Finite Group Databasebeta

← C107×#8949 #41034913

Subgroups — C107×#8949 #41034913

Order 27392.

584 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×SD16×C107C211yesmaximal, characteristic
2C2×#436×C107C211yesmaximal, characteristic
3C107×#1984C211yesmaximal, characteristic, complemented
4C2×Q8⋊C8×C107C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C107C211yesmaximal, characteristic
6C107×#1277C211yesmaximal, characteristic, complemented
7C107×#1273C211yesmaximal, characteristic, complemented
8C22×SD16×C107C411yescharacteristic
9C22×M16×C107—21no—
10C2×C4×Q8×C107C2211yescharacteristic
11C2×C4×D4×C107C2211yescharacteristic
12C4×SD16×C107—22no—
13C4×SD16×C107—22no—
14#436×C107—22no—
15#436×C107—22no—
16C2×#106×C107C411yescharacteristic
17C2×C4⋊C8×C107C2211yescharacteristic
18C2×C4⋊C8×C107C2211yescharacteristic
19C2×#103×C107C411yescharacteristic
20C2×#102×C107C411yescharacteristic
21C2×C22⋊C8×C107—21no—
22C2×C4×C8×C107C2211yescharacteristic
23C2×C4×C8×C107C2211yescharacteristic
24C2×C4×C8×C107C2211yescharacteristic
25#336×C107—21no—
26#336×C107—21no—
27Q8⋊C8×C107—22no—
28D4⋊C8×C107—22no—
29C22×Q8×C107C2×C411yescharacteristic
30C22×D4×C107C2×C411yescharacteristic
31C23×C4×C107—21no—
32C2×SD16×C107—22no—
33C2×SD16×C107—22no—
34C2×SD16×C107—22no—
35C2×M16×C107—24no—
36C2×M16×C107—42no—
37C2×M16×C107—42no—
38C22×C8×C107—21no—
39C22×C8×C107—21no—
40C22×C8×C107—21no—
41C22×C8×C107C2×C411yescharacteristic
42C22×C8×C107C2×C411yescharacteristic
43C22×C8×C107D411yescharacteristic
44C22×C8×C107D411yescharacteristic
45C4×Q8×C107—21no—
46C4×Q8×C107—21no—
47C4×Q8×C107—21no—
48C4×Q8×C107—21no—
49C4×D4×C107—21no—
50C4×D4×C107—21no—
51C4×D4×C107D412yes—
52C4×D4×C107D412yes—
53C2×C4⋊C4×C107—21no—
54C2×C4⋊C4×C107C2×C411yescharacteristic
55C2×C4⋊C4×C107C2×C411yescharacteristic
56C2×C22⋊C4×C107—21no—
57C2×C42×C107—21no—
58C2×C42×C107C2311yescharacteristic
59#106×C107—22no—
60C4⋊C8×C107—21no—
61C4⋊C8×C107—21no—
62C4⋊C8×C107—21no—
63C4⋊C8×C107D412yes—
64#103×C107—22no—
65#102×C107—22no—
66C22⋊C8×C107—24no—
67C4×C8×C107—21no—
68C4×C8×C107—21no—
69C4×C8×C107—21no—
70C4×C8×C107—21no—
71C4×C8×C107—21no—
72C4×C8×C107—21no—
73C24×C107—21no—
74C2×Q8×C107—21no—
75C2×Q8×C107—21no—
76C2×Q8×C107—21no—
77C2×Q8×C107—21no—
78C2×Q8×C107—21no—
79C2×Q8×C107M1612yescomplemented
80C2×D4×C107—21no—
81C2×D4×C107—21no—
82C2×D4×C107—21no—
83C2×D4×C107—21no—
84C2×D4×C107—21no—
85C2×D4×C107C22⋊C412yes—
86C22×C4×C107—21no—
87C22×C4×C107—21no—
88C22×C4×C107—22no—
89C22×C4×C107—22no—
90C22×C4×C107—21no—
91C22×C4×C107—41no—
92C22×C4×C107—41no—
93C22×C4×C107—41no—
94C22×C4×C107—41no—
95C22×C4×C107C22×C411yescharacteristic
96C22×C4×C107C2×D411yescharacteristic
97C22×C4×C107#4111yescharacteristic
98SD16×C107—28no—
99M16×C107—48no—
100C2×C8×C107—21no—
101C2×C8×C107—21no—
102C2×C8×C107—21no—
103C2×C8×C107—21no—
104C2×C8×C107—22no—
105C2×C8×C107—21no—
106C2×C8×C107—21no—
107C2×C8×C107—22no—
108C2×C8×C107—21no—
109C2×C8×C107—21no—
110C2×C8×C107—21no—
111C2×C8×C107—21no—
112C2×C8×C107—41no—
113C2×C8×C107—41no—
114C2×C8×C107—41no—
115C2×C8×C107—41no—
116C2×C8×C107—41no—
117C2×C8×C107—41no—
118C2×C8×C107—41no—
119C2×C8×C107M1612yescomplemented
120C2×C8×C107SD1612yescomplemented
121C4⋊C4×C107—21no—
122C4⋊C4×C107—21no—
123C4⋊C4×C107—21no—
124C4⋊C4×C107—41no—
125C4⋊C4×C107—41no—
126C4⋊C4×C107C22⋊C412yes—
127C22⋊C4×C107—22no—
128C22⋊C4×C107—22no—
129C42×C107—41no—
130C42×C107—41no—
131C42×C107C2×D411yescharacteristic
132C42×C107C2×D411yescharacteristic
133C42×C107C2×D411yescharacteristic
134C42×C107#4111yescharacteristic
135C23×C107—22no—
136C23×C107—41no—
137C23×C107—41no—
138C23×C107—41no—
139C23×C107—41no—
140C23×C107—41no—
141C23×C107—41no—
142C23×C107C4×D411yescharacteristic
143Q8×C107—22no—
144Q8×C107—22no—
145Q8×C107—41no—
146Q8×C107—41no—
147D4×C107—22no—
148D4×C107—22no—
149D4×C107—41no—
150D4×C107—41no—
151C2×C4×C107—21no—
152C2×C4×C107—21no—
153C2×C4×C107—22no—
154C2×C4×C107—22no—
155C2×C4×C107—41no—
156C2×C4×C107—41no—
157C2×C4×C107—41no—
158C2×C4×C107—41no—
159C2×C4×C107—42no—
160C2×C4×C107—42no—
161C2×C4×C107—42no—
162C2×C4×C107—42no—
163C2×C4×C107—41no—
164C2×C4×C107—41no—
165C2×C4×C107—41no—
166C2×C4×C107C2×C22⋊C411yescharacteristic
167C2×C4×C107C4×D411yescharacteristic
168C2×C4×C107#12011yescharacteristic
169C2×C4×C107#12111yescharacteristic
170C2×C4×C107#12111yescharacteristic
171C2×C4×C107#12311yescharacteristic
172C2×C4×C107C2×M1611yescharacteristic
173C2×C4×C107C2×M1611yescharacteristic
174C2×C4×C107#13111yescharacteristic
175C2×C4×C107#13111yescharacteristic
176C2×C4×C107C2×SD1611yescharacteristic
177C2×C4×C107#13511yescharacteristic
178C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C107#13711yescharacteristic
180C8×C107—22no—
181C8×C107—22no—
182C8×C107—42no—
183C8×C107—41no—
184C8×C107—42no—
185C8×C107—41no—
186C8×C107—81no—
187C22×C107—42no—
188C22×C107—42no—
189C22×C107—42no—
190C22×C107—81no—
191C22×C107—81no—
192C22×C107—81no—
193C22×C107—81no—
194C22×C107#38611yescharacteristic
195C22×C107#43511yescharacteristic
196C22×C107#43611yescharacteristic
197C22×C107C4×SD1611yescharacteristic
198C22×C107#44011yescharacteristic
199C22×C107#44311yescharacteristic
200C22×C107#44411yescharacteristic
201C4×C107—21no—
202C4×C107—21no—
203C4×C107—42no—
204C4×C107—42no—
205C4×C107—81no—
206C4×C107#40711yescharacteristic
207C4×C107#40811yescharacteristic
208C4×C107#43511yescharacteristic
209C4×C107#43611yescharacteristic
210C4×C107#45011yescharacteristic
211C4×C107#45211yescharacteristic
212C4×C107#46111yescharacteristic
213C4×C107#46311yescharacteristic
214#8949C10711yesmaximal, characteristic, direct product factor, Sylow
215C2×C107—82no—
216C2×C107#158311yescharacteristic
217C2×C107#158811yescharacteristic
218C2×C107#159011yescharacteristic
219C2×C107#159211yescharacteristic
220C2×C107#187011yescharacteristic
221C2×C107#187611yescharacteristic
222C2×C107#187711yescharacteristic
223C2×C4×SD16C2×C10711yescharacteristic
224C2×#436C2×C10711yescharacteristic
225#1984C2×C10711yescharacteristic, complemented
226C2×Q8⋊C8C2×C10711yescharacteristic, complemented
227C2×D4⋊C8C2×C10711yescharacteristic
228#1277C2×C10711yescharacteristic, complemented
229#1273C2×C10711yescharacteristic, complemented
230C107#894911yescharacteristic, direct product factor, Sylow
231C22×SD16C4×C10711yescharacteristic
232C22×M16—21no—
233C2×C4×Q8C22×C10711yescharacteristic
234C2×C4×D4C22×C10711yescharacteristic
235C4×SD16—22no—
236C4×SD16—22no—
237#436—22no—
238#436—22no—
239C2×#106C4×C10711yescharacteristic
240C2×C4⋊C8C22×C10711yescharacteristic
241C2×C4⋊C8C22×C10711yescharacteristic
242C2×#103C4×C10711yescharacteristic
243C2×#102C4×C10711yescharacteristic
244C2×C22⋊C8—21no—
245C2×C4×C8C22×C10711yescharacteristic
246C2×C4×C8C22×C10711yescharacteristic
247C2×C4×C8C22×C10711yescharacteristic
248#336—21no—
249#336—21no—
250Q8⋊C8—22no—
251D4⋊C8—22no—
252C22×Q8C2×C4×C10711yescharacteristic
253C22×D4C2×C4×C10711yescharacteristic
254C23×C4—21no—
255C2×SD16—22no—
256C2×SD16—22no—
257C2×SD16—22no—
258C2×M16—24no—
259C2×M16—42no—
260C2×M16—42no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8C2×C4×C10711yescharacteristic
265C22×C8C2×C4×C10711yescharacteristic
266C22×C8D4×C10711yescharacteristic
267C22×C8D4×C10711yescharacteristic
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4D4×C10712yes—
275C4×D4D4×C10712yes—
276C2×C4⋊C4—21no—
277C2×C4⋊C4C2×C4×C10711yescharacteristic
278C2×C4⋊C4C2×C4×C10711yescharacteristic
279C2×C22⋊C4—21no—
280C2×C42—21no—
281C2×C42C23×C10711yescharacteristic
282#106—22no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8D4×C10712yes—
287#103—22no—
288#102—22no—
289C22⋊C8—24no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—21no—
296C24—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8M16×C10712yescomplemented
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4C22⋊C4×C10712yes—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C22×C4×C10711yescharacteristic
319C22×C4C2×D4×C10711yescharacteristic
320C22×C4#41×C10711yescharacteristic
321SD16—28no—
322M16—48no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8M16×C10712yescomplemented
343C2×C8SD16×C10712yescomplemented
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4C22⋊C4×C10712yes—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C42—41no—
353C42—41no—
354C42C2×D4×C10711yescharacteristic
355C42C2×D4×C10711yescharacteristic
356C42C2×D4×C10711yescharacteristic
357C42#41×C10711yescharacteristic
358C23—22no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C4×D4×C10711yescharacteristic
366Q8—22no—
367Q8—22no—
368Q8—41no—
369Q8—41no—
370D4—22no—
371D4—22no—
372D4—41no—
373D4—41no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4C2×C22⋊C4×C10711yescharacteristic
390C2×C4C4×D4×C10711yescharacteristic
391C2×C4#120×C10711yescharacteristic
392C2×C4#121×C10711yescharacteristic
393C2×C4#121×C10711yescharacteristic
394C2×C4#123×C10711yescharacteristic
395C2×C4C2×M16×C10711yescharacteristic
396C2×C4C2×M16×C10711yescharacteristic
397C2×C4#131×C10711yescharacteristic
398C2×C4#131×C10711yescharacteristic
399C2×C4C2×SD16×C10711yescharacteristic
400C2×C4#135×C10711yescharacteristic
401C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
402C2×C4#137×C10711yescharacteristic
403C8—22no—
404C8—22no—
405C8—42no—
406C8—41no—
407C8—42no—
408C8—41no—
409C8—81no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22#386×C10711yescharacteristic
418C22#435×C10711yescharacteristic
419C22#436×C10711yescharacteristic
420C22C4×SD16×C10711yescharacteristic
421C22#440×C10711yescharacteristic
422C22#443×C10711yescharacteristic
423C22#444×C10711yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—81no—
429C4#407×C10711yescharacteristic
430C4#408×C10711yescharacteristic
431C4#435×C10711yescharacteristic
432C4#436×C10711yescharacteristic
433C4#450×C10711yescharacteristic
434C4#452×C10711yescharacteristic
435C4#461×C10711yescharacteristic
436C4#463×C10711yescharacteristic
437C2—82no—
438C2C107×#158311yescharacteristic
439C2C107×#158811yescharacteristic
440C2C107×#159011yescharacteristic
441C2C107×#159211yescharacteristic
442C2C107×#187011yescharacteristic
443C2C107×#187611yescharacteristic
444C2C107×#187711yescharacteristic
subgroupG/H
centerC22×C4×C107C2×D4
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC23×C107C4×D4
prime radicalC22×D4×C107C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C107 ◁ C2×C4×C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1984C2semidirect
4. C2×Q8⋊C8×C107C2semidirect
6. C107×#1277C2semidirect
7. C107×#1273C2semidirect
79. C2×Q8×C107M16semidirect
119. C2×C8×C107M16semidirect
120. C2×C8×C107SD16semidirect
214. #8949C107direct (N × H)
225. #1984C2×C107semidirect
226. C2×Q8⋊C8C2×C107semidirect
228. #1277C2×C107semidirect
229. #1273C2×C107semidirect
230. C107#8949direct (N × H)
302. C2×Q8M16×C107semidirect
342. C2×C8M16×C107semidirect
343. C2×C8SD16×C107semidirect

Maximal subgroups

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

subgroupindex
C2×C4×SD16×C1072
C2×#436×C1072
C107×#19842
C2×Q8⋊C8×C1072
C2×D4⋊C8×C1072
C107×#12772
C107×#12732
#8949107