Finite Group Databasebeta

← C107×#29154 #41055118

Subgroups — C107×#29154 #41055118

Order 27392.

612 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3160C211yesmaximal, characteristic, complemented
2C2×#443×C107C211yesmaximal, characteristic
3C107×#2031C214yesmaximal, complemented
4C107×#1976C212yesmaximal
5C107×#1833C212yesmaximal, complemented
6C107×#1814C212yesmaximal, complemented
7C107×#1812C212yesmaximal, complemented
8C107×#1772C211yesmaximal, characteristic, complemented
9C2×#135×C107C2211yescharacteristic
10C2×#131×C107C2212yes—
11#533×C107C2212yes—
12#500×C107—21no—
13#499×C107—21no—
14#499×C107—21no—
15#498×C107—21no—
16#443×C107—21no—
17#443×C107—21no—
18#443×C107—21no—
19#443×C107—21no—
20C2×#108×C107C2211yescharacteristic
21C2×#108×C107C2211yescharacteristic
22#427×C107C2212yes—
23#427×C107C2212yes—
24#427×C107C2211yescharacteristic
25#421×C107C2214yes—
26C2×#104×C107C2212yes—
27#410×C107C2214yes—
28#405×C107C2212yes—
29C2×C4×C8×C107C2211yescharacteristic
30#344×C107C2214yes—
31#339×C107C2212yes—
32H(3,ℤ/4)×C107C2214yes—
33C2×#41×C107C2312yes—
34#135×C107—21no—
35#135×C107—21no—
36#135×C107—21no—
37#135×C107—21no—
38C2×Q16×C107Q811yescharacteristic, complemented
39C2×SD16×C107Q812yescomplemented
40C2×D8×C107Q811yescharacteristic, complemented
41#131×C107—22no—
42#131×C107—22no—
43#131×C107—22no—
44#131×C107—22no—
45C2×M16×C107—22no—
46C2×M16×C107C2312yes—
47C2×M16×C107C2312yes—
48C22×C8×C107—22no—
49C22×C8×C107C2311yescharacteristic
50C22×C8×C107C2311yescharacteristic
51C4⋊Q8×C107—22no—
52#125×C107—22no—
53C22⋊Q8×C107—42no—
54C4×Q8×C107—42no—
55#117×C107C2312yes—
56#117×C107C2314yes—
57C2×C42×C107C2311yescharacteristic
58#108×C107—21no—
59#108×C107—21no—
60#108×C107—21no—
61#108×C107—21no—
62#107×C107—22no—
63#107×C107—22no—
64#107×C107—21no—
65#106×C107—22no—
66#106×C107—22no—
67#106×C107—21no—
68#104×C107—22no—
69#104×C107—22no—
70#104×C107—44no—
71#99×C107—44no—
72#97×C107—22no—
73C4×C8×C107—22no—
74C4×C8×C107D411yescharacteristic
75C4×C8×C107D411yescharacteristic
76C4×C8×C107D411yescharacteristic
77C4×C8×C107D411yescharacteristic
78#41×C107—22no—
79#41×C107—22no—
80#41×C107—22no—
81#41×C107—22no—
82C2×Q8×C107—42no—
83C2×Q8×C107C2×Q812yes—
84C2×D4×C107—22no—
85C2×D4×C107C2×Q812yes—
86C22×C4×C107—21no—
87C22×C4×C107—22no—
88C22×C4×C107C2411yescharacteristic
89Q16×C107—21no—
90Q16×C107—21no—
91SD16×C107—22no—
92SD16×C107—22no—
93D8×C107—21no—
94D8×C107—21no—
95M16×C107—22no—
96M16×C107—22no—
97M16×C107—22no—
98M16×C107—22no—
99M16×C107—42no—
100M16×C107—42no—
101C2×C8×C107—22no—
102C2×C8×C107—22no—
103C2×C8×C107—42no—
104C2×C8×C107—42no—
105C2×C8×C107C2×D411yescharacteristic
106C2×C8×C107C2×D411yescharacteristic
107C2×C8×C107C2×D411yescharacteristic
108C2×C8×C107C2×D411yescharacteristic
109C2×C8×C107C2×Q811yescharacteristic
110C2×C8×C107C2×Q811yescharacteristic
111C2×C8×C107#4111yescharacteristic
112C2×C8×C107#4111yescharacteristic
113C2×C8×C107#4111yescharacteristic
114C2×C8×C107#4111yescharacteristic
115C2×C8×C107#4111yescharacteristic
116C2×C8×C107#4111yescharacteristic
117C4⋊C4×C107—24no—
118C4⋊C4×C107—22no—
119C4⋊C4×C107—44no—
120C4⋊C4×C107—42no—
121C22⋊C4×C107—22no—
122C22⋊C4×C107—24no—
123C42×C107—21no—
124C42×C107—22no—
125C42×C107—24no—
126C42×C107C2×D411yescharacteristic
127C42×C107C2×D411yescharacteristic
128C23×C107—22no—
129C23×C107H(5,𝔽2)11yescharacteristic
130Q8×C107—22no—
131Q8×C107—22no—
132Q8×C107—84no—
133D4×C107—22no—
134D4×C107—22no—
135D4×C107—42no—
136D4×C107—42no—
137C2×C4×C107—21no—
138C2×C4×C107—21no—
139C2×C4×C107—22no—
140C2×C4×C107—42no—
141C2×C4×C107—42no—
142C2×C4×C107—42no—
143C2×C4×C107—44no—
144C2×C4×C107—42no—
145C2×C4×C107C22×D411yescharacteristic
146C2×C4×C107C22×Q811yescharacteristic
147C2×C4×C107C2×#4111yescharacteristic
148C2×C4×C107C2×#4111yescharacteristic
149C2×C4×C107C2×#4111yescharacteristic
150C2×C4×C107H(5,𝔽2)11yescharacteristic
151C8×C107—42no—
152C8×C107—42no—
153C8×C107C22⋊Q811yescharacteristic
154C8×C107C22⋊Q811yescharacteristic
155C8×C107C22⋊Q811yescharacteristic
156C8×C107C22⋊Q811yescharacteristic
157C8×C107#12411yescharacteristic
158C8×C107#12411yescharacteristic
159C8×C107#12411yescharacteristic
160C8×C107#12411yescharacteristic
161C22×C107—41no—
162C22×C107—42no—
163C22×C107—82no—
164C22×C107#53511yescharacteristic
165C22×C107#55411yescharacteristic
166C22×C107#55511yescharacteristic
167C4×C107—22no—
168C4×C107—41no—
169C4×C107—42no—
170C4×C107—82no—
171C4×C107—84no—
172C4×C107C2×C22⋊Q811yescharacteristic
173C4×C107C2×#12411yescharacteristic
174C4×C107#55411yescharacteristic
175C4×C107#55511yescharacteristic
176#29154C10711yesmaximal, characteristic, direct product factor, Sylow
177C2×C107—21no—
178C2×C107—21no—
179C2×C107—21no—
180C2×C107—82no—
181C2×C107#256311yescharacteristic
182#3160C2×C10711yescharacteristic, complemented
183C2×#443C2×C10711yescharacteristic
184#2031C2×C10714yescomplemented
185#1976C2×C10712yes—
186#1833C2×C10712yescomplemented
187#1814C2×C10712yescomplemented
188#1812C2×C10712yescomplemented
189#1772C2×C10711yescharacteristic, complemented
190C107#2915411yescharacteristic, direct product factor, Sylow
191C2×#135C22×C10711yescharacteristic
192C2×#131C22×C10712yes—
193#533C22×C10712yes—
194#500—21no—
195#499—21no—
196#499—21no—
197#498—21no—
198#443—21no—
199#443—21no—
200#443—21no—
201#443—21no—
202C2×#108C22×C10711yescharacteristic
203C2×#108C22×C10711yescharacteristic
204#427C22×C10711yescharacteristic
205#427C22×C10712yes—
206#427C22×C10712yes—
207#421C22×C10714yes—
208C2×#104C22×C10712yes—
209#410C22×C10714yes—
210#405C22×C10712yes—
211C2×C4×C8C22×C10711yescharacteristic
212#344C22×C10714yes—
213#339C22×C10712yes—
214H(3,ℤ/4)C22×C10714yes—
215C2×#41C23×C10712yes—
216#135—21no—
217#135—21no—
218#135—21no—
219#135—21no—
220C2×Q16Q8×C10711yescharacteristic, complemented
221C2×SD16Q8×C10712yescomplemented
222C2×D8Q8×C10711yescharacteristic, complemented
223#131—22no—
224#131—22no—
225#131—22no—
226#131—22no—
227C2×M16—22no—
228C2×M16C23×C10712yes—
229C2×M16C23×C10712yes—
230C22×C8—22no—
231C22×C8C23×C10711yescharacteristic
232C22×C8C23×C10711yescharacteristic
233C4⋊Q8—22no—
234#125—22no—
235C22⋊Q8—42no—
236C4×Q8—42no—
237#117C23×C10714yes—
238#117C23×C10712yes—
239C2×C42C23×C10711yescharacteristic
240#108—21no—
241#108—21no—
242#108—21no—
243#108—21no—
244#107—22no—
245#107—22no—
246#107—21no—
247#106—22no—
248#106—22no—
249#106—21no—
250#104—22no—
251#104—22no—
252#104—44no—
253#99—44no—
254#97—22no—
255C4×C8—22no—
256C4×C8D4×C10711yescharacteristic
257C4×C8D4×C10711yescharacteristic
258C4×C8D4×C10711yescharacteristic
259C4×C8D4×C10711yescharacteristic
260#41—22no—
261#41—22no—
262#41—22no—
263#41—22no—
264C2×Q8—42no—
265C2×Q8C2×Q8×C10712yes—
266C2×D4—22no—
267C2×D4C2×Q8×C10712yes—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4C24×C10711yescharacteristic
271Q16—21no—
272Q16—21no—
273SD16—22no—
274SD16—22no—
275D8—21no—
276D8—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—42no—
282M16—42no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8C2×D4×C10711yescharacteristic
288C2×C8C2×D4×C10711yescharacteristic
289C2×C8C2×D4×C10711yescharacteristic
290C2×C8C2×D4×C10711yescharacteristic
291C2×C8C2×Q8×C10711yescharacteristic
292C2×C8C2×Q8×C10711yescharacteristic
293C2×C8#41×C10711yescharacteristic
294C2×C8#41×C10711yescharacteristic
295C2×C8#41×C10711yescharacteristic
296C2×C8#41×C10711yescharacteristic
297C2×C8#41×C10711yescharacteristic
298C2×C8#41×C10711yescharacteristic
299C4⋊C4—24no—
300C4⋊C4—22no—
301C4⋊C4—44no—
302C4⋊C4—42no—
303C22⋊C4—22no—
304C22⋊C4—24no—
305C42—21no—
306C42—22no—
307C42—24no—
308C42C2×D4×C10711yescharacteristic
309C42C2×D4×C10711yescharacteristic
310C23—22no—
311C23H(5,𝔽2)×C10711yescharacteristic
312Q8—22no—
313Q8—22no—
314Q8—84no—
315D4—22no—
316D4—22no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4C22×D4×C10711yescharacteristic
328C2×C4C22×Q8×C10711yescharacteristic
329C2×C4C2×#41×C10711yescharacteristic
330C2×C4C2×#41×C10711yescharacteristic
331C2×C4C2×#41×C10711yescharacteristic
332C2×C4H(5,𝔽2)×C10711yescharacteristic
333C8—42no—
334C8—42no—
335C8C22⋊Q8×C10711yescharacteristic
336C8C22⋊Q8×C10711yescharacteristic
337C8C22⋊Q8×C10711yescharacteristic
338C8C22⋊Q8×C10711yescharacteristic
339C8#124×C10711yescharacteristic
340C8#124×C10711yescharacteristic
341C8#124×C10711yescharacteristic
342C8#124×C10711yescharacteristic
343C22—41no—
344C22—42no—
345C22—82no—
346C22#535×C10711yescharacteristic
347C22#554×C10711yescharacteristic
348C22#555×C10711yescharacteristic
349C4—22no—
350C4—41no—
351C4—42no—
352C4—84no—
353C4—82no—
354C4C2×C22⋊Q8×C10711yescharacteristic
355C4C2×#124×C10711yescharacteristic
356C4#554×C10711yescharacteristic
357C4#555×C10711yescharacteristic
358C2—21no—
359C2—21no—
360C2—21no—
361C2—82no—
362C2C107×#256311yescharacteristic
subgroupG/H
centerC4×C107#555
commutator, Frattini, cosocleC22×C4C24×C107
socleC2×C107#2563
prime radicalC2×#135×C107C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C107 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3160C2semidirect
3. C107×#2031C2semidirect
5. C107×#1833C2semidirect
6. C107×#1814C2semidirect
7. C107×#1812C2semidirect
8. C107×#1772C2semidirect
38. C2×Q16×C107Q8semidirect
39. C2×SD16×C107Q8semidirect
40. C2×D8×C107Q8semidirect
176. #29154C107direct (N × H)
182. #3160C2×C107semidirect
184. #2031C2×C107semidirect
186. #1833C2×C107semidirect
187. #1814C2×C107semidirect
188. #1812C2×C107semidirect
189. #1772C2×C107semidirect
190. C107#29154direct (N × H)
220. C2×Q16Q8×C107semidirect
221. C2×SD16Q8×C107semidirect
222. C2×D8Q8×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#31602
C2×#443×C1072
C107×#20312
C107×#19762
C107×#18332
C107×#18142
C107×#18122
C107×#17722
#29154107