Finite Group Databasebeta

← C107×#8998 #41034962

Subgroups — C107×#8998 #41034962

Order 27392.

414 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
1C107×#3172C211yesmaximal, characteristic
2C107×#2995C211yesmaximal, characteristic
3C107×#1995C211yesmaximal, characteristic, complemented
4C107×#1500C211yesmaximal, characteristic
5C107×#1497C211yesmaximal, characteristic, complemented
6C107×#1300C211yesmaximal, characteristic, complemented
7C107×#1299C211yesmaximal, characteristic, complemented
8#533×C107C2211yescharacteristic
9#529×C107C2211yescharacteristic
10#501×C107C411yescharacteristic, complemented
11#497×C107C411yescharacteristic, complemented
12#491×C107C411yescharacteristic, complemented
13#489×C107C411yescharacteristic, complemented
14#470×C107—21no—
15#468×C107—21no—
16#446×C107—21no—
17C4×Q16×C107—21no—
18C4×SD16×C107—21no—
19#436×C107—21no—
20#435×C107—21no—
21#435×C107—21no—
22#433×C107—21no—
23#432×C107C2211yescharacteristic
24#431×C107C2211yescharacteristic
25#424×C107—21no—
26#423×C107C2211yescharacteristic
27C4×M16×C107C2211yescharacteristic
28#376×C107C2211yescharacteristic
29#339×C107—21no—
30#339×C107—21no—
31#328×C107—21no—
32#327×C107—21no—
33Q8⋊C8×C107—21no—
34Q8⋊C8×C107—21no—
35C2×Q16×C107—21no—
36C2×SD16×C107—21no—
37C2×M16×C107—21no—
38C2×M16×C107—21no—
39C2×M16×C107D411yescharacteristic
40C2×M16×C107D411yescharacteristic
41C22×C8×C107—21no—
42C4⋊Q8×C107C2×C411yescharacteristic
43C4⋊Q8×C107C2×C411yescharacteristic
44#126×C107—21no—
45#125×C107—21no—
46#125×C107C2×C411yescharacteristic
47#124×C107C2×C411yescharacteristic
48#123×C107—21no—
49C22⋊Q8×C107—21no—
50C22⋊Q8×C107—21no—
51C22⋊Q8×C107D411yescharacteristic
52#121×C107D411yescharacteristic
53C4×Q8×C107—21no—
54C4×Q8×C107—21no—
55C4×Q8×C107D411yescharacteristic
56C4×D4×C107—21no—
57C4×D4×C107D411yescharacteristic
58#117×C107—21no—
59#117×C107—21no—
60C2×C42×C107—21no—
61C2×C42×C107C2311yescharacteristic
62#107×C107—21no—
63#106×C107—21no—
64C4⋊C8×C107—21no—
65C4⋊C8×C107—21no—
66C4⋊C8×C107—21no—
67C4⋊C8×C107—21no—
68C4⋊C8×C107—21no—
69C4⋊C8×C107D411yescharacteristic
70C4⋊C8×C107D411yescharacteristic
71#103×C107—21no—
72#103×C107—21no—
73#103×C107—21no—
74#102×C107—21no—
75C22⋊C8×C107—21no—
76C22⋊C8×C107—21no—
77C22⋊C8×C107—21no—
78C22⋊C8×C107—21no—
79#97×C107—21no—
80#97×C107—21no—
81#97×C107C2×C411yescharacteristic
82#97×C107C2×C411yescharacteristic
83C4×C8×C107—21no—
84C4×C8×C107—21no—
85C4×C8×C107—21no—
86#95×C107—21no—
87#95×C107—21no—
88C2×Q8×C107—21no—
89C2×Q8×C107—21no—
90C2×Q8×C107C22⋊C411yescharacteristic
91C2×D4×C107—21no—
92C2×D4×C107C22⋊C411yescharacteristic
93C22×C4×C107—21no—
94C22×C4×C107—41no—
95C22×C4×C107C2×D411yescharacteristic
96C22×C4×C107C2×D411yescharacteristic
97C22×C4×C107#4111yescharacteristic
98Q16×C107—42no—
99SD16×C107—42no—
100M16×C107—42no—
101M16×C107—41no—
102M16×C107—41no—
103M16×C107—81no—
104C2×C8×C107—21no—
105C2×C8×C107—21no—
106C2×C8×C107—21no—
107C2×C8×C107—21no—
108C2×C8×C107—21no—
109C2×C8×C107—21no—
110C2×C8×C107—41no—
111C2×C8×C107—81no—
112C4⋊C4×C107—21no—
113C4⋊C4×C107—21no—
114C4⋊C4×C107—21no—
115C4⋊C4×C107—21no—
116C4⋊C4×C107—21no—
117C4⋊C4×C107—21no—
118C4⋊C4×C107—21no—
119C4⋊C4×C107—21no—
120C4⋊C4×C107—41no—
121C4⋊C4×C107—41no—
122C4⋊C4×C107C22⋊C411yescharacteristic
123C4⋊C4×C107C22⋊C411yescharacteristic
124C22⋊C4×C107—21no—
125C22⋊C4×C107—21no—
126C22⋊C4×C107—21no—
127C22⋊C4×C107—21no—
128C22⋊C4×C107—21no—
129C22⋊C4×C107—41no—
130C42×C107—21no—
131C42×C107—22no—
132C42×C107—41no—
133C42×C107—41no—
134C42×C107C22×C411yescharacteristic
135C42×C107C2×D411yescharacteristic
136C42×C107C2×D411yescharacteristic
137C42×C107#4111yescharacteristic
138C23×C107—21no—
139C23×C107#12111yescharacteristic
140Q8×C107—41no—
141Q8×C107—41no—
142Q8×C107—41no—
143Q8×C107—42no—
144D4×C107—41no—
145D4×C107—81no—
146C2×C4×C107—21no—
147C2×C4×C107—21no—
148C2×C4×C107—21no—
149C2×C4×C107—21no—
150C2×C4×C107—21no—
151C2×C4×C107—41no—
152C2×C4×C107—41no—
153C2×C4×C107—41no—
154C2×C4×C107—41no—
155C2×C4×C107—42no—
156C2×C4×C107—41no—
157C2×C4×C107—41no—
158C2×C4×C107—81no—
159C2×C4×C107—81no—
160C2×C4×C107C2×C22⋊C411yescharacteristic
161C2×C4×C107C4×D411yescharacteristic
162C2×C4×C107C4×D411yescharacteristic
163C2×C4×C107#12011yescharacteristic
164C2×C4×C107#12111yescharacteristic
165C2×C4×C107#12311yescharacteristic
166C8×C107—22no—
167C8×C107—41no—
168C8×C107—41no—
169C8×C107—41no—
170C8×C107—41no—
171C8×C107—41no—
172C8×C107—81no—
173C22×C107—21no—
174C22×C107—21no—
175C22×C107—21no—
176C22×C107—41no—
177C22×C107—41no—
178C22×C107—41no—
179C22×C107#38611yescharacteristic
180C4×C107—21no—
181C4×C107—21no—
182C4×C107—21no—
183C4×C107—21no—
184C4×C107—21no—
185C4×C107—41no—
186C4×C107—41no—
187C4×C107—41no—
188C4×C107—82no—
189C4×C107—81no—
190C4×C107—81no—
191C4×C107#45511yescharacteristic
192C4×C107#45611yescharacteristic
193#8998C10711yesmaximal, characteristic, direct product factor, Sylow
194C2×C107—41no—
195C2×C107—81no—
196C2×C107#188111yescharacteristic
197C2×C107#188211yescharacteristic
198C2×C107#188411yescharacteristic
199#3172C2×C10711yescharacteristic
200#2995C2×C10711yescharacteristic
201#1995C2×C10711yescharacteristic, complemented
202#1500C2×C10711yescharacteristic
203#1497C2×C10711yescharacteristic, complemented
204#1300C2×C10711yescharacteristic, complemented
205#1299C2×C10711yescharacteristic, complemented
206C107#899811yescharacteristic, direct product factor, Sylow
207#533C22×C10711yescharacteristic
208#529C22×C10711yescharacteristic
209#501C4×C10711yescharacteristic, complemented
210#497C4×C10711yescharacteristic, complemented
211#491C4×C10711yescharacteristic, complemented
212#489C4×C10711yescharacteristic, complemented
213#470—21no—
214#468—21no—
215#446—21no—
216C4×Q16—21no—
217C4×SD16—21no—
218#436—21no—
219#435—21no—
220#435—21no—
221#433—21no—
222#432C22×C10711yescharacteristic
223#431C22×C10711yescharacteristic
224#424—21no—
225#423C22×C10711yescharacteristic
226C4×M16C22×C10711yescharacteristic
227#376C22×C10711yescharacteristic
228#339—21no—
229#339—21no—
230#328—21no—
231#327—21no—
232Q8⋊C8—21no—
233Q8⋊C8—21no—
234C2×Q16—21no—
235C2×SD16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16D4×C10711yescharacteristic
239C2×M16D4×C10711yescharacteristic
240C22×C8—21no—
241C4⋊Q8C2×C4×C10711yescharacteristic
242C4⋊Q8C2×C4×C10711yescharacteristic
243#126—21no—
244#125—21no—
245#125C2×C4×C10711yescharacteristic
246#124C2×C4×C10711yescharacteristic
247#123—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8D4×C10711yescharacteristic
251#121D4×C10711yescharacteristic
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8D4×C10711yescharacteristic
255C4×D4—21no—
256C4×D4D4×C10711yescharacteristic
257#117—21no—
258#117—21no—
259C2×C42—21no—
260C2×C42C23×C10711yescharacteristic
261#107—21no—
262#106—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C10711yescharacteristic
269C4⋊C8D4×C10711yescharacteristic
270#103—21no—
271#103—21no—
272#103—21no—
273#102—21no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278#97—21no—
279#97—21no—
280#97C2×C4×C10711yescharacteristic
281#97C2×C4×C10711yescharacteristic
282C4×C8—21no—
283C4×C8—21no—
284C4×C8—21no—
285#95—21no—
286#95—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8C22⋊C4×C10711yescharacteristic
290C2×D4—21no—
291C2×D4C22⋊C4×C10711yescharacteristic
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C10711yescharacteristic
295C22×C4C2×D4×C10711yescharacteristic
296C22×C4#41×C10711yescharacteristic
297Q16—42no—
298SD16—42no—
299M16—42no—
300M16—41no—
301M16—41no—
302M16—81no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—41no—
310C2×C8—81no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4C22⋊C4×C10711yescharacteristic
322C4⋊C4C22⋊C4×C10711yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C42—21no—
330C42—22no—
331C42—41no—
332C42—41no—
333C42C22×C4×C10711yescharacteristic
334C42C2×D4×C10711yescharacteristic
335C42C2×D4×C10711yescharacteristic
336C42#41×C10711yescharacteristic
337C23—21no—
338C23#121×C10711yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—41no—
342Q8—42no—
343D4—41no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C22⋊C4×C10711yescharacteristic
360C2×C4C4×D4×C10711yescharacteristic
361C2×C4C4×D4×C10711yescharacteristic
362C2×C4#120×C10711yescharacteristic
363C2×C4#121×C10711yescharacteristic
364C2×C4#123×C10711yescharacteristic
365C8—22no—
366C8—41no—
367C8—41no—
368C8—41no—
369C8—41no—
370C8—41no—
371C8—81no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#386×C10711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4#455×C10711yescharacteristic
391C4#456×C10711yescharacteristic
392C2—41no—
393C2—81no—
394C2C107×#188111yescharacteristic
395C2C107×#188211yescharacteristic
396C2C107×#188411yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#386
prime radical#121×C107D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1995C2semidirect
5. C107×#1497C2semidirect
6. C107×#1300C2semidirect
7. C107×#1299C2semidirect
10. #501×C107C4semidirect
11. #497×C107C4semidirect
12. #491×C107C4semidirect
13. #489×C107C4semidirect
193. #8998C107direct (N × H)
201. #1995C2×C107semidirect
203. #1497C2×C107semidirect
204. #1300C2×C107semidirect
205. #1299C2×C107semidirect
206. C107#8998direct (N × H)
209. #501C4×C107semidirect
210. #497C4×C107semidirect
211. #491C4×C107semidirect
212. #489C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#31722
C107×#29952
C107×#19952
C107×#15002
C107×#14972
C107×#13002
C107×#12992
#8998107