Finite Group Databasebeta

← C107×#10186 #41036150

Subgroups — C107×#10186 #41036150

Order 27392.

528 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×#3229C211yesmaximal, characteristic, complemented
2C107×#3077C211yesmaximal, characteristic
3C2×#461×C107C211yesmaximal, characteristic
4C107×#1546C211yesmaximal, characteristic, complemented
5C107×#1481C211yesmaximal, characteristic, complemented
6C107×#1460C211yesmaximal, characteristic
7C107×#1301C211yesmaximal, characteristic, complemented
8C22×SD16×C107—21no—
9#533×C107C2211yescharacteristic
10C2×C4⋊Q8×C107C2211yescharacteristic
11C2×C4×D4×C107C2211yescharacteristic
12#498×C107—21no—
13#487×C107—21no—
14#483×C107—22no—
15#478×C107—22no—
16#476×C107—21no—
17#475×C107—22no—
18#474×C107—21no—
19#461×C107—22no—
20#461×C107—22no—
21#431×C107C2211yescharacteristic
22#431×C107C2211yescharacteristic
23#428×C107—21no—
24#423×C107C2211yescharacteristic
25C2×C4⋊C8×C107C2211yescharacteristic
26#418×C107—21no—
27C2×#103×C107—21no—
28#332×C107—22no—
29Q8⋊C8×C107—22no—
30#323×C107—22no—
31C22×Q8×C107—21no—
32C22×D4×C107D411yescharacteristic
33C23×C4×C107—21no—
34C2×SD16×C107—24no—
35C2×SD16×C107—42no—
36C2×SD16×C107—42no—
37C2×M16×C107—21no—
38C22×C8×C107—21no—
39C4⋊Q8×C107—21no—
40C4⋊Q8×C107—21no—
41C4⋊Q8×C107—21no—
42C4⋊Q8×C107D412yes—
43C4⋊Q8×C107D411yescharacteristic
44C4⋊Q8×C107D411yescharacteristic
45#125×C107—21no—
46C22⋊Q8×C107—21no—
47C22⋊Q8×C107—21no—
48C4×Q8×C107—21no—
49C4×Q8×C107—21no—
50C4×D4×C107—21no—
51C4×D4×C107—21no—
52C4×D4×C107—21no—
53C4×D4×C107—21no—
54#117×C107—21no—
55C2×C4⋊C4×C107—21no—
56C2×C4⋊C4×C107—21no—
57C2×C4⋊C4×C107D411yescharacteristic
58C2×C22⋊C4×C107—21no—
59C2×C42×C107C2311yescharacteristic
60#107×C107—22no—
61#106×C107—22no—
62#106×C107—24no—
63C4⋊C8×C107—21no—
64C4⋊C8×C107—21no—
65C4⋊C8×C107—21no—
66C4⋊C8×C107—21no—
67C4⋊C8×C107D412yes—
68C4⋊C8×C107D412yes—
69#103×C107—24no—
70#103×C107—24no—
71#102×C107—22no—
72#102×C107—22no—
73C22⋊C8×C107—21no—
74C22⋊C8×C107D412yes—
75C4×C8×C107—21no—
76C4×C8×C107—21no—
77C24×C107—21no—
78C2×Q8×C107—21no—
79C2×Q8×C107—22no—
80C2×Q8×C107—21no—
81C2×Q8×C107—41no—
82C2×Q8×C107—41no—
83C2×Q8×C107—41no—
84C2×Q8×C107—41no—
85C2×Q8×C107—41no—
86C2×D4×C107—21no—
87C2×D4×C107—21no—
88C2×D4×C107—21no—
89C2×D4×C107—21no—
90C2×D4×C107—21no—
91C2×D4×C107SD1612yes—
92C22×C4×C107—21no—
93C22×C4×C107—41no—
94C22×C4×C107—41no—
95C22×C4×C107—41no—
96C22×C4×C107—82no—
97C22×C4×C107C2×D411yescharacteristic
98C22×C4×C107C2×D411yescharacteristic
99C22×C4×C107#4111yescharacteristic
100SD16×C107—48no—
101M16×C107—41no—
102M16×C107—41no—
103C2×C8×C107—22no—
104C2×C8×C107—22no—
105C2×C8×C107—22no—
106C2×C8×C107—41no—
107C2×C8×C107—41no—
108C2×C8×C107—41no—
109C4⋊C4×C107—21no—
110C4⋊C4×C107—21no—
111C4⋊C4×C107—21no—
112C4⋊C4×C107—22no—
113C4⋊C4×C107—21no—
114C4⋊C4×C107—21no—
115C4⋊C4×C107—22no—
116C4⋊C4×C107—21no—
117C4⋊C4×C107—41no—
118C4⋊C4×C107—41no—
119C4⋊C4×C107—41no—
120C4⋊C4×C107—41no—
121C22⋊C4×C107—41no—
122C22⋊C4×C107—41no—
123C22⋊C4×C107—41no—
124C42×C107—41no—
125C42×C107C2×D411yescharacteristic
126C42×C107C2×D411yescharacteristic
127C42×C107C2×D411yescharacteristic
128C42×C107C2×D411yescharacteristic
129C23×C107—22no—
130C23×C107—41no—
131C23×C107—41no—
132C23×C107—81no—
133C23×C107—81no—
134C23×C107#12111yescharacteristic
135Q8×C107—42no—
136Q8×C107—42no—
137Q8×C107—42no—
138Q8×C107—42no—
139Q8×C107—81no—
140Q8×C107—81no—
141D4×C107—22no—
142D4×C107—22no—
143D4×C107—41no—
144D4×C107—41no—
145C2×C4×C107—22no—
146C2×C4×C107—41no—
147C2×C4×C107—41no—
148C2×C4×C107—41no—
149C2×C4×C107—41no—
150C2×C4×C107—42no—
151C2×C4×C107—82no—
152C2×C4×C107—81no—
153C2×C4×C107—81no—
154C2×C4×C107—82no—
155C2×C4×C107—81no—
156C2×C4×C107#12011yescharacteristic
157C2×C4×C107#12011yescharacteristic
158C2×C4×C107#12011yescharacteristic
159C2×C4×C107#12111yescharacteristic
160C2×C4×C107#12111yescharacteristic
161C2×C4×C107#12711yescharacteristic
162C2×C4×C107C2×SD1611yescharacteristic
163C2×C4×C107#13511yescharacteristic
164C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C107#13711yescharacteristic
166C8×C107—42no—
167C8×C107—42no—
168C8×C107—42no—
169C8×C107—81no—
170C22×C107—21no—
171C22×C107—21no—
172C22×C107—42no—
173C22×C107—82no—
174C22×C107—82no—
175C22×C107—81no—
176C22×C107—81no—
177C22×C107#39211yescharacteristic
178C22×C107#46511yescharacteristic
179C22×C107#46811yescharacteristic
180C4×C107—21no—
181C4×C107—21no—
182C4×C107—21no—
183C4×C107—82no—
184C4×C107—81no—
185C4×C107—81no—
186C4×C107—81no—
187C4×C107#44811yescharacteristic
188C4×C107#44911yescharacteristic
189C4×C107#45011yescharacteristic
190C4×C107#45211yescharacteristic
191C4×C107#47112yes—
192#10186C10711yesmaximal, characteristic, direct product factor, Sylow
193C2×C107—21no—
194C2×C107—21no—
195C2×C107—82no—
196C2×C107#200011yescharacteristic
197C2×C107#200911yescharacteristic
198C2×C107#201911yescharacteristic
199#3229C2×C10711yescharacteristic, complemented
200#3077C2×C10711yescharacteristic
201C2×#461C2×C10711yescharacteristic
202#1546C2×C10711yescharacteristic, complemented
203#1481C2×C10711yescharacteristic, complemented
204#1460C2×C10711yescharacteristic
205#1301C2×C10711yescharacteristic, complemented
206C107#1018611yescharacteristic, direct product factor, Sylow
207C22×SD16—21no—
208#533C22×C10711yescharacteristic
209C2×C4⋊Q8C22×C10711yescharacteristic
210C2×C4×D4C22×C10711yescharacteristic
211#498—21no—
212#487—21no—
213#483—22no—
214#478—22no—
215#476—21no—
216#475—22no—
217#474—21no—
218#461—22no—
219#461—22no—
220#431C22×C10711yescharacteristic
221#431C22×C10711yescharacteristic
222#428—21no—
223#423C22×C10711yescharacteristic
224C2×C4⋊C8C22×C10711yescharacteristic
225#418—21no—
226C2×#103—21no—
227#332—22no—
228Q8⋊C8—22no—
229#323—22no—
230C22×Q8—21no—
231C22×D4D4×C10711yescharacteristic
232C23×C4—21no—
233C2×SD16—24no—
234C2×SD16—42no—
235C2×SD16—42no—
236C2×M16—21no—
237C22×C8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C10712yes—
242C4⋊Q8D4×C10711yescharacteristic
243C4⋊Q8D4×C10711yescharacteristic
244#125—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253#117—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C10711yescharacteristic
257C2×C22⋊C4—21no—
258C2×C42C23×C10711yescharacteristic
259#107—22no—
260#106—22no—
261#106—24no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8D4×C10712yes—
267C4⋊C8D4×C10712yes—
268#103—24no—
269#103—24no—
270#102—22no—
271#102—22no—
272C22⋊C8—21no—
273C22⋊C8D4×C10712yes—
274C4×C8—21no—
275C4×C8—21no—
276C24—21no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4SD16×C10712yes—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—82no—
296C22×C4C2×D4×C10711yescharacteristic
297C22×C4C2×D4×C10711yescharacteristic
298C22×C4#41×C10711yescharacteristic
299SD16—48no—
300M16—41no—
301M16—41no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—41no—
324C42C2×D4×C10711yescharacteristic
325C42C2×D4×C10711yescharacteristic
326C42C2×D4×C10711yescharacteristic
327C42C2×D4×C10711yescharacteristic
328C23—22no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23#121×C10711yescharacteristic
334Q8—42no—
335Q8—42no—
336Q8—42no—
337Q8—42no—
338Q8—81no—
339Q8—81no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4#120×C10711yescharacteristic
356C2×C4#120×C10711yescharacteristic
357C2×C4#120×C10711yescharacteristic
358C2×C4#121×C10711yescharacteristic
359C2×C4#121×C10711yescharacteristic
360C2×C4#127×C10711yescharacteristic
361C2×C4C2×SD16×C10711yescharacteristic
362C2×C4#135×C10711yescharacteristic
363C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
364C2×C4#137×C10711yescharacteristic
365C8—42no—
366C8—42no—
367C8—42no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—82no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22#392×C10711yescharacteristic
377C22#465×C10711yescharacteristic
378C22#468×C10711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4#448×C10711yescharacteristic
387C4#449×C10711yescharacteristic
388C4#450×C10711yescharacteristic
389C4#452×C10711yescharacteristic
390C4#471×C10712yes—
391C2—21no—
392C2—21no—
393C2—82no—
394C2C107×#200011yescharacteristic
395C2C107×#200911yescharacteristic
396C2C107×#201911yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3229C2semidirect
4. C107×#1546C2semidirect
5. C107×#1481C2semidirect
7. C107×#1301C2semidirect
192. #10186C107direct (N × H)
199. #3229C2×C107semidirect
202. #1546C2×C107semidirect
203. #1481C2×C107semidirect
205. #1301C2×C107semidirect
206. C107#10186direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32292
C107×#30772
C2×#461×C1072
C107×#15462
C107×#14812
C107×#14602
C107×#13012
#10186107