Finite Group Databasebeta

← C107×#12193 #41038157

Subgroups — C107×#12193 #41038157

Order 27392.

442 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2764C211yesmaximal, characteristic, complemented
2C107×#2022C211yesmaximal, characteristic
3C107×#1607C211yesmaximal, characteristic
4C107×#1601C211yesmaximal, characteristic
5C107×#1351C211yesmaximal, characteristic, complemented
6C107×#1344C211yesmaximal, characteristic, complemented
7C107×#1317C211yesmaximal, characteristic, complemented
8#534×C107C2211yescharacteristic
9C2×#123×C107—21no—
10#480×C107—21no—
11#448×C107—21no—
12C2×#99×C107—21no—
13#400×C107—21no—
14#398×C107—21no—
15#397×C107C2211yescharacteristic
16#393×C107C2211yescharacteristic
17#391×C107—21no—
18#388×C107—21no—
19#385×C107—21no—
20#383×C107—21no—
21#381×C107C2211yescharacteristic
22#342×C107C2211yescharacteristic
23#327×C107—21no—
24#327×C107—21no—
25#323×C107C2211yescharacteristic
26#323×C107C2211yescharacteristic
27C22×Q8×C107D411yescharacteristic
28C22×D4×C107—21no—
29C23×C4×C107D411yescharacteristic
30C2×SD16×C107—41no—
31#123×C107—42no—
32#123×C107—41no—
33#123×C107—42no—
34#121×C107—21no—
35#121×C107—21no—
36#120×C107—41no—
37C2×C4⋊C4×C107—21no—
38C2×C4⋊C4×C107—21no—
39C2×C4⋊C4×C107—21no—
40C2×C4⋊C4×C107—41no—
41C2×C4⋊C4×C107D411yescharacteristic
42C2×C22⋊C4×C107—21no—
43C2×C22⋊C4×C107—21no—
44C2×C22⋊C4×C107—21no—
45C2×C22⋊C4×C107—41no—
46C2×C22⋊C4×C107D411yescharacteristic
47C2×C22⋊C4×C107C2311yescharacteristic
48C2×C42×C107—21no—
49#107×C107—41no—
50#103×C107—41no—
51#102×C107—41no—
52#99×C107—42no—
53C22⋊C8×C107—21no—
54C22⋊C8×C107—21no—
55#95×C107—21no—
56#95×C107—21no—
57#95×C107—21no—
58#95×C107—21no—
59#95×C107—21no—
60#95×C107—21no—
61#95×C107—21no—
62#95×C107—21no—
63#95×C107D411yescharacteristic
64#95×C107D411yescharacteristic
65C24×C107—21no—
66C24×C107C2×D411yescharacteristic
67C2×Q8×C107—42no—
68C2×Q8×C107—41no—
69C2×D4×C107—21no—
70C2×D4×C107—21no—
71C2×D4×C107—41no—
72C2×D4×C107—41no—
73C2×D4×C107—41no—
74C2×D4×C107—41no—
75C2×D4×C107—41no—
76C2×D4×C107—41no—
77C22×C4×C107—21no—
78C22×C4×C107—21no—
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—41no—
87C22×C4×C107—41no—
88C22×C4×C107—41no—
89C22×C4×C107C2×D411yescharacteristic
90C22×C4×C107C2×D411yescharacteristic
91SD16×C107—82no—
92C2×C8×C107—41no—
93C2×C8×C107—41no—
94C4⋊C4×C107—21no—
95C4⋊C4×C107—21no—
96C4⋊C4×C107—41no—
97C4⋊C4×C107—44no—
98C4⋊C4×C107—81no—
99C4⋊C4×C107—81no—
100C4⋊C4×C107—81no—
101C22⋊C4×C107—22no—
102C22⋊C4×C107—41no—
103C22⋊C4×C107—42no—
104C22⋊C4×C107—41no—
105C22⋊C4×C107—41no—
106C22⋊C4×C107—44no—
107C22⋊C4×C107—41no—
108C22⋊C4×C107—41no—
109C22⋊C4×C107—41no—
110C22⋊C4×C107—41no—
111C42×C107—42no—
112C23×C107—21no—
113C23×C107—21no—
114C23×C107—41no—
115C23×C107—41no—
116C23×C107—41no—
117C23×C107—41no—
118C23×C107—41no—
119C23×C107—81no—
120C23×C107—81no—
121C23×C107#12011yescharacteristic
122C23×C107#13511yescharacteristic
123C23×C107AGL(1,ℤ/8)11yescharacteristic
124Q8×C107—42no—
125Q8×C107—81no—
126D4×C107—81no—
127D4×C107—81no—
128D4×C107—81no—
129D4×C107—81no—
130D4×C107—81no—
131D4×C107—81no—
132C2×C4×C107—22no—
133C2×C4×C107—21no—
134C2×C4×C107—21no—
135C2×C4×C107—41no—
136C2×C4×C107—41no—
137C2×C4×C107—41no—
138C2×C4×C107—41no—
139C2×C4×C107—41no—
140C2×C4×C107—41no—
141C2×C4×C107—42no—
142C2×C4×C107—42no—
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—41no—
154C2×C4×C107—41no—
155C2×C4×C107—41no—
156C2×C4×C107—41no—
157C2×C4×C107—41no—
158C2×C4×C107—41no—
159C2×C4×C107—81no—
160C2×C4×C107—81no—
161C2×C4×C107—81no—
162C8×C107—81no—
163C8×C107—81no—
164C22×C107—21no—
165C22×C107—21no—
166C22×C107—21no—
167C22×C107—21no—
168C22×C107—41no—
169C22×C107—41no—
170C22×C107—41no—
171C22×C107—41no—
172C22×C107—81no—
173C22×C107—82no—
174C22×C107—81no—
175C22×C107—81no—
176C22×C107—81no—
177C22×C107—161no—
178C22×C107#44911yescharacteristic
179C22×C107#45311yescharacteristic
180C22×C107B(4,𝔽2)11yescharacteristic
181C4×C107—41no—
182C4×C107—42no—
183C4×C107—41no—
184C4×C107—81no—
185C4×C107—81no—
186C4×C107—81no—
187C4×C107—82no—
188C4×C107—81no—
189C4×C107—81no—
190C4×C107—81no—
191#12193C10711yesmaximal, characteristic, direct product factor, Sylow
192C2×C107—21no—
193C2×C107—21no—
194C2×C107—41no—
195C2×C107—41no—
196C2×C107—161no—
197C2×C107#160011yescharacteristic
198C2×C107#219711yescharacteristic
199C2×C107#220111yescharacteristic
200#2764C2×C10711yescharacteristic, complemented
201#2022C2×C10711yescharacteristic
202#1607C2×C10711yescharacteristic
203#1601C2×C10711yescharacteristic
204#1351C2×C10711yescharacteristic, complemented
205#1344C2×C10711yescharacteristic, complemented
206#1317C2×C10711yescharacteristic, complemented
207C107#1219311yescharacteristic, direct product factor, Sylow
208#534C22×C10711yescharacteristic
209C2×#123—21no—
210#480—21no—
211#448—21no—
212C2×#99—21no—
213#400—21no—
214#398—21no—
215#397C22×C10711yescharacteristic
216#393C22×C10711yescharacteristic
217#391—21no—
218#388—21no—
219#385—21no—
220#383—21no—
221#381C22×C10711yescharacteristic
222#342C22×C10711yescharacteristic
223#327—21no—
224#327—21no—
225#323C22×C10711yescharacteristic
226#323C22×C10711yescharacteristic
227C22×Q8D4×C10711yescharacteristic
228C22×D4—21no—
229C23×C4D4×C10711yescharacteristic
230C2×SD16—41no—
231#123—42no—
232#123—41no—
233#123—42no—
234#121—21no—
235#121—21no—
236#120—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—41no—
241C2×C4⋊C4D4×C10711yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4D4×C10711yescharacteristic
247C2×C22⋊C4C23×C10711yescharacteristic
248C2×C42—21no—
249#107—41no—
250#103—41no—
251#102—41no—
252#99—42no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95D4×C10711yescharacteristic
264#95D4×C10711yescharacteristic
265C24—21no—
266C24C2×D4×C10711yescharacteristic
267C2×Q8—42no—
268C2×Q8—41no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4C2×D4×C10711yescharacteristic
290C22×C4C2×D4×C10711yescharacteristic
291SD16—82no—
292C2×C8—41no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—44no—
298C4⋊C4—81no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C22⋊C4—22no—
302C22⋊C4—41no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—44no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C42—42no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—81no—
320C23—81no—
321C23#120×C10711yescharacteristic
322C23#135×C10711yescharacteristic
323C23AGL(1,ℤ/8)×C10711yescharacteristic
324Q8—42no—
325Q8—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
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—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C8—81no—
363C8—81no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—161no—
378C22#449×C10711yescharacteristic
379C22#453×C10711yescharacteristic
380C22B(4,𝔽2)×C10711yescharacteristic
381C4—41no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—81no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2C107×#160011yescharacteristic
397C2C107×#219711yescharacteristic
398C2C107×#220111yescharacteristic
subgroupG/H
center, socleC22×C107B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C107
prime radical#534×C107C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C2×C22⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2764C2semidirect
5. C107×#1351C2semidirect
6. C107×#1344C2semidirect
7. C107×#1317C2semidirect
191. #12193C107direct (N × H)
200. #2764C2×C107semidirect
204. #1351C2×C107semidirect
205. #1344C2×C107semidirect
206. #1317C2×C107semidirect
207. C107#12193direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#27642
C107×#20222
C107×#16072
C107×#16012
C107×#13512
C107×#13442
C107×#13172
#12193107