Finite Group Databasebeta

← C107×#9716 #41035680

Subgroups — C107×#9716 #41035680

Order 27392.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2850C211yesmaximal, characteristic
2C107×#1797C211yesmaximal, characteristic, complemented
3C2×#328×C107C212yesmaximal, complemented
4C2×#327×C107C212yesmaximal
5C107×#1434C211yesmaximal, characteristic, complemented
6C2×#124×C107C411yescharacteristic, complemented
7C2×C22⋊Q8×C107C2211yescharacteristic
8C2×#121×C107C2211yescharacteristic
9C22×C42×C107C2211yescharacteristic
10C2×C4⋊C8×C107—21no—
11C2×C22⋊C8×C107C2212yes—
12#391×C107C411yescharacteristic, complemented
13#390×C107C411yescharacteristic, complemented
14#388×C107—21no—
15#388×C107—21no—
16#386×C107—21no—
17#386×C107—21no—
18#382×C107C411yescharacteristic, complemented
19C2×#95×C107—21no—
20C2×#95×C107—21no—
21C2×#95×C107C2212yes—
22#336×C107—21no—
23#328×C107—24no—
24#327×C107—24no—
25C22×Q8×C107C2×C411yescharacteristic
26C22×D4×C107—21no—
27C22×D4×C107C2×C411yescharacteristic
28C23×C4×C107—22no—
29C23×C4×C107D411yescharacteristic
30C23×C4×C107D411yescharacteristic
31C23×C4×C107C2311yescharacteristic
32C22×C8×C107—22no—
33#124×C107—42no—
34C22⋊Q8×C107—22no—
35C22⋊Q8×C107—22no—
36#121×C107—22no—
37#121×C107—22no—
38C2×C4⋊C4×C107—21no—
39C2×C4⋊C4×C107C2×C411yescharacteristic
40C2×C4⋊C4×C107C2×C411yescharacteristic
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×C107—21no—
47C2×C42×C107—42no—
48C2×C42×C107C2×C411yescharacteristic
49C2×C42×C107C2×C411yescharacteristic
50C2×C42×C107D411yescharacteristic
51C2×C42×C107D411yescharacteristic
52C4⋊C8×C107—42no—
53C22⋊C8×C107—22no—
54C22⋊C8×C107—22no—
55#95×C107—21no—
56#95×C107—21no—
57#95×C107—21no—
58#95×C107—21no—
59#95×C107—22no—
60#95×C107—42no—
61#95×C107—42no—
62#95×C107D414yes—
63C24×C107—21no—
64C24×C107C2×D411yescharacteristic
65C2×Q8×C107—22no—
66C2×Q8×C107—41no—
67C2×Q8×C107—41no—
68C2×D4×C107—22no—
69C2×D4×C107—41no—
70C2×D4×C107—41no—
71C2×D4×C107—42no—
72C2×D4×C107—42no—
73C2×D4×C107—41no—
74C2×D4×C107—41no—
75C22×C4×C107—22no—
76C22×C4×C107—21no—
77C22×C4×C107—21no—
78C22×C4×C107—22no—
79C22×C4×C107—21no—
80C22×C4×C107—21no—
81C22×C4×C107—21no—
82C22×C4×C107—24no—
83C22×C4×C107—41no—
84C22×C4×C107—41no—
85C22×C4×C107—41no—
86C22×C4×C107—41no—
87C22×C4×C107—41no—
88C22×C4×C107—42no—
89C22×C4×C107—42no—
90C22×C4×C107—42no—
91C22×C4×C107—42no—
92C22×C4×C107—42no—
93C22×C4×C107—42no—
94C22×C4×C107C22⋊C411yescharacteristic
95C22×C4×C107C22⋊C411yescharacteristic
96C22×C4×C107C22⋊C411yescharacteristic
97C22×C4×C107C22⋊C411yescharacteristic
98C22×C4×C107C22×C411yescharacteristic
99C22×C4×C107C2×D411yescharacteristic
100C22×C4×C107C2×D412yes—
101C22×C4×C107#4112yes—
102C2×C8×C107—42no—
103C2×C8×C107—42no—
104C2×C8×C107—42no—
105C4⋊C4×C107—22no—
106C4⋊C4×C107—22no—
107C4⋊C4×C107—41no—
108C4⋊C4×C107—41no—
109C22⋊C4×C107—42no—
110C22⋊C4×C107—42no—
111C22⋊C4×C107—42no—
112C22⋊C4×C107—42no—
113C22⋊C4×C107—42no—
114C22⋊C4×C107—41no—
115C22⋊C4×C107—41no—
116C42×C107—22no—
117C42×C107—22no—
118C42×C107—41no—
119C42×C107—41no—
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×C107#13512yes—
134C23×C107AGL(1,ℤ/8)11yescharacteristic
135C23×C107#13711yescharacteristic
136Q8×C107—82no—
137D4×C107—82no—
138D4×C107—82no—
139D4×C107—82no—
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—21no—
155C2×C4×C107—42no—
156C2×C4×C107—42no—
157C2×C4×C107—44no—
158C2×C4×C107—42no—
159C2×C4×C107—42no—
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—44no—
172C2×C4×C107—82no—
173C2×C4×C107—82no—
174C2×C4×C107—82no—
175C2×C4×C107—82no—
176C2×C4×C107#9912yes—
177C2×C4×C107C4×D412yes—
178C2×C4×C107#12411yescharacteristic
179C2×C4×C107#12711yescharacteristic
180C8×C107—82no—
181C22×C107—22no—
182C22×C107—22no—
183C22×C107—21no—
184C22×C107—21no—
185C22×C107—21no—
186C22×C107—21no—
187C22×C107—22no—
188C22×C107—22no—
189C22×C107—81no—
190C22×C107—81no—
191C22×C107—81no—
192C22×C107—81no—
193C22×C107—81no—
194C22×C107—81no—
195C22×C107—81no—
196C22×C107#39011yescharacteristic
197C22×C107C2×#9911yescharacteristic
198C22×C107#41011yescharacteristic
199C22×C107#41611yescharacteristic
200C22×C107#41711yescharacteristic
201C22×C107#42111yescharacteristic
202C22×C107#42111yescharacteristic
203C22×C107#46312yes—
204C22×C107#46412yes—
205C4×C107—21no—
206C4×C107—22no—
207C4×C107—21no—
208C4×C107—22no—
209C4×C107—41no—
210C4×C107—41no—
211C4×C107—41no—
212C4×C107—84no—
213C4×C107—81no—
214C4×C107—81no—
215C4×C107—81no—
216#9716C10711yesmaximal, characteristic, direct product factor, Sylow
217C2×C107—22no—
218C2×C107—22no—
219C2×C107—161no—
220C2×C107#151211yescharacteristic
221C2×C107#151311yescharacteristic
222C2×C107#151611yescharacteristic
223C2×C107#152111yescharacteristic
224C2×C107#196311yescharacteristic
225C2×C107#196411yescharacteristic
226C2×C107#198311yescharacteristic
227#2850C2×C10711yescharacteristic
228#1797C2×C10711yescharacteristic, complemented
229C2×#328C2×C10712yescomplemented
230C2×#327C2×C10712yes—
231#1434C2×C10711yescharacteristic, complemented
232C107#971611yescharacteristic, direct product factor, Sylow
233C2×#124C4×C10711yescharacteristic, complemented
234C2×C22⋊Q8C22×C10711yescharacteristic
235C2×#121C22×C10711yescharacteristic
236C22×C42C22×C10711yescharacteristic
237C2×C4⋊C8—21no—
238C2×C22⋊C8C22×C10712yes—
239#391C4×C10711yescharacteristic, complemented
240#390C4×C10711yescharacteristic, complemented
241#388—21no—
242#388—21no—
243#386—21no—
244#386—21no—
245#382C4×C10711yescharacteristic, complemented
246C2×#95—21no—
247C2×#95—21no—
248C2×#95C22×C10712yes—
249#336—21no—
250#328—24no—
251#327—24no—
252C22×Q8C2×C4×C10711yescharacteristic
253C22×D4—21no—
254C22×D4C2×C4×C10711yescharacteristic
255C23×C4—22no—
256C23×C4D4×C10711yescharacteristic
257C23×C4D4×C10711yescharacteristic
258C23×C4C23×C10711yescharacteristic
259C22×C8—22no—
260#124—42no—
261C22⋊Q8—22no—
262C22⋊Q8—22no—
263#121—22no—
264#121—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C10711yescharacteristic
267C2×C4⋊C4C2×C4×C10711yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C42—42no—
275C2×C42C2×C4×C10711yescharacteristic
276C2×C42C2×C4×C10711yescharacteristic
277C2×C42D4×C10711yescharacteristic
278C2×C42D4×C10711yescharacteristic
279C4⋊C8—42no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—22no—
287#95—42no—
288#95—42no—
289#95D4×C10714yes—
290C24—21no—
291C24C2×D4×C10711yescharacteristic
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×D4—22no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4C22⋊C4×C10711yescharacteristic
322C22×C4C22⋊C4×C10711yescharacteristic
323C22×C4C22⋊C4×C10711yescharacteristic
324C22×C4C22⋊C4×C10711yescharacteristic
325C22×C4C22×C4×C10711yescharacteristic
326C22×C4C2×D4×C10711yescharacteristic
327C22×C4C2×D4×C10712yes—
328C22×C4#41×C10712yes—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—22no—
344C42—22no—
345C42—41no—
346C42—41no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23C2×C22⋊C4×C10711yescharacteristic
359C23#121×C10712yes—
360C23#135×C10712yes—
361C23AGL(1,ℤ/8)×C10711yescharacteristic
362C23#137×C10711yescharacteristic
363Q8—82no—
364D4—82no—
365D4—82no—
366D4—82no—
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—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
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—41no—
398C2×C4—44no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4#99×C10712yes—
404C2×C4C4×D4×C10712yes—
405C2×C4#124×C10711yescharacteristic
406C2×C4#127×C10711yescharacteristic
407C8—82no—
408C22—22no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—22no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22#390×C10711yescharacteristic
424C22C2×#99×C10711yescharacteristic
425C22#410×C10711yescharacteristic
426C22#416×C10711yescharacteristic
427C22#417×C10711yescharacteristic
428C22#421×C10711yescharacteristic
429C22#421×C10711yescharacteristic
430C22#463×C10712yes—
431C22#464×C10712yes—
432C4—21no—
433C4—22no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—81no—
441C4—81no—
442C4—81no—
443C2—22no—
444C2—22no—
445C2—161no—
446C2C107×#151211yescharacteristic
447C2C107×#151311yescharacteristic
448C2C107×#151611yescharacteristic
449C2C107×#152111yescharacteristic
450C2C107×#196311yescharacteristic
451C2C107×#196411yescharacteristic
452C2C107×#198311yescharacteristic
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
2. C107×#1797C2semidirect
3. C2×#328×C107C2semidirect
5. C107×#1434C2semidirect
6. C2×#124×C107C4semidirect
12. #391×C107C4semidirect
13. #390×C107C4semidirect
18. #382×C107C4semidirect
216. #9716C107direct (N × H)
228. #1797C2×C107semidirect
229. C2×#328C2×C107semidirect
231. #1434C2×C107semidirect
232. C107#9716direct (N × H)
233. C2×#124C4×C107semidirect
239. #391C4×C107semidirect
240. #390C4×C107semidirect
245. #382C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#28502
C107×#17972
C2×#328×C1072
C2×#327×C1072
C107×#14342
#9716107