Finite Group Databasebeta

← C107×#7753 #41033717

Subgroups — C107×#7753 #41033717

Order 27392.

504 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2732C211yesmaximal, characteristic
2C107×#2058C211yesmaximal, characteristic, complemented
3C107×#2024C211yesmaximal, characteristic, complemented
4C107×#2013C211yesmaximal, characteristic
5C107×#1272C211yesmaximal, characteristic, complemented
6C107×#1271C211yesmaximal, characteristic, complemented
7C107×#1270C211yesmaximal, characteristic
8C22×SD16×C107—21no—
9C2×C4⋊Q8×C107C2211yescharacteristic
10C2×C22⋊Q8×C107—21no—
11C2×#106×C107—21no—
12C2×#103×C107—21no—
13C2×#103×C107—21no—
14#399×C107—21no—
15#398×C107—21no—
16#396×C107—21no—
17#391×C107C2211yescharacteristic
18#390×C107C2211yescharacteristic
19#389×C107C2211yescharacteristic
20#386×C107—21no—
21#385×C107—21no—
22#340×C107—21no—
23#340×C107—21no—
24#336×C107C2211yescharacteristic
25#336×C107C2211yescharacteristic
26#336×C107C2211yescharacteristic
27C22×Q8×C107—21no—
28C22×Q8×C107D411yescharacteristic
29C22×D4×C107D411yescharacteristic
30C23×C4×C107—21no—
31C2×SD16×C107—42no—
32C2×SD16×C107—42no—
33C2×SD16×C107—42no—
34C22×C8×C107—21no—
35C22×C8×C107—21no—
36C22×C8×C107—21no—
37C4⋊Q8×C107—42no—
38C22⋊Q8×C107—42no—
39C22⋊Q8×C107—42no—
40C2×C4⋊C4×C107—21no—
41C2×C4⋊C4×C107—21no—
42C2×C4⋊C4×C107—21no—
43C2×C4⋊C4×C107—21no—
44C2×C4⋊C4×C107—21no—
45C2×C4⋊C4×C107—21no—
46C2×C4⋊C4×C107D411yescharacteristic
47C2×C4⋊C4×C107D411yescharacteristic
48C2×C4⋊C4×C107D411yescharacteristic
49C2×C4⋊C4×C107D411yescharacteristic
50C2×C22⋊C4×C107—21no—
51C2×C22⋊C4×C107—21no—
52C2×C22⋊C4×C107—21no—
53C2×C22⋊C4×C107—21no—
54C2×C22⋊C4×C107—21no—
55C2×C42×C107C2311yescharacteristic
56#106×C107—42no—
57#103×C107—42no—
58#103×C107—42no—
59#95×C107—21no—
60#95×C107—21no—
61#95×C107—21no—
62#95×C107—21no—
63C24×C107—21no—
64C2×Q8×C107—21no—
65C2×Q8×C107—22no—
66C2×Q8×C107—41no—
67C2×Q8×C107—41no—
68C2×Q8×C107—41no—
69C2×Q8×C107—41no—
70C2×Q8×C107—41no—
71C2×Q8×C107—41no—
72C2×Q8×C107—41no—
73C2×Q8×C107SD1612yescomplemented
74C2×D4×C107—21no—
75C2×D4×C107—41no—
76C2×D4×C107—41no—
77C2×D4×C107SD1612yes—
78C22×C4×C107—21no—
79C22×C4×C107—21no—
80C22×C4×C107—21no—
81C22×C4×C107—21no—
82C22×C4×C107—21no—
83C22×C4×C107—42no—
84C22×C4×C107—41no—
85C22×C4×C107—81no—
86C22×C4×C107—81no—
87C22×C4×C107C2×D411yescharacteristic
88C22×C4×C107C2×D411yescharacteristic
89C22×C4×C107C2×D411yescharacteristic
90SD16×C107—48no—
91C2×C8×C107—22no—
92C2×C8×C107—22no—
93C2×C8×C107—41no—
94C2×C8×C107—41no—
95C2×C8×C107—41no—
96C2×C8×C107—41no—
97C2×C8×C107—41no—
98C2×C8×C107—41no—
99C2×C8×C107—41no—
100C4⋊C4×C107—22no—
101C4⋊C4×C107—22no—
102C4⋊C4×C107—21no—
103C4⋊C4×C107—21no—
104C4⋊C4×C107—41no—
105C4⋊C4×C107—41no—
106C4⋊C4×C107—41no—
107C4⋊C4×C107—42no—
108C4⋊C4×C107—42no—
109C4⋊C4×C107—41no—
110C4⋊C4×C107—41no—
111C4⋊C4×C107—41no—
112C4⋊C4×C107—41no—
113C4⋊C4×C107—81no—
114C22⋊C4×C107—42no—
115C22⋊C4×C107—41no—
116C22⋊C4×C107—41no—
117C22⋊C4×C107—41no—
118C22⋊C4×C107—41no—
119C22⋊C4×C107—81no—
120C22⋊C4×C107—81no—
121C42×C107—41no—
122C23×C107—22no—
123C23×C107—41no—
124C23×C107—41no—
125C23×C107—41no—
126C23×C107—41no—
127C23×C107—41no—
128C23×C107—41no—
129C23×C107#12011yescharacteristic
130Q8×C107—42no—
131Q8×C107—42no—
132Q8×C107—42no—
133Q8×C107—81no—
134Q8×C107—81no—
135Q8×C107—81no—
136D4×C107—42no—
137D4×C107—81no—
138C2×C4×C107—21no—
139C2×C4×C107—21no—
140C2×C4×C107—21no—
141C2×C4×C107—21no—
142C2×C4×C107—21no—
143C2×C4×C107—21no—
144C2×C4×C107—22no—
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—41no—
154C2×C4×C107—41no—
155C2×C4×C107—41no—
156C2×C4×C107—41no—
157C2×C4×C107—41no—
158C2×C4×C107—42no—
159C2×C4×C107—41no—
160C2×C4×C107—84no—
161C2×C4×C107—81no—
162C2×C4×C107—81no—
163C2×C4×C107C2×SD1611yescharacteristic
164C2×C4×C107C2×SD1611yescharacteristic
165C2×C4×C107#13511yescharacteristic
166C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C107#13711yescharacteristic
168C2×C4×C107#13711yescharacteristic
169C8×C107—42no—
170C8×C107—42no—
171C8×C107—81no—
172C22×C107—42no—
173C22×C107—42no—
174C22×C107—42no—
175C22×C107—81no—
176C22×C107—81no—
177C22×C107—81no—
178C22×C107—81no—
179C22×C107#44811yescharacteristic
180C22×C107#45011yescharacteristic
181C22×C107#45211yescharacteristic
182C22×C107#45311yescharacteristic
183C22×C107#45511yescharacteristic
184C22×C107#45611yescharacteristic
185C22×C107B(4,𝔽2)11yescharacteristic
186C4×C107—21no—
187C4×C107—21no—
188C4×C107—21no—
189C4×C107—21no—
190C4×C107—21no—
191C4×C107—21no—
192C4×C107—42no—
193C4×C107—82no—
194C4×C107—81no—
195C4×C107—81no—
196C4×C107—81no—
197C4×C107—81no—
198#7753C10711yesmaximal, characteristic, direct product factor, Sylow
199C2×C107—82no—
200C2×C107#159611yescharacteristic
201C2×C107#160111yescharacteristic
202C2×C107#160311yescharacteristic
203C2×C107#163111yescharacteristic
204C2×C107#164311yescharacteristic
205C2×C107#165111yescharacteristic
206C2×C107#166111yescharacteristic
207#2732C2×C10711yescharacteristic
208#2058C2×C10711yescharacteristic, complemented
209#2024C2×C10711yescharacteristic, complemented
210#2013C2×C10711yescharacteristic
211#1272C2×C10711yescharacteristic, complemented
212#1271C2×C10711yescharacteristic, complemented
213#1270C2×C10711yescharacteristic
214C107#775311yescharacteristic, direct product factor, Sylow
215C22×SD16—21no—
216C2×C4⋊Q8C22×C10711yescharacteristic
217C2×C22⋊Q8—21no—
218C2×#106—21no—
219C2×#103—21no—
220C2×#103—21no—
221#399—21no—
222#398—21no—
223#396—21no—
224#391C22×C10711yescharacteristic
225#390C22×C10711yescharacteristic
226#389C22×C10711yescharacteristic
227#386—21no—
228#385—21no—
229#340—21no—
230#340—21no—
231#336C22×C10711yescharacteristic
232#336C22×C10711yescharacteristic
233#336C22×C10711yescharacteristic
234C22×Q8—21no—
235C22×Q8D4×C10711yescharacteristic
236C22×D4D4×C10711yescharacteristic
237C23×C4—21no—
238C2×SD16—42no—
239C2×SD16—42no—
240C2×SD16—42no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C4⋊Q8—42no—
245C22⋊Q8—42no—
246C22⋊Q8—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4D4×C10711yescharacteristic
254C2×C4⋊C4D4×C10711yescharacteristic
255C2×C4⋊C4D4×C10711yescharacteristic
256C2×C4⋊C4D4×C10711yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C42C23×C10711yescharacteristic
263#106—42no—
264#103—42no—
265#103—42no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270C24—21no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8SD16×C10712yescomplemented
281C2×D4—21no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4SD16×C10712yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—81no—
293C22×C4—81no—
294C22×C4C2×D4×C10711yescharacteristic
295C22×C4C2×D4×C10711yescharacteristic
296C22×C4C2×D4×C10711yescharacteristic
297SD16—48no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C42—41no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#120×C10711yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—42no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343D4—42no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—84no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4C2×SD16×C10711yescharacteristic
371C2×C4C2×SD16×C10711yescharacteristic
372C2×C4#135×C10711yescharacteristic
373C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
374C2×C4#137×C10711yescharacteristic
375C2×C4#137×C10711yescharacteristic
376C8—42no—
377C8—42no—
378C8—81no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#448×C10711yescharacteristic
387C22#450×C10711yescharacteristic
388C22#452×C10711yescharacteristic
389C22#453×C10711yescharacteristic
390C22#455×C10711yescharacteristic
391C22#456×C10711yescharacteristic
392C22B(4,𝔽2)×C10711yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—82no—
404C4—81no—
405C2—82no—
406C2C107×#159611yescharacteristic
407C2C107×#160111yescharacteristic
408C2C107×#160311yescharacteristic
409C2C107×#163111yescharacteristic
410C2C107×#164311yescharacteristic
411C2C107×#165111yescharacteristic
412C2C107×#166111yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2058C2semidirect
3. C107×#2024C2semidirect
5. C107×#1272C2semidirect
6. C107×#1271C2semidirect
73. C2×Q8×C107SD16semidirect
198. #7753C107direct (N × H)
208. #2058C2×C107semidirect
209. #2024C2×C107semidirect
211. #1272C2×C107semidirect
212. #1271C2×C107semidirect
214. C107#7753direct (N × H)
280. C2×Q8SD16×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#27322
C107×#20582
C107×#20242
C107×#20132
C107×#12722
C107×#12712
C107×#12702
#7753107