11724no—
373D4—5868no—
374D4—5868no—
375D4—11724no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—28no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—2932no—
384C2×C4—2932no—
385C2×C4—2932no—
386C2×C4—2932no—
387C2×C4—2932no—
388C2×C4—5868no—
389C2×C4—5862no—
390C2×C4—5862no—
391C2×C4—5862no—
392C2×C4—5862no—
393C2×C4—5862no—
394C2×C4—11724no—
395C2×C4—11724no—
396C2×C4—11724no—
397C2×C4C23×D29312yes—
398C2×C4C23×D29312yes—
399C2×C4C23×D29312yes—
400C2×C4C23×D29312yes—
401C2×C4C23×D29312yes—
402C2×C4C23×D29312yes—
403C22—28no—
404C22—22no—
405C22—22no—
406C22—2934no—
407C22—5868no—
408C22—5862no—
409C22—5862no—
410C22—5862no—
411C22—5862no—
412C22—5862no—
413C22—5862no—
414C22—5862no—
415C22—5862no—
416C22—117216no—
417C22—11724no—
418C22—11724no—
419C22#41×D29312yes—
420C22C2×#1798980214yes—
421C22C2×#1798980212yes—
422C22#2262767012yes—
423C22C24×D29311yescharacteristic
424C4—22no—
425C4—22no—
426C4—22no—
427C4—22no—
428C4—22no—
429C4—22no—
430C4—5862no—
431C4—5862no—
432C4—5862no—
433C4—5862no—
434C4—5862no—
435C2—24no—
436C2—5864no—
437C2—11722no—
438C2—11722no—
439C2#3403680314yesdirect product factor
440C2C2×#41×D29311yescharacteristic
441C2C22×#1798980211yescharacteristic
442C2C2×#2262767011yescharacteristic
subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×#117×C293C2
socleC23×C293C24
prime radicalC2×#22627594C2
hypercenterC2×#117D293
hypocenterC293C2×#551
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #34036803C2direct (N × H)
2. C2×#22627619C2semidirect
3. C2×#22627618C2semidirect
4. C2×#22627612C2semidirect
5. C2×#22627609C2semidirect
6. C2×#22627609C2semidirect
7. C2×#22627607C2semidirect
8. C2×#22627602C2semidirect
9. C2×#22627601C2semidirect
11. C2×C4×D1172C2semidirect
12. C2×#22627584C2semidirect
13. C2×#22627581C2semidirect
14. C22×#17989779C2semidirect
15. C2×C22⋊C4×D293C2semidirect
16. C2×#117×C293C2semidirect
18. C22×Dic586C22semidirect
25. C22×C4×D293C22semidirect
26. #22627619C22semidirect
27. #22627618C22semidirect
28. #22627612C22semidirect
29. #22627609C22semidirect
30. #22627609C22semidirect
31. #22627607C22semidirect
32. #22627602C22semidirect
33. #22627601C22semidirect
35. C4×D1172C22semidirect
36. #22627584C22semidirect
37. #22627581C22semidirect
38. C2×C4⋊Dic293C22semidirect
39. C2×#17989781C22semidirect
40. C2×#17989781C22semidirect
41. C2×#17989781C22semidirect
42. C2×#17989781C22semidirect
43. C2×#17989781C22semidirect
53. C2×#17989779C22semidirect
54. C2×#17989779C22semidirect
55. C2×#17989779C22semidirect
56. C2×#17989779C22semidirect
57. C22⋊C4×D293C22semidirect
58. C2×C4×Dic293C22semidirect
60. #117×C293C22semidirect
61. C2×C4⋊C4×C293C22semidirect
62. C2×C4⋊C4×C293C22semidirect
65. C2×C42×C293C22semidirect
66. C2×C42×C293C22semidirect
75. C2×Dic586C23semidirect
94. C2×C4×D293C23semidirect
95. C4⋊Dic293C23semidirect
96. #17989781C23semidirect
97. #17989781C23semidirect
98. #17989781C23semidirect
99. #17989781C23semidirect
100. #17989781C23semidirect
110. #17989779C23semidirect
111. #17989779C23semidirect
112. #17989779C23semidirect
113. C4×Dic293C23semidirect
123. C4⋊C4×C293C23semidirect
124. C4⋊C4×C293C23semidirect
127. C42×C293C23semidirect
128. C42×C293C23semidirect
214. C2×C293#551semidirect
221. C293C2×#551semidirect
236. C2×#117D293semidirect
261. #117C2×D293semidirect
268. C2×C4⋊C4C2×D293semidirect
269. C2×C4⋊C4C2×D293semidirect
287. C2×C42C2×D293semidirect
288. C2×C42C2×D293semidirect
332. C4⋊C4C22×D293semidirect
333. C4⋊C4C22×D293semidirect
349. C42C22×D293semidirect
350. C42C22×D293semidirect
439. C2#34036803direct (N × H)

Maximal subgroups

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

subgroupindex
#340368032
C2×#226276192
C2×#226276182
C2×#226276122
C2×#226276092
C2×#226276072
C2×#226276022
C2×#226276012
C2×#226275942
C2×C4×D11722
C2×#226275842
C2×#226275812
C22×#179897792
C2×C22⋊C4×D2932
C2×#117×C2932
C2×#551293