Finite Group Databasebeta

← C107×#9118 #41035082

Subgroups — C107×#9118 #41035082

Order 27392.

674 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#432×C107C211yesmaximal, characteristic, complemented
2C107×#2854C211yesmaximal, characteristic
3C2×#327×C107C212yesmaximal
4C107×#1434C211yesmaximal, characteristic, complemented
5C107×#1294C212yesmaximal, complemented
6C2×#123×C107—21no—
7C2×#121×C107C2211yescharacteristic
8C22×C42×C107C2211yescharacteristic
9#432×C107—24no—
10C2×C4⋊C8×C107—21no—
11C2×C22⋊C8×C107C2212yes—
12C2×#97×C107—21no—
13#390×C107C411yescharacteristic, complemented
14#390×C107C411yescharacteristic, complemented
15#389×C107C411yescharacteristic, complemented
16#389×C107C411yescharacteristic, complemented
17#388×C107—21no—
18#388×C107—21no—
19#386×C107—21no—
20#380×C107C2211yescharacteristic
21C2×#95×C107—21no—
22C2×#95×C107—21no—
23C2×#95×C107C2212yes—
24#327×C107—24no—
25C22×D4×C107—21no—
26C22×D4×C107C2×C411yescharacteristic
27C23×C4×C107—22no—
28C23×C4×C107D411yescharacteristic
29C23×C4×C107D411yescharacteristic
30C23×C4×C107C2311yescharacteristic
31C22×C8×C107—22no—
32#123×C107—44no—
33#121×C107—22no—
34#121×C107—22no—
35C2×C4⋊C4×C107—21no—
36C2×C4⋊C4×C107—21no—
37C2×C4⋊C4×C107C2×C411yescharacteristic
38C2×C4⋊C4×C107C2×C411yescharacteristic
39C2×C4⋊C4×C107C2×C411yescharacteristic
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×C42×C107—22no—
47C2×C42×C107—22no—
48C2×C42×C107C2×C411yescharacteristic
49C2×C42×C107C2×C411yescharacteristic
50C2×C42×C107D411yescharacteristic
51C2×C42×C107D411yescharacteristic
52C4⋊C8×C107—24no—
53C22⋊C8×C107—22no—
54C22⋊C8×C107D414yes—
55#97×C107—24no—
56#95×C107—24no—
57#95×C107—21no—
58#95×C107—21no—
59#95×C107—21no—
60#95×C107—22no—
61#95×C107—22no—
62#95×C107—42no—
63C24×C107—21no—
64C24×C107C2×D411yescharacteristic
65C2×D4×C107—22no—
66C2×D4×C107—41no—
67C2×D4×C107—41no—
68C2×D4×C107—42no—
69C2×D4×C107—42no—
70C2×D4×C107—41no—
71C2×D4×C107—41no—
72C22×C4×C107—22no—
73C22×C4×C107—22no—
74C22×C4×C107—21no—
75C22×C4×C107—22no—
76C22×C4×C107—21no—
77C22×C4×C107—22no—
78C22×C4×C107—24no—
79C22×C4×C107—21no—
80C22×C4×C107—21no—
81C22×C4×C107—21no—
82C22×C4×C107—41no—
83C22×C4×C107—41no—
84C22×C4×C107—41no—
85C22×C4×C107—42no—
86C22×C4×C107—42no—
87C22×C4×C107—42no—
88C22×C4×C107—42no—
89C22×C4×C107—42no—
90C22×C4×C107—42no—
91C22×C4×C107C22⋊C411yescharacteristic
92C22×C4×C107C22⋊C411yescharacteristic
93C22×C4×C107C22⋊C411yescharacteristic
94C22×C4×C107C22⋊C411yescharacteristic
95C22×C4×C107C22×C411yescharacteristic
96C22×C4×C107C2×D411yescharacteristic
97C22×C4×C107C2×D412yes—
98C22×C4×C107#4112yes—
99C2×C8×C107—24no—
100C2×C8×C107—42no—
101C2×C8×C107—42no—
102C4⋊C4×C107—22no—
103C4⋊C4×C107—41no—
104C4⋊C4×C107—41no—
105C4⋊C4×C107—42no—
106C4⋊C4×C107—42no—
107C22⋊C4×C107—42no—
108C22⋊C4×C107—42no—
109C22⋊C4×C107—42no—
110C22⋊C4×C107—42no—
111C22⋊C4×C107—42no—
112C22⋊C4×C107—41no—
113C22⋊C4×C107—41no—
114C42×C107—22no—
115C42×C107—22no—
116C42×C107—21no—
117C42×C107—21no—
118C42×C107—21no—
119C42×C107—21no—
120C23×C107—21no—
121C23×C107—21no—
122C23×C107—21no—
123C23×C107—21no—
124C23×C107—41no—
125C23×C107—41no—
126C23×C107—41no—
127C23×C107—41no—
128C23×C107—41no—
129C23×C107—41no—
130C23×C107—41no—
131C23×C107C2×C22⋊C411yescharacteristic
132C23×C107#12112yes—
133C23×C107AGL(1,ℤ/8)11yescharacteristic
134C23×C107AGL(1,ℤ/8)12yes—
135C23×C107#13711yescharacteristic
136D4×C107—82no—
137D4×C107—82no—
138D4×C107—82no—
139C2×C4×C107—21no—
140C2×C4×C107—21no—
141C2×C4×C107—21no—
142C2×C4×C107—21no—
143C2×C4×C107—21no—
144C2×C4×C107—21no—
145C2×C4×C107—21no—
146C2×C4×C107—21no—
147C2×C4×C107—21no—
148C2×C4×C107—21no—
149C2×C4×C107—21no—
150C2×C4×C107—21no—
151C2×C4×C107—21no—
152C2×C4×C107—21no—
153C2×C4×C107—21no—
154C2×C4×C107—42no—
155C2×C4×C107—42no—
156C2×C4×C107—44no—
157C2×C4×C107—42no—
158C2×C4×C107—42no—
159C2×C4×C107—44no—
160C2×C4×C107—44no—
161C2×C4×C107—44no—
162C2×C4×C107—41no—
163C2×C4×C107—41no—
164C2×C4×C107—41no—
165C2×C4×C107—41no—
166C2×C4×C107—41no—
167C2×C4×C107—41no—
168C2×C4×C107—41no—
169C2×C4×C107—41no—
170C2×C4×C107—41no—
171C2×C4×C107—82no—
172C2×C4×C107—82no—
173C2×C4×C107—82no—
174C2×C4×C107—82no—
175C2×C4×C107#10412yes—
176C2×C4×C107C4×D412yes—
177C2×C4×C107#12011yescharacteristic
178C2×C4×C107#12311yescharacteristic
179C8×C107—44no—
180C22×C107—22no—
181C22×C107—22no—
182C22×C107—22no—
183C22×C107—21no—
184C22×C107—21no—
185C22×C107—21no—
186C22×C107—21no—
187C22×C107—22no—
188C22×C107—81no—
189C22×C107—81no—
190C22×C107—81no—
191C22×C107—81no—
192C22×C107—81no—
193C22×C107—81no—
194C22×C107—81no—
195C22×C107#38611yescharacteristic
196C22×C107#41011yescharacteristic
197C22×C107#41011yescharacteristic
198C22×C107#41711yescharacteristic
199C22×C107#41811yescharacteristic
200C22×C107C2×#10411yescharacteristic
201C22×C107#42111yescharacteristic
202C22×C107#46812yes—
203C22×C107#46912yes—
204C4×C107—22no—
205C4×C107—21no—
206C4×C107—22no—
207C4×C107—21no—
208C4×C107—41no—
209C4×C107—41no—
210C4×C107—41no—
211C4×C107—84no—
212C4×C107—81no—
213C4×C107—81no—
214C4×C107—81no—
215#9118C10711yesmaximal, characteristic, direct product factor, Sylow
216C2×C107—22no—
217C2×C107—22no—
218C2×C107—161no—
219C2×C107#150511yescharacteristic
220C2×C107#150911yescharacteristic
221C2×C107#151211yescharacteristic
222C2×C107#151411yescharacteristic
223C2×C107#187111yescharacteristic
224C2×C107#189511yescharacteristic
225C2×C107#189911yescharacteristic
226C2×#432C2×C10711yescharacteristic, complemented
227#2854C2×C10711yescharacteristic
228C2×#327C2×C10712yes—
229#1434C2×C10711yescharacteristic, complemented
230#1294C2×C10712yescomplemented
231C107#911811yescharacteristic, direct product factor, Sylow
232C2×#123—21no—
233C2×#121C22×C10711yescharacteristic
234C22×C42C22×C10711yescharacteristic
235#432—24no—
236C2×C4⋊C8—21no—
237C2×C22⋊C8C22×C10712yes—
238C2×#97—21no—
239#390C4×C10711yescharacteristic, complemented
240#390C4×C10711yescharacteristic, complemented
241#389C4×C10711yescharacteristic, complemented
242#389C4×C10711yescharacteristic, complemented
243#388—21no—
244#388—21no—
245#386—21no—
246#380C22×C10711yescharacteristic
247C2×#95—21no—
248C2×#95—21no—
249C2×#95C22×C10712yes—
250#327—24no—
251C22×D4—21no—
252C22×D4C2×C4×C10711yescharacteristic
253C23×C4—22no—
254C23×C4D4×C10711yescharacteristic
255C23×C4D4×C10711yescharacteristic
256C23×C4C23×C10711yescharacteristic
257C22×C8—22no—
258#123—44no—
259#121—22no—
260#121—22no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4C2×C4×C10711yescharacteristic
264C2×C4⋊C4C2×C4×C10711yescharacteristic
265C2×C4⋊C4C2×C4×C10711yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42C2×C4×C10711yescharacteristic
275C2×C42C2×C4×C10711yescharacteristic
276C2×C42D4×C10711yescharacteristic
277C2×C42D4×C10711yescharacteristic
278C4⋊C8—24no—
279C22⋊C8—22no—
280C22⋊C8D4×C10714yes—
281#97—24no—
282#95—24no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—22no—
287#95—22no—
288#95—42no—
289C24—21no—
290C24C2×D4×C10711yescharacteristic
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4C22⋊C4×C10711yescharacteristic
318C22×C4C22⋊C4×C10711yescharacteristic
319C22×C4C22⋊C4×C10711yescharacteristic
320C22×C4C22⋊C4×C10711yescharacteristic
321C22×C4C22×C4×C10711yescharacteristic
322C22×C4C2×D4×C10711yescharacteristic
323C22×C4C2×D4×C10712yes—
324C22×C4#41×C10712yes—
325C2×C8—24no—
326C2×C8—42no—
327C2×C8—42no—
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C42—22no—
341C42—22no—
342C42—21no—
343C42—21no—
344C42—21no—
345C42—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23C2×C22⋊C4×C10711yescharacteristic
358C23#121×C10712yes—
359C23AGL(1,ℤ/8)×C10711yescharacteristic
360C23AGL(1,ℤ/8)×C10712yes—
361C23#137×C10711yescharacteristic
362D4—82no—
363D4—82no—
364D4—82no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4#104×C10712yes—
402C2×C4C4×D4×C10712yes—
403C2×C4#120×C10711yescharacteristic
404C2×C4#123×C10711yescharacteristic
405C8—44no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22#386×C10711yescharacteristic
422C22#410×C10711yescharacteristic
423C22#410×C10711yescharacteristic
424C22#417×C10711yescharacteristic
425C22#418×C10711yescharacteristic
426C22C2×#104×C10711yescharacteristic
427C22#421×C10711yescharacteristic
428C22#468×C10712yes—
429C22#469×C10712yes—
430C4—22no—
431C4—21no—
432C4—22no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—84no—
438C4—81no—
439C4—81no—
440C4—81no—
441C2—22no—
442C2—22no—
443C2—161no—
444C2C107×#150511yescharacteristic
445C2C107×#150911yescharacteristic
446C2C107×#151211yescharacteristic
447C2C107×#151411yescharacteristic
448C2C107×#187111yescharacteristic
449C2C107×#189511yescharacteristic
450C2C107×#189911yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC2×#121×C107C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#432×C107C2semidirect
4. C107×#1434C2semidirect
5. C107×#1294C2semidirect
13. #390×C107C4semidirect
14. #390×C107C4semidirect
15. #389×C107C4semidirect
16. #389×C107C4semidirect
215. #9118C107direct (N × H)
226. C2×#432C2×C107semidirect
229. #1434C2×C107semidirect
230. #1294C2×C107semidirect
231. C107#9118direct (N × H)
239. #390C4×C107semidirect
240. #390C4×C107semidirect
241. #389C4×C107semidirect
242. #389C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#432×C1072
C107×#28542
C2×#327×C1072
C107×#14342
C107×#12942
#9118107