Finite Group Databasebeta

← C107×#8967 #41034931

Subgroups — C107×#8967 #41034931

Order 27392.

908 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2973C211yesmaximal, characteristic, complemented
2C4×#120×C107C211yesmaximal, characteristic
3C107×#1779C212yesmaximal, complemented
4C107×#1459C211yesmaximal, characteristic, complemented
5C107×#1282C212yesmaximal, complemented
6C24×C4×C107C2211yescharacteristic
7C2×#120×C107C411yescharacteristic
8C2×C4×D4×C107—21no—
9C2×C4×D4×C107C2211yescharacteristic
10#435×C107—24no—
11#432×C107—21no—
12#407×C107—21no—
13C2×C22⋊C8×C107—24no—
14C2×C22⋊C8×C107C2212yes—
15C2×C22⋊C8×C107C2212yes—
16#386×C107—21no—
17#386×C107C411yescharacteristic
18#385×C107—21no—
19#385×C107C411yescharacteristic
20#379×C107C411yescharacteristic
21C4×C22⋊C4×C107—21no—
22C4×C22⋊C4×C107C2211yescharacteristic
23#324×C107—21no—
24#323×C107—21no—
25C25×C107C2×C411yescharacteristic
26C22×D4×C107—21no—
27C22×D4×C107C2×C411yescharacteristic
28C23×C4×C107—21no—
29C23×C4×C107—22no—
30C23×C4×C107—21no—
31C23×C4×C107—22no—
32C23×C4×C107—44no—
33C23×C4×C107C2×C411yescharacteristic
34C23×C4×C107D411yescharacteristic
35C23×C4×C107C2311yescharacteristic
36C2×M16×C107—22no—
37C22×C8×C107—22no—
38C22×C8×C107D414yescomplemented
39#120×C107—22no—
40#120×C107—22no—
41C4×D4×C107—22no—
42C4×D4×C107—22no—
43C4×D4×C107—44no—
44C2×C4⋊C4×C107—21no—
45C2×C4⋊C4×C107D411yescharacteristic
46C2×C22⋊C4×C107—21no—
47C2×C22⋊C4×C107—21no—
48C2×C22⋊C4×C107—21no—
49C2×C22⋊C4×C107—21no—
50C2×C22⋊C4×C107C2×C411yescharacteristic
51C2×C22⋊C4×C107C2×C411yescharacteristic
52C2×C22⋊C4×C107C2×C411yescharacteristic
53C2×C22⋊C4×C107D411yescharacteristic
54C2×C42×C107—21no—
55C2×C42×C107D411yescharacteristic
56C4⋊C8×C107—22no—
57C22⋊C8×C107—22no—
58C22⋊C8×C107—22no—
59C22⋊C8×C107—22no—
60C22⋊C8×C107—22no—
61C22⋊C8×C107—22no—
62C22⋊C8×C107—48no—
63#97×C107—22no—
64#95×C107—21no—
65#95×C107—21no—
66#95×C107—21no—
67C24×C107—21no—
68C24×C107—22no—
69C24×C107—21no—
70C24×C107—22no—
71C24×C107—42no—
72C24×C107—42no—
73C24×C107C22⋊C411yescharacteristic
74C24×C107M1612yescomplemented
75C24×C107C22×C411yescharacteristic
76C2×D4×C107—24no—
77C2×D4×C107—22no—
78C2×D4×C107—21no—
79C2×D4×C107—21no—
80C2×D4×C107—22no—
81C2×D4×C107—42no—
82C2×D4×C107—42no—
83C22×C4×C107—28no—
84C22×C4×C107—24no—
85C22×C4×C107—21no—
86C22×C4×C107—21no—
87C22×C4×C107—22no—
88C22×C4×C107—21no—
89C22×C4×C107—21no—
90C22×C4×C107—21no—
91C22×C4×C107—42no—
92C22×C4×C107—42no—
93C22×C4×C107—42no—
94C22×C4×C107—44no—
95C22×C4×C107—42no—
96C22×C4×C107—44no—
97C22×C4×C107—42no—
98C22×C4×C107—42no—
99C22×C4×C107—44no—
100C22×C4×C107—41no—
101C22×C4×C107—42no—
102C22×C4×C107—41no—
103C22×C4×C107C22⋊C411yescharacteristic
104C22×C4×C107C22⋊C411yescharacteristic
105C22×C4×C107C22⋊C411yescharacteristic
106C22×C4×C107C2×D412yes—
107C22×C4×C107C2×D411yescharacteristic
108C22×C4×C107C2×D411yescharacteristic
109C22×C4×C107#4112yes—
110M16×C107—82no—
111C2×C8×C107—24no—
112C2×C8×C107—44no—
113C2×C8×C107—44no—
114C2×C8×C107—42no—
115C4⋊C4×C107—22no—
116C4⋊C4×C107—42no—
117C22⋊C4×C107—24no—
118C22⋊C4×C107—22no—
119C22⋊C4×C107—21no—
120C22⋊C4×C107—22no—
121C22⋊C4×C107—22no—
122C22⋊C4×C107—42no—
123C22⋊C4×C107—42no—
124C22⋊C4×C107—42no—
125C22⋊C4×C107M1612yescomplemented
126C42×C107—21no—
127C42×C107—21no—
128C42×C107—42no—
129C23×C107—22no—
130C23×C107—22no—
131C23×C107—24no—
132C23×C107—24no—
133C23×C107—22no—
134C23×C107—24no—
135C23×C107—21no—
136C23×C107—21no—
137C23×C107—21no—
138C23×C107—41no—
139C23×C107—44no—
140C23×C107—41no—
141C23×C107—41no—
142C23×C107—42no—
143C23×C107—41no—
144C23×C107—42no—
145C23×C107—44no—
146C23×C107—48no—
147C23×C107—41no—
148C23×C107—41no—
149C23×C107—41no—
150C23×C107—41no—
151C23×C107—42no—
152C23×C107C2×C22⋊C411yescharacteristic
153C23×C107C4×D412yes—
154C23×C107C2×M1611yescharacteristic
155C23×C107C2×M1611yescharacteristic
156C23×C107#13112yes—
157D4×C107—48no—
158D4×C107—42no—
159D4×C107—42no—
160C2×C4×C107—22no—
161C2×C4×C107—24no—
162C2×C4×C107—22no—
163C2×C4×C107—24no—
164C2×C4×C107—21no—
165C2×C4×C107—21no—
166C2×C4×C107—21no—
167C2×C4×C107—21no—
168C2×C4×C107—22no—
169C2×C4×C107—21no—
170C2×C4×C107—41no—
171C2×C4×C107—42no—
172C2×C4×C107—48no—
173C2×C4×C107—44no—
174C2×C4×C107—41no—
175C2×C4×C107—41no—
176C2×C4×C107—42no—
177C2×C4×C107—41no—
178C2×C4×C107—41no—
179C2×C4×C107—42no—
180C2×C4×C107—44no—
181C2×C4×C107—41no—
182C2×C4×C107—41no—
183C2×C4×C107—41no—
184C2×C4×C107—41no—
185C2×C4×C107—41no—
186C2×C4×C107—81no—
187C2×C4×C107#12011yescharacteristic
188C2×C4×C107#12112yes—
189C2×C4×C107#12311yescharacteristic
190C8×C107—44no—
191C8×C107—82no—
192C22×C107—21no—
193C22×C107—22no—
194C22×C107—21no—
195C22×C107—22no—
196C22×C107—24no—
197C22×C107—28no—
198C22×C107—41no—
199C22×C107—41no—
200C22×C107—42no—
201C22×C107—42no—
202C22×C107—42no—
203C22×C107—42no—
204C22×C107—44no—
205C22×C107—44no—
206C22×C107—44no—
207C22×C107—42no—
208C22×C107—42no—
209C22×C107—42no—
210C22×C107—42no—
211C22×C107—41no—
212C22×C107—41no—
213C22×C107—41no—
214C22×C107—81no—
215C22×C107#38611yescharacteristic
216C22×C107#40711yescharacteristic
217C22×C107#40811yescharacteristic
218C22×C107#43512yes—
219C22×C107#43612yes—
220C4×C107—22no—
221C4×C107—21no—
222C4×C107—42no—
223C4×C107—41no—
224C4×C107—42no—
225C4×C107—41no—
226C4×C107—41no—
227C4×C107—81no—
228C4×C107B(4,𝔽2)12yes—
229#8967C10711yesmaximal, characteristic, direct product factor, Sylow
230C2×C107—21no—
231C2×C107—21no—
232C2×C107—22no—
233C2×C107—22no—
234C2×C107—44no—
235C2×C107—81no—
236C2×C107#187011yescharacteristic
237C2×C107#188911yescharacteristic
238C2×C107#189111yescharacteristic
239#2973C2×C10711yescharacteristic, complemented
240C4×#120C2×C10711yescharacteristic
241#1779C2×C10712yescomplemented
242#1459C2×C10711yescharacteristic, complemented
243#1282C2×C10712yescomplemented
244C107#896711yescharacteristic, direct product factor, Sylow
245C24×C4C22×C10711yescharacteristic
246C2×#120C4×C10711yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C22×C10711yescharacteristic
249#435—24no—
250#432—21no—
251#407—21no—
252C2×C22⋊C8—24no—
253C2×C22⋊C8C22×C10712yes—
254C2×C22⋊C8C22×C10712yes—
255#386—21no—
256#386C4×C10711yescharacteristic
257#385—21no—
258#385C4×C10711yescharacteristic
259#379C4×C10711yescharacteristic
260C4×C22⋊C4—21no—
261C4×C22⋊C4C22×C10711yescharacteristic
262#324—21no—
263#323—21no—
264C25C2×C4×C10711yescharacteristic
265C22×D4—21no—
266C22×D4C2×C4×C10711yescharacteristic
267C23×C4—21no—
268C23×C4—22no—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—44no—
272C23×C4C2×C4×C10711yescharacteristic
273C23×C4D4×C10711yescharacteristic
274C23×C4C23×C10711yescharacteristic
275C2×M16—22no—
276C22×C8—22no—
277C22×C8D4×C10714yescomplemented
278#120—22no—
279#120—22no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—44no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4D4×C10711yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4C2×C4×C10711yescharacteristic
290C2×C22⋊C4C2×C4×C10711yescharacteristic
291C2×C22⋊C4C2×C4×C10711yescharacteristic
292C2×C22⋊C4D4×C10711yescharacteristic
293C2×C42—21no—
294C2×C42D4×C10711yescharacteristic
295C4⋊C8—22no—
296C22⋊C8—22no—
297C22⋊C8—22no—
298C22⋊C8—22no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301C22⋊C8—48no—
302#97—22no—
303#95—21no—
304#95—21no—
305#95—21no—
306C24—21no—
307C24—22no—
308C24—21no—
309C24—22no—
310C24—42no—
311C24—42no—
312C24C22⋊C4×C10711yescharacteristic
313C24M16×C10712yescomplemented
314C24C22×C4×C10711yescharacteristic
315C2×D4—24no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—22no—
320C2×D4—42no—
321C2×D4—42no—
322C22×C4—28no—
323C22×C4—24no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—44no—
334C22×C4—42no—
335C22×C4—44no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—44no—
339C22×C4—41no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4C22⋊C4×C10711yescharacteristic
343C22×C4C22⋊C4×C10711yescharacteristic
344C22×C4C22⋊C4×C10711yescharacteristic
345C22×C4C2×D4×C10712yes—
346C22×C4C2×D4×C10711yescharacteristic
347C22×C4C2×D4×C10711yescharacteristic
348C22×C4#41×C10712yes—
349M16—82no—
350C2×C8—24no—
351C2×C8—44no—
352C2×C8—44no—
353C2×C8—42no—
354C4⋊C4—22no—
355C4⋊C4—42no—
356C22⋊C4—24no—
357C22⋊C4—22no—
358C22⋊C4—21no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4M16×C10712yescomplemented
365C42—21no—
366C42—21no—
367C42—42no—
368C23—22no—
369C23—22no—
370C23—24no—
371C23—24no—
372C23—22no—
373C23—24no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—44no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—41no—
383C23—42no—
384C23—44no—
385C23—48no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23C2×C22⋊C4×C10711yescharacteristic
392C23C4×D4×C10712yes—
393C23C2×M16×C10711yescharacteristic
394C23C2×M16×C10711yescharacteristic
395C23#131×C10712yes—
396D4—48no—
397D4—42no—
398D4—42no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—48no—
412C2×C4—44no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—81no—
426C2×C4#120×C10711yescharacteristic
427C2×C4#121×C10712yes—
428C2×C4#123×C10711yescharacteristic
429C8—44no—
430C8—82no—
431C22—21no—
432C22—22no—
433C22—21no—
434C22—22no—
435C22—24no—
436C22—28no—
437C22—41no—
438C22—41no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—44no—
444C22—44no—
445C22—44no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22#386×C10711yescharacteristic
455C22#407×C10711yescharacteristic
456C22#408×C10711yescharacteristic
457C22#435×C10712yes—
458C22#436×C10712yes—
459C4—22no—
460C4—21no—
461C4—42no—
462C4—41no—
463C4—42no—
464C4—41no—
465C4—41no—
466C4—81no—
467C4B(4,𝔽2)×C10712yes—
468C2—21no—
469C2—21no—
470C2—22no—
471C2—22no—
472C2—44no—
473C2—81no—
474C2C107×#187011yescharacteristic
475C2C107×#188911yescharacteristic
476C2C107×#189111yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutatorC24C22×C4×C107
Frattini, cosocleC23×C4C23×C107
socleC22×C107#386
prime radicalC2×#120×C107C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2973C2semidirect
3. C107×#1779C2semidirect
4. C107×#1459C2semidirect
5. C107×#1282C2semidirect
38. C22×C8×C107D4semidirect
74. C24×C107M16semidirect
125. C22⋊C4×C107M16semidirect
229. #8967C107direct (N × H)
239. #2973C2×C107semidirect
241. #1779C2×C107semidirect
242. #1459C2×C107semidirect
243. #1282C2×C107semidirect
244. C107#8967direct (N × H)
277. C22×C8D4×C107semidirect
313. C24M16×C107semidirect
364. C22⋊C4M16×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#29732
C4×#120×C1072
C107×#17792
C107×#14592
C107×#12822
#8967107