Finite Group Databasebeta

← C107×#10007 #41035971

Subgroups — C107×#10007 #41035971

Order 27392.

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

normal subgroups only

This group has 534 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×#3234C211yesmaximal, characteristic
2C107×#3112C211yesmaximal, characteristic
3C107×#2584C211yesmaximal, characteristic, complemented
4C107×#1980C211yesmaximal, characteristic
5C107×#1528C211yesmaximal, characteristic, complemented
6C107×#1491C211yesmaximal, characteristic, complemented
7C107×#1285C211yesmaximal, characteristic, complemented
8#532×C107C2211yescharacteristic
9C2×#125×C107C2211yescharacteristic
10C2×C4×Q8×C107C2211yescharacteristic
11#501×C107—21no—
12#490×C107—21no—
13#481×C107—21no—
14#480×C107—21no—
15#480×C107—21no—
16#478×C107—22no—
17#477×C107—21no—
18#460×C107—21no—
19#448×C107—21no—
20#440×C107—22no—
21#432×C107C2211yescharacteristic
22#432×C107C2211yescharacteristic
23C2×#104×C107—22no—
24C4×M16×C107C2211yescharacteristic
25#398×C107—21no—
26#395×C107—21no—
27#389×C107—21no—
28#389×C107—21no—
29#389×C107—22no—
30C4×C4⋊C4×C107C2211yescharacteristic
31#330×C107—22no—
32Q8⋊C8×C107—22no—
33C2×#41×C107—21no—
34C22×Q8×C107D411yescharacteristic
35C2×SD16×C107—22no—
36C2×M16×C107—21no—
37C4⋊Q8×C107D411yescharacteristic
38#127×C107D411yescharacteristic
39#125×C107—21no—
40#125×C107—21no—
41#125×C107—21no—
42#125×C107—21no—
43#124×C107—21no—
44#121×C107—21no—
45#121×C107—21no—
46C4×Q8×C107—21no—
47C4×Q8×C107—21no—
48C4×Q8×C107—21no—
49C4×Q8×C107—21no—
50C4×D4×C107—21no—
51C4×D4×C107—21no—
52C2×C4⋊C4×C107—21no—
53C2×C4⋊C4×C107—22no—
54C2×C4⋊C4×C107—21no—
55C2×C4⋊C4×C107—21no—
56C2×C4⋊C4×C107—21no—
57C2×C4⋊C4×C107—22no—
58C2×C4⋊C4×C107D411yescharacteristic
59C2×C4⋊C4×C107D411yescharacteristic
60C2×C4⋊C4×C107D411yescharacteristic
61C2×C42×C107—21no—
62C2×C42×C107D412yes—
63C2×C42×C107C2311yescharacteristic
64#107×C107—22no—
65#107×C107—22no—
66#106×C107—22no—
67C4⋊C8×C107—21no—
68C4⋊C8×C107D412yes—
69#104×C107—44no—
70#103×C107—22no—
71#102×C107—22no—
72#102×C107—22no—
73#102×C107—22no—
74C22⋊C8×C107—21no—
75C22⋊C8×C107—21no—
76#97×C107—21no—
77#97×C107—21no—
78#97×C107D412yes—
79C4×C8×C107—21no—
80#95×C107—22no—
81#95×C107—22no—
82#95×C107—21no—
83#41×C107—42no—
84#41×C107—42no—
85C2×Q8×C107—21no—
86C2×Q8×C107—21no—
87C2×Q8×C107—21no—
88C2×Q8×C107—42no—
89C2×D4×C107—21no—
90C2×D4×C107—21no—
91C2×D4×C107—21no—
92C2×D4×C107—41no—
93C22×C4×C107—22no—
94C22×C4×C107—21no—
95C22×C4×C107—21no—
96C22×C4×C107—21no—
97C22×C4×C107—21no—
98C22×C4×C107—41no—
99C22×C4×C107C2×D411yescharacteristic
100C22×C4×C107C2×D411yescharacteristic
101C22×C4×C107C2×D411yescharacteristic
102SD16×C107—44no—
103M16×C107—22no—
104M16×C107—41no—
105C2×C8×C107—22no—
106C2×C8×C107—22no—
107C2×C8×C107—41no—
108C4⋊C4×C107—24no—
109C4⋊C4×C107—21no—
110C4⋊C4×C107—21no—
111C4⋊C4×C107—21no—
112C4⋊C4×C107—21no—
113C4⋊C4×C107—21no—
114C4⋊C4×C107—21no—
115C4⋊C4×C107—21no—
116C4⋊C4×C107—21no—
117C4⋊C4×C107—44no—
118C4⋊C4×C107—41no—
119C4⋊C4×C107—41no—
120C4⋊C4×C107—41no—
121C4⋊C4×C107—41no—
122C4⋊C4×C107—41no—
123C4⋊C4×C107—41no—
124C4⋊C4×C107—82no—
125C22⋊C4×C107—41no—
126C22⋊C4×C107—41no—
127C42×C107—42no—
128C42×C107—41no—
129C42×C107—41no—
130C42×C107C2×D411yescharacteristic
131C42×C107C2×D411yescharacteristic
132C42×C107C2×D411yescharacteristic
133C42×C107#4111yescharacteristic
134C23×C107—41no—
135C23×C107#12011yescharacteristic
136Q8×C107—22no—
137Q8×C107—22no—
138Q8×C107—41no—
139Q8×C107—41no—
140Q8×C107—42no—
141D4×C107—42no—
142D4×C107—42no—
143D4×C107—42no—
144D4×C107—81no—
145D4×C107—81no—
146C2×C4×C107—21no—
147C2×C4×C107—21no—
148C2×C4×C107—22no—
149C2×C4×C107—24no—
150C2×C4×C107—22no—
151C2×C4×C107—41no—
152C2×C4×C107—42no—
153C2×C4×C107—41no—
154C2×C4×C107—41no—
155C2×C4×C107—42no—
156C2×C4×C107—42no—
157C2×C4×C107—41no—
158C2×C4×C107—41no—
159C2×C4×C107—41no—
160C2×C4×C107—41no—
161C2×C4×C107—41no—
162C2×C4×C107—41no—
163C2×C4×C107—41no—
164C2×C4×C107—41no—
165C2×C4×C107—82no—
166C2×C4×C107#12011yescharacteristic
167C2×C4×C107#12011yescharacteristic
168C2×C4×C107#12111yescharacteristic
169C2×C4×C107#12111yescharacteristic
170C2×C4×C107#12111yescharacteristic
171C2×C4×C107#12711yescharacteristic
172C8×C107—42no—
173C8×C107—42no—
174C8×C107—42no—
175C22×C107—21no—
176C22×C107—21no—
177C22×C107—81no—
178C22×C107—81no—
179C22×C107—81no—
180C22×C107#39211yescharacteristic
181C22×C107#45311yescharacteristic
182C22×C107#45411yescharacteristic
183C4×C107—21no—
184C4×C107—21no—
185C4×C107—21no—
186C4×C107—21no—
187C4×C107—21no—
188C4×C107—44no—
189C4×C107—42no—
190C4×C107—81no—
191C4×C107—81no—
192C4×C107—81no—
193C4×C107—81no—
194C4×C107#45612yes—
195#10007C10711yesmaximal, characteristic, direct product factor, Sylow
196C2×C107—21no—
197C2×C107—21no—
198C2×C107—161no—
199C2×C107#200511yescharacteristic
200C2×C107#200611yescharacteristic
201C2×C107#201011yescharacteristic
202#3234C2×C10711yescharacteristic
203#3112C2×C10711yescharacteristic
204#2584C2×C10711yescharacteristic, complemented
205#1980C2×C10711yescharacteristic
206#1528C2×C10711yescharacteristic, complemented
207#1491C2×C10711yescharacteristic, complemented
208#1285C2×C10711yescharacteristic, complemented
209C107#1000711yescharacteristic, direct product factor, Sylow
210#532C22×C10711yescharacteristic
211C2×#125C22×C10711yescharacteristic
212C2×C4×Q8C22×C10711yescharacteristic
213#501—21no—
214#490—21no—
215#481—21no—
216#480—21no—
217#480—21no—
218#478—22no—
219#477—21no—
220#460—21no—
221#448—21no—
222#440—22no—
223#432C22×C10711yescharacteristic
224#432C22×C10711yescharacteristic
225C2×#104—22no—
226C4×M16C22×C10711yescharacteristic
227#398—21no—
228#395—21no—
229#389—21no—
230#389—21no—
231#389—22no—
232C4×C4⋊C4C22×C10711yescharacteristic
233#330—22no—
234Q8⋊C8—22no—
235C2×#41—21no—
236C22×Q8D4×C10711yescharacteristic
237C2×SD16—22no—
238C2×M16—21no—
239C4⋊Q8D4×C10711yescharacteristic
240#127D4×C10711yescharacteristic
241#125—21no—
242#125—21no—
243#125—21no—
244#125—21no—
245#124—21no—
246#121—21no—
247#121—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—21no—
253C4×D4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4D4×C10711yescharacteristic
261C2×C4⋊C4D4×C10711yescharacteristic
262C2×C4⋊C4D4×C10711yescharacteristic
263C2×C42—21no—
264C2×C42D4×C10712yes—
265C2×C42C23×C10711yescharacteristic
266#107—22no—
267#107—22no—
268#106—22no—
269C4⋊C8—21no—
270C4⋊C8D4×C10712yes—
271#104—44no—
272#103—22no—
273#102—22no—
274#102—22no—
275#102—22no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278#97—21no—
279#97—21no—
280#97D4×C10712yes—
281C4×C8—21no—
282#95—22no—
283#95—22no—
284#95—21no—
285#41—42no—
286#41—42no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—42no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4C2×D4×C10711yescharacteristic
302C22×C4C2×D4×C10711yescharacteristic
303C22×C4C2×D4×C10711yescharacteristic
304SD16—44no—
305M16—22no—
306M16—41no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—41no—
310C4⋊C4—24no—
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—44no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—82no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C42—42no—
330C42—41no—
331C42—41no—
332C42C2×D4×C10711yescharacteristic
333C42C2×D4×C10711yescharacteristic
334C42C2×D4×C10711yescharacteristic
335C42#41×C10711yescharacteristic
336C23—41no—
337C23#120×C10711yescharacteristic
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—42no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—81no—
347D4—81no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4#120×C10711yescharacteristic
369C2×C4#120×C10711yescharacteristic
370C2×C4#121×C10711yescharacteristic
371C2×C4#121×C10711yescharacteristic
372C2×C4#121×C10711yescharacteristic
373C2×C4#127×C10711yescharacteristic
374C8—42no—
375C8—42no—
376C8—42no—
377C22—21no—
378C22—21no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22#392×C10711yescharacteristic
383C22#453×C10711yescharacteristic
384C22#454×C10711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—44no—
391C4—42no—
392C4—81no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4#456×C10712yes—
397C2—21no—
398C2—21no—
399C2—161no—
400C2C107×#200511yescharacteristic
401C2C107×#200611yescharacteristic
402C2C107×#201011yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC2×C42C23×C107
prime radical#532×C107C22
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
3. C107×#2584C2semidirect
5. C107×#1528C2semidirect
6. C107×#1491C2semidirect
7. C107×#1285C2semidirect
195. #10007C107direct (N × H)
204. #2584C2×C107semidirect
206. #1528C2×C107semidirect
207. #1491C2×C107semidirect
208. #1285C2×C107semidirect
209. C107#10007direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32342
C107×#31122
C107×#25842
C107×#19802
C107×#15282
C107×#14912
C107×#12852
#10007107