Finite Group Databasebeta

← C107×#9187 #41035151

Subgroups — C107×#9187 #41035151

Order 27392.

560 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2973C211yesmaximal, characteristic, complemented
2C107×#2631C211yesmaximal, characteristic
3C4×#100×C107C211yesmaximal, characteristic, complemented
4C107×#1527C212yesmaximal, complemented
5C107×#1288C212yesmaximal, complemented
6C2×#124×C107C2211yescharacteristic
7C2×C4×D4×C107C2211yescharacteristic
8#435×C107—24no—
9#432×C107C2212yes—
10C2×#100×C107—21no—
11#407×C107—21no—
12C2×C22⋊C8×C107—21no—
13C4×M16×C107C2212yes—
14#397×C107—21no—
15#393×C107C411yescharacteristic
16#393×C107C411yescharacteristic
17#392×C107—21no—
18#392×C107C411yescharacteristic
19#392×C107C411yescharacteristic
20#386×C107—21no—
21#386×C107—21no—
22#383×C107C2211yescharacteristic
23#343×C107—21no—
24#329×C107—24no—
25C22×Q8×C107C2×C411yescharacteristic
26C22×D4×C107—21no—
27C22×D4×C107—21no—
28C22×D4×C107C2×C411yescharacteristic
29C22×D4×C107D411yescharacteristic
30C23×C4×C107D411yescharacteristic
31C23×C4×C107D411yescharacteristic
32C2×M16×C107—22no—
33C2×M16×C107—22no—
34C22×C8×C107—22no—
35#124×C107—22no—
36#124×C107—22no—
37C4×D4×C107—22no—
38C4×D4×C107—22no—
39C2×C4⋊C4×C107D411yescharacteristic
40C2×C22⋊C4×C107—21no—
41C2×C22⋊C4×C107—21no—
42C2×C22⋊C4×C107—21no—
43C2×C22⋊C4×C107—21no—
44C2×C22⋊C4×C107—21no—
45C2×C22⋊C4×C107—21no—
46C2×C22⋊C4×C107C2×C411yescharacteristic
47C2×C22⋊C4×C107C2×C411yescharacteristic
48C2×C42×C107C2311yescharacteristic
49C4⋊C8×C107—22no—
50#100×C107—24no—
51C22⋊C8×C107—22no—
52C22⋊C8×C107—22no—
53C22⋊C8×C107—22no—
54#97×C107—22no—
55#97×C107D414yescomplemented
56C4×C8×C107—22no—
57#95×C107—21no—
58#95×C107—21no—
59#95×C107—21no—
60#95×C107—21no—
61#95×C107C2×C411yescharacteristic
62#95×C107C2×C411yescharacteristic
63C24×C107—21no—
64C24×C107C22⋊C411yescharacteristic
65C24×C107C22⋊C411yescharacteristic
66C2×Q8×C107—22no—
67C2×Q8×C107—81no—
68C2×D4×C107—22no—
69C2×D4×C107—22no—
70C2×D4×C107—22no—
71C2×D4×C107—41no—
72C2×D4×C107—42no—
73C2×D4×C107—42no—
74C2×D4×C107—81no—
75C2×D4×C107—81no—
76C2×D4×C107—81no—
77C2×D4×C107—81no—
78C2×D4×C107—81no—
79C22×C4×C107—21no—
80C22×C4×C107—21no—
81C22×C4×C107—21no—
82C22×C4×C107—21no—
83C22×C4×C107—21no—
84C22×C4×C107—21no—
85C22×C4×C107—21no—
86C22×C4×C107—81no—
87C22×C4×C107—81no—
88C22×C4×C107C22⋊C411yescharacteristic
89C22×C4×C107C22⋊C411yescharacteristic
90C22×C4×C107C22×C411yescharacteristic
91C22×C4×C107C2×D411yescharacteristic
92C22×C4×C107C2×D411yescharacteristic
93M16×C107—24no—
94M16×C107—42no—
95M16×C107—82no—
96C2×C8×C107—24no—
97C2×C8×C107—42no—
98C2×C8×C107—82no—
99C4⋊C4×C107—22no—
100C22⋊C4×C107—22no—
101C22⋊C4×C107—22no—
102C22⋊C4×C107—41no—
103C22⋊C4×C107—42no—
104C22⋊C4×C107—41no—
105C22⋊C4×C107—81no—
106C22⋊C4×C107—81no—
107C22⋊C4×C107—81no—
108C22⋊C4×C107—81no—
109C42×C107C2×D412yes—
110C42×C107#4112yes—
111C23×C107—21no—
112C23×C107—21no—
113C23×C107—21no—
114C23×C107—21no—
115C23×C107—21no—
116C23×C107—41no—
117C23×C107—41no—
118C23×C107—41no—
119C23×C107—41no—
120C23×C107—41no—
121C23×C107—41no—
122C23×C107—41no—
123C23×C107—41no—
124C23×C107—41no—
125C23×C107—41no—
126C23×C107—41no—
127C23×C107#10412yes—
128C23×C107C2×C22⋊C411yescharacteristic
129Q8×C107—82no—
130D4×C107—44no—
131D4×C107—82no—
132D4×C107—84no—
133D4×C107—84no—
134C2×C4×C107—21no—
135C2×C4×C107—21no—
136C2×C4×C107—21no—
137C2×C4×C107—21no—
138C2×C4×C107—41no—
139C2×C4×C107—41no—
140C2×C4×C107—42no—
141C2×C4×C107—42no—
142C2×C4×C107—41no—
143C2×C4×C107—41no—
144C2×C4×C107—41no—
145C2×C4×C107—41no—
146C2×C4×C107—41no—
147C2×C4×C107—41no—
148C2×C4×C107—41no—
149C2×C4×C107—41no—
150C2×C4×C107—41no—
151C2×C4×C107—41no—
152C2×C4×C107—41no—
153C2×C4×C107—81no—
154C2×C4×C107—81no—
155C2×C4×C107C4×D412yes—
156C2×C4×C107#12011yescharacteristic
157C2×C4×C107#12112yes—
158C2×C4×C107#12311yescharacteristic
159C8×C107—44no—
160C8×C107—44no—
161C22×C107—21no—
162C22×C107—21no—
163C22×C107—22no—
164C22×C107—42no—
165C22×C107—42no—
166C22×C107—41no—
167C22×C107—41no—
168C22×C107—41no—
169C22×C107—41no—
170C22×C107—41no—
171C22×C107—81no—
172C22×C107—81no—
173C22×C107—81no—
174C22×C107—81no—
175C22×C107—81no—
176C22×C107—81no—
177C22×C107—81no—
178C22×C107—81no—
179C22×C107—81no—
180C22×C107#38611yescharacteristic
181C22×C107C2×#10411yescharacteristic
182C22×C107#42111yescharacteristic
183C4×C107—22no—
184C4×C107—21no—
185C4×C107—21no—
186C4×C107—22no—
187C4×C107—41no—
188C4×C107—41no—
189C4×C107—81no—
190C4×C107—81no—
191C4×C107—81no—
192#9187C10711yesmaximal, characteristic, direct product factor, Sylow
193C2×C107—21no—
194C2×C107—21no—
195C2×C107—42no—
196C2×C107—81no—
197C2×C107—161no—
198C2×C107#187111yescharacteristic
199C2×C107#191111yescharacteristic
200C2×C107#191411yescharacteristic
201#2973C2×C10711yescharacteristic, complemented
202#2631C2×C10711yescharacteristic
203C4×#100C2×C10711yescharacteristic, complemented
204#1527C2×C10712yescomplemented
205#1288C2×C10712yescomplemented
206C107#918711yescharacteristic, direct product factor, Sylow
207C2×#124C22×C10711yescharacteristic
208C2×C4×D4C22×C10711yescharacteristic
209#435—24no—
210#432C22×C10712yes—
211C2×#100—21no—
212#407—21no—
213C2×C22⋊C8—21no—
214C4×M16C22×C10712yes—
215#397—21no—
216#393C4×C10711yescharacteristic
217#393C4×C10711yescharacteristic
218#392—21no—
219#392C4×C10711yescharacteristic
220#392C4×C10711yescharacteristic
221#386—21no—
222#386—21no—
223#383C22×C10711yescharacteristic
224#343—21no—
225#329—24no—
226C22×Q8C2×C4×C10711yescharacteristic
227C22×D4—21no—
228C22×D4—21no—
229C22×D4C2×C4×C10711yescharacteristic
230C22×D4D4×C10711yescharacteristic
231C23×C4D4×C10711yescharacteristic
232C23×C4D4×C10711yescharacteristic
233C2×M16—22no—
234C2×M16—22no—
235C22×C8—22no—
236#124—22no—
237#124—22no—
238C4×D4—22no—
239C4×D4—22no—
240C2×C4⋊C4D4×C10711yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4C2×C4×C10711yescharacteristic
248C2×C22⋊C4C2×C4×C10711yescharacteristic
249C2×C42C23×C10711yescharacteristic
250C4⋊C8—22no—
251#100—24no—
252C22⋊C8—22no—
253C22⋊C8—22no—
254C22⋊C8—22no—
255#97—22no—
256#97D4×C10714yescomplemented
257C4×C8—22no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95C2×C4×C10711yescharacteristic
263#95C2×C4×C10711yescharacteristic
264C24—21no—
265C24C22⋊C4×C10711yescharacteristic
266C24C22⋊C4×C10711yescharacteristic
267C2×Q8—22no—
268C2×Q8—81no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—81no—
276C2×D4—81no—
277C2×D4—81no—
278C2×D4—81no—
279C2×D4—81no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C22⋊C4×C10711yescharacteristic
290C22×C4C22⋊C4×C10711yescharacteristic
291C22×C4C22×C4×C10711yescharacteristic
292C22×C4C2×D4×C10711yescharacteristic
293C22×C4C2×D4×C10711yescharacteristic
294M16—24no—
295M16—42no—
296M16—82no—
297C2×C8—24no—
298C2×C8—42no—
299C2×C8—82no—
300C4⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—41no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C42C2×D4×C10712yes—
311C42#41×C10712yes—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23#104×C10712yes—
329C23C2×C22⋊C4×C10711yescharacteristic
330Q8—82no—
331D4—44no—
332D4—82no—
333D4—84no—
334D4—84no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4C4×D4×C10712yes—
357C2×C4#120×C10711yescharacteristic
358C2×C4#121×C10712yes—
359C2×C4#123×C10711yescharacteristic
360C8—44no—
361C8—44no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—42no—
366C22—42no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22#386×C10711yescharacteristic
382C22C2×#104×C10711yescharacteristic
383C22#421×C10711yescharacteristic
384C4—22no—
385C4—21no—
386C4—21no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—81no—
392C4—81no—
393C2—21no—
394C2—21no—
395C2—42no—
396C2—81no—
397C2—161no—
398C2C107×#187111yescharacteristic
399C2C107×#191111yescharacteristic
400C2C107×#191411yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC107×#2631C2
LCSG ▷ C22×C4 ▷ 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×#2973C2semidirect
3. C4×#100×C107C2semidirect
4. C107×#1527C2semidirect
5. C107×#1288C2semidirect
55. #97×C107D4semidirect
192. #9187C107direct (N × H)
201. #2973C2×C107semidirect
203. C4×#100C2×C107semidirect
204. #1527C2×C107semidirect
205. #1288C2×C107semidirect
206. C107#9187direct (N × H)
256. #97D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#29732
C107×#26312
C4×#100×C1072
C107×#15272
C107×#12882
#9187107