Finite Group Databasebeta

← C107×#8981 #41034945

Subgroups — C107×#8981 #41034945

Order 27392.

664 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C107C211yesmaximal, characteristic
2D4×C4⋊C4×C107C211yesmaximal, characteristic
3C107×#1990C211yesmaximal, characteristic, complemented
4C107×#1981C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C107C211yesmaximal, characteristic
6C107×#1296C211yesmaximal, characteristic, complemented
7C107×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C107C2211yescharacteristic
9C2×C4×D4×C107—21no—
10C2×C4×D4×C107C2211yescharacteristic
11C22×C4⋊C4×C107—21no—
12#474×C107—22no—
13#474×C107C414yescomplemented
14C2×#107×C107—21no—
15C2×C4⋊C8×C107C2211yescharacteristic
16C2×C4⋊C8×C107C2211yescharacteristic
17C2×#103×C107—21no—
18C2×#103×C107—21no—
19C2×#102×C107—21no—
20C2×C4×C8×C107C2211yescharacteristic
21#389×C107—21no—
22#385×C107—22no—
23#384×C107C2211yescharacteristic
24#380×C107—21no—
25C4×C4⋊C4×C107C2211yescharacteristic
26#340×C107—22no—
27D4⋊C8×C107—22no—
28C22×Q8×C107—21no—
29C22×D4×C107D411yescharacteristic
30C23×C4×C107—21no—
31C23×C4×C107—22no—
32C22×C8×C107—21no—
33C22×C8×C107—21no—
34C22×C8×C107—21no—
35C4⋊Q8×C107—21no—
36C4⋊Q8×C107—21no—
37C4⋊Q8×C107—21no—
38C4⋊Q8×C107C2×C412yescomplemented
39C4×D4×C107—21no—
40C4×D4×C107—21no—
41C4×D4×C107—42no—
42C4×D4×C107—42no—
43C4×D4×C107C2×C412yes—
44C4×D4×C107D412yes—
45C2×C4⋊C4×C107—21no—
46C2×C4⋊C4×C107—21no—
47C2×C4⋊C4×C107—22no—
48C2×C4⋊C4×C107—21no—
49C2×C4⋊C4×C107—21no—
50C2×C4⋊C4×C107—42no—
51C2×C4⋊C4×C107—42no—
52C2×C4⋊C4×C107D411yescharacteristic
53C2×C4⋊C4×C107D411yescharacteristic
54C2×C4⋊C4×C107D411yescharacteristic
55C2×C4⋊C4×C107D412yes—
56C2×C22⋊C4×C107—21no—
57C2×C22⋊C4×C107—22no—
58C2×C42×C107—21no—
59C2×C42×C107C2311yescharacteristic
60#107×C107—24no—
61C4⋊C8×C107—21no—
62C4⋊C8×C107—21no—
63C4⋊C8×C107—21no—
64C4⋊C8×C107C2×C412yescomplemented
65#103×C107—42no—
66#103×C107—42no—
67#102×C107—24no—
68C4×C8×C107—21no—
69C4×C8×C107—21no—
70#95×C107—22no—
71#95×C107—21no—
72C24×C107—21no—
73C2×Q8×C107—22no—
74C2×Q8×C107—41no—
75C2×Q8×C107—41no—
76C2×Q8×C107—41no—
77C2×Q8×C107—41no—
78C2×Q8×C107—41no—
79C2×D4×C107—21no—
80C2×D4×C107—21no—
81C2×D4×C107—21no—
82C2×D4×C107C22⋊C412yes—
83C2×D4×C107SD1612yes—
84C2×D4×C107Q1612yes—
85C22×C4×C107—21no—
86C22×C4×C107—21no—
87C22×C4×C107—22no—
88C22×C4×C107—22no—
89C22×C4×C107—21no—
90C22×C4×C107—22no—
91C22×C4×C107—44no—
92C22×C4×C107—41no—
93C22×C4×C107—41no—
94C22×C4×C107—41no—
95C22×C4×C107—41no—
96C22×C4×C107—44no—
97C22×C4×C107—41no—
98C22×C4×C107—82no—
99C22×C4×C107C2×D411yescharacteristic
100C22×C4×C107C2×D411yescharacteristic
101C22×C4×C107C2×D411yescharacteristic
102C2×C8×C107—22no—
103C2×C8×C107—22no—
104C2×C8×C107—41no—
105C2×C8×C107—41no—
106C2×C8×C107—41no—
107C2×C8×C107—41no—
108C2×C8×C107—41no—
109C2×C8×C107—41no—
110C2×C8×C107—41no—
111C4⋊C4×C107—21no—
112C4⋊C4×C107—21no—
113C4⋊C4×C107—22no—
114C4⋊C4×C107—22no—
115C4⋊C4×C107—21no—
116C4⋊C4×C107—21no—
117C4⋊C4×C107—42no—
118C4⋊C4×C107—44no—
119C4⋊C4×C107—41no—
120C4⋊C4×C107—41no—
121C4⋊C4×C107—41no—
122C4⋊C4×C107—41no—
123C4⋊C4×C107—41no—
124C4⋊C4×C107—41no—
125C4⋊C4×C107C22⋊C412yes—
126C4⋊C4×C107D812yes—
127C22⋊C4×C107—22no—
128C22⋊C4×C107—22no—
129C22⋊C4×C107—44no—
130C42×C107—41no—
131C42×C107—41no—
132C42×C107C22×C411yescharacteristic
133C42×C107C2×D411yescharacteristic
134C42×C107#4111yescharacteristic
135C42×C107#4111yescharacteristic
136C23×C107—22no—
137C23×C107—22no—
138C23×C107—22no—
139C23×C107—41no—
140C23×C107—41no—
141C23×C107—41no—
142C23×C107—41no—
143C23×C107#12011yescharacteristic
144Q8×C107—42no—
145Q8×C107—42no—
146Q8×C107—81no—
147Q8×C107—81no—
148D4×C107—22no—
149D4×C107—22no—
150D4×C107—22no—
151D4×C107#10314yescomplemented
152C2×C4×C107—21no—
153C2×C4×C107—21no—
154C2×C4×C107—22no—
155C2×C4×C107—22no—
156C2×C4×C107—41no—
157C2×C4×C107—41no—
158C2×C4×C107—41no—
159C2×C4×C107—41no—
160C2×C4×C107—42no—
161C2×C4×C107—42no—
162C2×C4×C107—42no—
163C2×C4×C107—42no—
164C2×C4×C107—42no—
165C2×C4×C107—42no—
166C2×C4×C107—41no—
167C2×C4×C107—41no—
168C2×C4×C107—42no—
169C2×C4×C107—42no—
170C2×C4×C107—41no—
171C2×C4×C107—88no—
172C2×C4×C107—81no—
173C2×C4×C107—81no—
174C2×C4×C107C2×C22⋊C411yescharacteristic
175C2×C4×C107C4×D411yescharacteristic
176C2×C4×C107C4×D411yescharacteristic
177C2×C4×C107#12111yescharacteristic
178C2×C4×C107#12111yescharacteristic
179C2×C4×C107#12311yescharacteristic
180C2×C4×C107C2×D811yescharacteristic
181C2×C4×C107C2×SD1611yescharacteristic
182C2×C4×C107C2×Q1611yescharacteristic
183C2×C4×C107#13511yescharacteristic
184C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C107#13711yescharacteristic
188C8×C107—42no—
189C8×C107—42no—
190C8×C107—81no—
191C22×C107—24no—
192C22×C107—42no—
193C22×C107—42no—
194C22×C107—42no—
195C22×C107—42no—
196C22×C107—42no—
197C22×C107—42no—
198C22×C107#38611yescharacteristic
199C22×C107#44711yescharacteristic
200C22×C107#44911yescharacteristic
201C22×C107#45011yescharacteristic
202C22×C107#45111yescharacteristic
203C22×C107#45511yescharacteristic
204C22×C107#45611yescharacteristic
205C4×C107—21no—
206C4×C107—21no—
207C4×C107—42no—
208C4×C107—42no—
209C4×C107—82no—
210C4×C107—82no—
211C4×C107—81no—
212C4×C107C2×#10311yescharacteristic
213C4×C107#41711yescharacteristic
214C4×C107C4×D811yescharacteristic
215C4×C107#44211yescharacteristic
216C4×C107#45911yescharacteristic
217C4×C107#46311yescharacteristic
218C4×C107#48311yescharacteristic
219C4×C107#48411yescharacteristic
220#8981C10711yesmaximal, characteristic, direct product factor, Sylow
221C2×C107—44no—
222C2×C107#163911yescharacteristic
223C2×C107#164411yescharacteristic
224C2×C107#164911yescharacteristic
225C2×C107#165411yescharacteristic
226C2×C107#187211yescharacteristic
227C2×C107#187911yescharacteristic
228C2×C107#188211yescharacteristic
229C2×#474C2×C10711yescharacteristic
230D4×C4⋊C4C2×C10711yescharacteristic
231#1990C2×C10711yescharacteristic, complemented
232#1981C2×C10711yescharacteristic, complemented
233C2×D4⋊C8C2×C10711yescharacteristic
234#1296C2×C10711yescharacteristic, complemented
235#1279C2×C10711yescharacteristic, complemented
236C107#898111yescharacteristic, direct product factor, Sylow
237C2×C4⋊Q8C22×C10711yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4C22×C10711yescharacteristic
240C22×C4⋊C4—21no—
241#474—22no—
242#474C4×C10714yescomplemented
243C2×#107—21no—
244C2×C4⋊C8C22×C10711yescharacteristic
245C2×C4⋊C8C22×C10711yescharacteristic
246C2×#103—21no—
247C2×#103—21no—
248C2×#102—21no—
249C2×C4×C8C22×C10711yescharacteristic
250#389—21no—
251#385—22no—
252#384C22×C10711yescharacteristic
253#380—21no—
254C4×C4⋊C4C22×C10711yescharacteristic
255#340—22no—
256D4⋊C8—22no—
257C22×Q8—21no—
258C22×D4D4×C10711yescharacteristic
259C23×C4—21no—
260C23×C4—22no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8C2×C4×C10712yescomplemented
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—42no—
271C4×D4—42no—
272C4×D4C2×C4×C10712yes—
273C4×D4D4×C10712yes—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4D4×C10711yescharacteristic
282C2×C4⋊C4D4×C10711yescharacteristic
283C2×C4⋊C4D4×C10711yescharacteristic
284C2×C4⋊C4D4×C10712yes—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—22no—
287C2×C42—21no—
288C2×C42C23×C10711yescharacteristic
289#107—24no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8C2×C4×C10712yescomplemented
294#103—42no—
295#103—42no—
296#102—24no—
297C4×C8—21no—
298C4×C8—21no—
299#95—22no—
300#95—21no—
301C24—21no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4C22⋊C4×C10712yes—
312C2×D4SD16×C10712yes—
313C2×D4Q16×C10712yes—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—44no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—44no—
326C22×C4—41no—
327C22×C4—82no—
328C22×C4C2×D4×C10711yescharacteristic
329C22×C4C2×D4×C10711yescharacteristic
330C22×C4C2×D4×C10711yescharacteristic
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—42no—
347C4⋊C4—44no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4C22⋊C4×C10712yes—
355C4⋊C4D8×C10712yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—44no—
359C42—41no—
360C42—41no—
361C42C22×C4×C10711yescharacteristic
362C42C2×D4×C10711yescharacteristic
363C42#41×C10711yescharacteristic
364C42#41×C10711yescharacteristic
365C23—22no—
366C23—22no—
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23#120×C10711yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—81no—
376Q8—81no—
377D4—22no—
378D4—22no—
379D4—22no—
380D4#103×C10714yescomplemented
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—88no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4C2×C22⋊C4×C10711yescharacteristic
404C2×C4C4×D4×C10711yescharacteristic
405C2×C4C4×D4×C10711yescharacteristic
406C2×C4#121×C10711yescharacteristic
407C2×C4#121×C10711yescharacteristic
408C2×C4#123×C10711yescharacteristic
409C2×C4C2×D8×C10711yescharacteristic
410C2×C4C2×SD16×C10711yescharacteristic
411C2×C4C2×Q16×C10711yescharacteristic
412C2×C4#135×C10711yescharacteristic
413C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
414C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
415C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
416C2×C4#137×C10711yescharacteristic
417C8—42no—
418C8—42no—
419C8—81no—
420C22—24no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22#386×C10711yescharacteristic
428C22#447×C10711yescharacteristic
429C22#449×C10711yescharacteristic
430C22#450×C10711yescharacteristic
431C22#451×C10711yescharacteristic
432C22#455×C10711yescharacteristic
433C22#456×C10711yescharacteristic
434C4—21no—
435C4—21no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4—82no—
440C4—81no—
441C4C2×#103×C10711yescharacteristic
442C4#417×C10711yescharacteristic
443C4C4×D8×C10711yescharacteristic
444C4#442×C10711yescharacteristic
445C4#459×C10711yescharacteristic
446C4#463×C10711yescharacteristic
447C4#483×C10711yescharacteristic
448C4#484×C10711yescharacteristic
449C2—44no—
450C2C107×#163911yescharacteristic
451C2C107×#164411yescharacteristic
452C2C107×#164911yescharacteristic
453C2C107×#165411yescharacteristic
454C2C107×#187211yescharacteristic
455C2C107×#187911yescharacteristic
456C2C107×#188211yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1990C2semidirect
4. C107×#1981C2semidirect
6. C107×#1296C2semidirect
7. C107×#1279C2semidirect
13. #474×C107C4semidirect
38. C4⋊Q8×C107C2×C4semidirect
64. C4⋊C8×C107C2×C4semidirect
151. D4×C107#103semidirect
220. #8981C107direct (N × H)
231. #1990C2×C107semidirect
232. #1981C2×C107semidirect
234. #1296C2×C107semidirect
235. #1279C2×C107semidirect
236. C107#8981direct (N × H)
242. #474C4×C107semidirect
267. C4⋊Q8C2×C4×C107semidirect
293. C4⋊C8C2×C4×C107semidirect
380. D4#103×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1072
D4×C4⋊C4×C1072
C107×#19902
C107×#19812
C2×D4⋊C8×C1072
C107×#12962
C107×#12792
#8981107