Finite Group Databasebeta

← C107×#9370 #41035334

Subgroups — C107×#9370 #41035334

Order 27392.

424 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3219C211yesmaximal, characteristic
2C107×#2967C211yesmaximal, characteristic, complemented
3C107×#1521C211yesmaximal, characteristic, complemented
4C107×#1514C211yesmaximal, characteristic, complemented
5C107×#1484C211yesmaximal, characteristic, complemented
6C107×#1288C211yesmaximal, characteristic, complemented
7C107×#1287C211yesmaximal, characteristic, complemented
8#532×C107C2211yescharacteristic
9#529×C107C2211yescharacteristic
10#497×C107C411yescharacteristic, complemented
11#496×C107C411yescharacteristic, complemented
12#491×C107C411yescharacteristic, complemented
13#490×C107C411yescharacteristic, complemented
14#464×C107—21no—
15#463×C107—21no—
16#452×C107—21no—
17#449×C107—21no—
18#446×C107—21no—
19#436×C107—21no—
20#435×C107—21no—
21#435×C107—21no—
22#433×C107—21no—
23#432×C107C2211yescharacteristic
24#432×C107C2211yescharacteristic
25#431×C107C2211yescharacteristic
26#405×C107—21no—
27C4×M16×C107C2211yescharacteristic
28#383×C107C2211yescharacteristic
29#328×C107—21no—
30#327×C107—21no—
31#327×C107—21no—
32#327×C107—21no—
33D4⋊C8×C107—21no—
34D4⋊C8×C107—21no—
35C2×#41×C107—21no—
36C2×Q16×C107—21no—
37C2×SD16×C107—21no—
38C2×SD16×C107—21no—
39C2×D8×C107—21no—
40C2×M16×C107—21no—
41C2×M16×C107—21no—
42C22×C8×C107—21no—
43C4⋊Q8×C107C2×C411yescharacteristic
44#127×C107C2×C411yescharacteristic
45#126×C107—21no—
46#125×C107C2×C411yescharacteristic
47#124×C107—21no—
48#124×C107C2×C411yescharacteristic
49#123×C107—21no—
50C22⋊Q8×C107D411yescharacteristic
51#121×C107—21no—
52#121×C107—21no—
53#121×C107D411yescharacteristic
54C4×Q8×C107D411yescharacteristic
55C4×D4×C107—21no—
56C4×D4×C107—21no—
57C4×D4×C107—21no—
58C4×D4×C107D411yescharacteristic
59#117×C107—21no—
60C2×C42×C107C2311yescharacteristic
61C4⋊C8×C107—21no—
62C4⋊C8×C107—21no—
63C4⋊C8×C107—21no—
64C4⋊C8×C107—21no—
65C4⋊C8×C107—21no—
66#103×C107—21no—
67#103×C107—21no—
68#102×C107—21no—
69#102×C107—21no—
70C22⋊C8×C107—21no—
71C22⋊C8×C107—21no—
72C22⋊C8×C107—21no—
73C22⋊C8×C107—21no—
74C22⋊C8×C107D411yescharacteristic
75C22⋊C8×C107D411yescharacteristic
76#97×C107—21no—
77#97×C107—21no—
78#97×C107—21no—
79#97×C107C2×C411yescharacteristic
80#97×C107C2×C411yescharacteristic
81C4×C8×C107—21no—
82C4×C8×C107—21no—
83C4×C8×C107D411yescharacteristic
84C4×C8×C107D411yescharacteristic
85#95×C107—21no—
86#95×C107—21no—
87#95×C107—21no—
88#41×C107—81no—
89#41×C107—81no—
90C2×Q8×C107—21no—
91C2×Q8×C107C22⋊C411yescharacteristic
92C2×D4×C107—21no—
93C2×D4×C107—21no—
94C2×D4×C107—21no—
95C2×D4×C107—21no—
96C2×D4×C107—41no—
97C2×D4×C107C22⋊C411yescharacteristic
98C22×C4×C107—21no—
99C22×C4×C107—41no—
100C22×C4×C107—41no—
101C22×C4×C107C2×D411yescharacteristic
102C22×C4×C107C2×D411yescharacteristic
103C22×C4×C107#4111yescharacteristic
104Q16×C107—81no—
105SD16×C107—81no—
106SD16×C107—81no—
107D8×C107—81no—
108M16×C107—42no—
109M16×C107—42no—
110C2×C8×C107—21no—
111C2×C8×C107—21no—
112C2×C8×C107—21no—
113C2×C8×C107—21no—
114C2×C8×C107—21no—
115C2×C8×C107—21no—
116C2×C8×C107—42no—
117C2×C8×C107—41no—
118C4⋊C4×C107—21no—
119C4⋊C4×C107—21no—
120C4⋊C4×C107—21no—
121C4⋊C4×C107—21no—
122C4⋊C4×C107—21no—
123C4⋊C4×C107—21no—
124C4⋊C4×C107C22⋊C411yescharacteristic
125C4⋊C4×C107C22⋊C411yescharacteristic
126C22⋊C4×C107—21no—
127C22⋊C4×C107—21no—
128C22⋊C4×C107—21no—
129C22⋊C4×C107—21no—
130C22⋊C4×C107—21no—
131C22⋊C4×C107—41no—
132C22⋊C4×C107—41no—
133C42×C107—21no—
134C42×C107C22×C411yescharacteristic
135C42×C107C2×D411yescharacteristic
136C42×C107C2×D411yescharacteristic
137C42×C107#4111yescharacteristic
138C23×C107—21no—
139C23×C107—41no—
140C23×C107#12111yescharacteristic
141Q8×C107—41no—
142Q8×C107—41no—
143Q8×C107—41no—
144D4×C107—41no—
145D4×C107—41no—
146D4×C107—41no—
147D4×C107—42no—
148D4×C107—81no—
149D4×C107—81no—
150D4×C107—82no—
151C2×C4×C107—21no—
152C2×C4×C107—21no—
153C2×C4×C107—21no—
154C2×C4×C107—41no—
155C2×C4×C107—41no—
156C2×C4×C107—41no—
157C2×C4×C107—41no—
158C2×C4×C107—41no—
159C2×C4×C107—41no—
160C2×C4×C107—82no—
161C2×C4×C107—81no—
162C2×C4×C107—81no—
163C2×C4×C107—81no—
164C2×C4×C107C2×C22⋊C411yescharacteristic
165C2×C4×C107C4×D411yescharacteristic
166C2×C4×C107C4×D411yescharacteristic
167C2×C4×C107#12011yescharacteristic
168C2×C4×C107#12111yescharacteristic
169C2×C4×C107#12311yescharacteristic
170C8×C107—22no—
171C8×C107—41no—
172C8×C107—41no—
173C8×C107—41no—
174C8×C107—41no—
175C8×C107—41no—
176C8×C107—81no—
177C22×C107—21no—
178C22×C107—21no—
179C22×C107—21no—
180C22×C107—41no—
181C22×C107—41no—
182C22×C107—41no—
183C22×C107—81no—
184C22×C107—81no—
185C22×C107—81no—
186C22×C107#38611yescharacteristic
187C4×C107—21no—
188C4×C107—21no—
189C4×C107—21no—
190C4×C107—21no—
191C4×C107—21no—
192C4×C107—21no—
193C4×C107—41no—
194C4×C107—41no—
195C4×C107—41no—
196C4×C107—81no—
197C4×C107—161no—
198#9370C10711yesmaximal, characteristic, direct product factor, Sylow
199C2×C107—41no—
200C2×C107—81no—
201C2×C107—161no—
202C2×C107#188111yescharacteristic
203C2×C107#190611yescharacteristic
204C2×C107#191011yescharacteristic
205#3219C2×C10711yescharacteristic
206#2967C2×C10711yescharacteristic, complemented
207#1521C2×C10711yescharacteristic, complemented
208#1514C2×C10711yescharacteristic, complemented
209#1484C2×C10711yescharacteristic, complemented
210#1288C2×C10711yescharacteristic, complemented
211#1287C2×C10711yescharacteristic, complemented
212C107#937011yescharacteristic, direct product factor, Sylow
213#532C22×C10711yescharacteristic
214#529C22×C10711yescharacteristic
215#497C4×C10711yescharacteristic, complemented
216#496C4×C10711yescharacteristic, complemented
217#491C4×C10711yescharacteristic, complemented
218#490C4×C10711yescharacteristic, complemented
219#464—21no—
220#463—21no—
221#452—21no—
222#449—21no—
223#446—21no—
224#436—21no—
225#435—21no—
226#435—21no—
227#433—21no—
228#432C22×C10711yescharacteristic
229#432C22×C10711yescharacteristic
230#431C22×C10711yescharacteristic
231#405—21no—
232C4×M16C22×C10711yescharacteristic
233#383C22×C10711yescharacteristic
234#328—21no—
235#327—21no—
236#327—21no—
237#327—21no—
238D4⋊C8—21no—
239D4⋊C8—21no—
240C2×#41—21no—
241C2×Q16—21no—
242C2×SD16—21no—
243C2×SD16—21no—
244C2×D8—21no—
245C2×M16—21no—
246C2×M16—21no—
247C22×C8—21no—
248C4⋊Q8C2×C4×C10711yescharacteristic
249#127C2×C4×C10711yescharacteristic
250#126—21no—
251#125C2×C4×C10711yescharacteristic
252#124—21no—
253#124C2×C4×C10711yescharacteristic
254#123—21no—
255C22⋊Q8D4×C10711yescharacteristic
256#121—21no—
257#121—21no—
258#121D4×C10711yescharacteristic
259C4×Q8D4×C10711yescharacteristic
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4D4×C10711yescharacteristic
264#117—21no—
265C2×C42C23×C10711yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271#103—21no—
272#103—21no—
273#102—21no—
274#102—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8D4×C10711yescharacteristic
280C22⋊C8D4×C10711yescharacteristic
281#97—21no—
282#97—21no—
283#97—21no—
284#97C2×C4×C10711yescharacteristic
285#97C2×C4×C10711yescharacteristic
286C4×C8—21no—
287C4×C8—21no—
288C4×C8D4×C10711yescharacteristic
289C4×C8D4×C10711yescharacteristic
290#95—21no—
291#95—21no—
292#95—21no—
293#41—81no—
294#41—81no—
295C2×Q8—21no—
296C2×Q8C22⋊C4×C10711yescharacteristic
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4C22⋊C4×C10711yescharacteristic
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4C2×D4×C10711yescharacteristic
307C22×C4C2×D4×C10711yescharacteristic
308C22×C4#41×C10711yescharacteristic
309Q16—81no—
310SD16—81no—
311SD16—81no—
312D8—81no—
313M16—42no—
314M16—42no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—42no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4C22⋊C4×C10711yescharacteristic
330C4⋊C4C22⋊C4×C10711yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C42—21no—
339C42C22×C4×C10711yescharacteristic
340C42C2×D4×C10711yescharacteristic
341C42C2×D4×C10711yescharacteristic
342C42#41×C10711yescharacteristic
343C23—21no—
344C23—41no—
345C23#121×C10711yescharacteristic
346Q8—41no—
347Q8—41no—
348Q8—41no—
349D4—41no—
350D4—41no—
351D4—41no—
352D4—42no—
353D4—81no—
354D4—81no—
355D4—82no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4C2×C22⋊C4×C10711yescharacteristic
370C2×C4C4×D4×C10711yescharacteristic
371C2×C4C4×D4×C10711yescharacteristic
372C2×C4#120×C10711yescharacteristic
373C2×C4#121×C10711yescharacteristic
374C2×C4#123×C10711yescharacteristic
375C8—22no—
376C8—41no—
377C8—41no—
378C8—41no—
379C8—41no—
380C8—41no—
381C8—81no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22#386×C10711yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—81no—
402C4—161no—
403C2—41no—
404C2—81no—
405C2—161no—
406C2C107×#188111yescharacteristic
407C2C107×#190611yescharacteristic
408C2C107×#191011yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC107×#3219C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2967C2semidirect
3. C107×#1521C2semidirect
4. C107×#1514C2semidirect
5. C107×#1484C2semidirect
6. C107×#1288C2semidirect
7. C107×#1287C2semidirect
10. #497×C107C4semidirect
11. #496×C107C4semidirect
12. #491×C107C4semidirect
13. #490×C107C4semidirect
198. #9370C107direct (N × H)
206. #2967C2×C107semidirect
207. #1521C2×C107semidirect
208. #1514C2×C107semidirect
209. #1484C2×C107semidirect
210. #1288C2×C107semidirect
211. #1287C2×C107semidirect
212. C107#9370direct (N × H)
215. #497C4×C107semidirect
216. #496C4×C107semidirect
217. #491C4×C107semidirect
218. #490C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#32192
C107×#29672
C107×#15212
C107×#15142
C107×#14842
C107×#12882
C107×#12872
#9370107