Finite Group Databasebeta

← C107×#19228 #41045192

Subgroups — C107×#19228 #41045192

Order 27392.

584 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3248C212yesmaximal
2C107×#3170C211yesmaximal, characteristic, complemented
3C107×#2966C211yesmaximal, characteristic
4C107×#1694C211yesmaximal, characteristic, complemented
5C107×#1693C211yesmaximal, characteristic, complemented
6C107×#1690C211yesmaximal, characteristic, complemented
7C107×#1689C211yesmaximal, characteristic, complemented
8C107×#1680C212yesmaximal, complemented
9C107×#1679C212yesmaximal, complemented
10C2×#334×C107C211yesmaximal, characteristic, complemented
11C107×#1552C212yesmaximal, complemented
12#533×C107C2212yes—
13#529×C107C2211yescharacteristic
14#500×C107C2211yescharacteristic
15#494×C107C2211yescharacteristic
16#487×C107C2212yes—
17#479×C107—22no—
18#475×C107C2212yes—
19#474×C107C2212yes—
20#467×C107—21no—
21#467×C107—21no—
22#467×C107—22no—
23#465×C107—22no—
24#464×C107—22no—
25#462×C107C2212yes—
26#461×C107C2212yes—
27#446×C107C2211yescharacteristic
28C8×Q8×C107C2211yescharacteristic
29C4×Q16×C107—21no—
30C4×Q16×C107—21no—
31#436×C107C2211yescharacteristic
32#435×C107—21no—
33C8×D4×C107—21no—
34C8×D4×C107C2211yescharacteristic
35#433×C107—21no—
36#432×C107C2211yescharacteristic
37C2×C4⋊C8×C107C2212yes—
38#405×C107—21no—
39C2×C4×C8×C107C2211yescharacteristic
40#334×C107C2212yes—
41#334×C107C2211yescharacteristic
42#334×C107C2211yescharacteristic
43#332×C107C2212yes—
44#332×C107C2212yes—
45#332×C107C2212yes—
46#332×C107C2212yes—
47C2×Q16×C107—22no—
48C2×Q16×C107—21no—
49C2×Q16×C107—21no—
50C2×SD16×C107—22no—
51C2×M16×C107—21no—
52C22×C8×C107—22no—
53C22×C8×C107—21no—
54C22×C8×C107D411yescharacteristic
55C22×C8×C107D411yescharacteristic
56C4⋊Q8×C107C2312yes—
57C4⋊Q8×C107C2312yes—
58#126×C107—21no—
59#125×C107—22no—
60#125×C107D411yescharacteristic
61#124×C107D411yescharacteristic
62#123×C107—21no—
63C22⋊Q8×C107—22no—
64C22⋊Q8×C107—22no—
65C22⋊Q8×C107D411yescharacteristic
66#121×C107D411yescharacteristic
67C4×Q8×C107—22no—
68C4×Q8×C107—22no—
69C4×Q8×C107C2311yescharacteristic
70C4×D4×C107—21no—
71C4×D4×C107C2311yescharacteristic
72#117×C107—21no—
73#117×C107—22no—
74C2×C42×C107C2311yescharacteristic
75#107×C107—21no—
76#107×C107—21no—
77#107×C107—22no—
78#106×C107—22no—
79C4⋊C8×C107—21no—
80C4⋊C8×C107—21no—
81C4⋊C8×C107—22no—
82C4⋊C8×C107C2312yes—
83C4⋊C8×C107C2312yes—
84C4⋊C8×C107C2311yescharacteristic
85C4⋊C8×C107C2311yescharacteristic
86#103×C107—22no—
87#103×C107—22no—
88#103×C107—22no—
89#103×C107—22no—
90#103×C107—22no—
91#102×C107—22no—
92C22⋊C8×C107—21no—
93C22⋊C8×C107—21no—
94C22⋊C8×C107—21no—
95#97×C107—21no—
96#97×C107—21no—
97C4×C8×C107—21no—
98C4×C8×C107D411yescharacteristic
99C4×C8×C107D411yescharacteristic
100C4×C8×C107C2311yescharacteristic
101C4×C8×C107C2311yescharacteristic
102C2×Q8×C107—22no—
103C2×Q8×C107—22no—
104C2×Q8×C107C2×D411yescharacteristic
105C2×D4×C107—21no—
106C2×D4×C107C2×D411yescharacteristic
107C22×C4×C107—21no—
108C22×C4×C107C2×D411yescharacteristic
109C22×C4×C107C2×D411yescharacteristic
110C22×C4×C107#4111yescharacteristic
111Q16×C107—42no—
112Q16×C107—42no—
113Q16×C107—82no—
114SD16×C107—82no—
115M16×C107—42no—
116C2×C8×C107—22no—
117C2×C8×C107—21no—
118C2×C8×C107—21no—
119C2×C8×C107—22no—
120C2×C8×C107—22no—
121C2×C8×C107—41no—
122C2×C8×C107—42no—
123C2×C8×C107—82no—
124C2×C8×C107C2×D411yescharacteristic
125C2×C8×C107C2×D411yescharacteristic
126C2×C8×C107C2×D411yescharacteristic
127C2×C8×C107C2×D411yescharacteristic
128C4⋊C4×C107—21no—
129C4⋊C4×C107—21no—
130C4⋊C4×C107—21no—
131C4⋊C4×C107—21no—
132C4⋊C4×C107—22no—
133C4⋊C4×C107—22no—
134C4⋊C4×C107—22no—
135C4⋊C4×C107—22no—
136C4⋊C4×C107—42no—
137C4⋊C4×C107—42no—
138C4⋊C4×C107C2×D411yescharacteristic
139C4⋊C4×C107C2×D411yescharacteristic
140C22⋊C4×C107—21no—
141C22⋊C4×C107—21no—
142C22⋊C4×C107—21no—
143C22⋊C4×C107—21no—
144C22⋊C4×C107—21no—
145C22⋊C4×C107—42no—
146C42×C107—21no—
147C42×C107—42no—
148C42×C107C2×D411yescharacteristic
149C42×C107C2×D411yescharacteristic
150C42×C107#4111yescharacteristic
151C42×C107C2411yescharacteristic
152C23×C107—21no—
153C23×C107#12111yescharacteristic
154Q8×C107—22no—
155Q8×C107—42no—
156Q8×C107—42no—
157Q8×C107—42no—
158Q8×C107—42no—
159D4×C107—22no—
160D4×C107—42no—
161C2×C4×C107—22no—
162C2×C4×C107—21no—
163C2×C4×C107—21no—
164C2×C4×C107—22no—
165C2×C4×C107—21no—
166C2×C4×C107—21no—
167C2×C4×C107—21no—
168C2×C4×C107—41no—
169C2×C4×C107—41no—
170C2×C4×C107—42no—
171C2×C4×C107—42no—
172C2×C4×C107#12111yescharacteristic
173C2×C4×C107#12111yescharacteristic
174C2×C4×C107#12111yescharacteristic
175C2×C4×C107C22×D411yescharacteristic
176C2×C4×C107C22×D411yescharacteristic
177C2×C4×C107C2×#4111yescharacteristic
178C8×C107—21no—
179C8×C107—21no—
180C8×C107—21no—
181C8×C107—41no—
182C8×C107—41no—
183C8×C107—42no—
184C8×C107—42no—
185C8×C107#13512yes—
186C22×C107—21no—
187C22×C107—21no—
188C22×C107—41no—
189C22×C107—41no—
190C22×C107—41no—
191C22×C107#47312yes—
192C22×C107C2×#12111yescharacteristic
193C4×C107—21no—
194C4×C107—21no—
195C4×C107—21no—
196C4×C107—21no—
197C4×C107—41no—
198C4×C107—41no—
199C4×C107—41no—
200C4×C107—82no—
201C4×C107—82no—
202C4×C107C2×#13511yescharacteristic
203C4×C107#57511yescharacteristic
204C4×C107#57712yes—
205#19228C10711yesmaximal, characteristic, direct product factor, Sylow
206C2×C107—22no—
207C2×C107—81no—
208C2×C107#303511yescharacteristic
209C2×C107#306011yescharacteristic
210C2×C107C2×#47311yescharacteristic
211#3248C2×C10712yes—
212#3170C2×C10711yescharacteristic, complemented
213#2966C2×C10711yescharacteristic
214#1694C2×C10711yescharacteristic, complemented
215#1693C2×C10711yescharacteristic, complemented
216#1690C2×C10711yescharacteristic, complemented
217#1689C2×C10711yescharacteristic, complemented
218#1680C2×C10712yescomplemented
219#1679C2×C10712yescomplemented
220C2×#334C2×C10711yescharacteristic, complemented
221#1552C2×C10712yescomplemented
222C107#1922811yescharacteristic, direct product factor, Sylow
223#533C22×C10712yes—
224#529C22×C10711yescharacteristic
225#500C22×C10711yescharacteristic
226#494C22×C10711yescharacteristic
227#487C22×C10712yes—
228#479—22no—
229#475C22×C10712yes—
230#474C22×C10712yes—
231#467—21no—
232#467—21no—
233#467—22no—
234#465—22no—
235#464—22no—
236#462C22×C10712yes—
237#461C22×C10712yes—
238#446C22×C10711yescharacteristic
239C8×Q8C22×C10711yescharacteristic
240C4×Q16—21no—
241C4×Q16—21no—
242#436C22×C10711yescharacteristic
243#435—21no—
244C8×D4—21no—
245C8×D4C22×C10711yescharacteristic
246#433—21no—
247#432C22×C10711yescharacteristic
248C2×C4⋊C8C22×C10712yes—
249#405—21no—
250C2×C4×C8C22×C10711yescharacteristic
251#334C22×C10712yes—
252#334C22×C10711yescharacteristic
253#334C22×C10711yescharacteristic
254#332C22×C10712yes—
255#332C22×C10712yes—
256#332C22×C10712yes—
257#332C22×C10712yes—
258C2×Q16—22no—
259C2×Q16—21no—
260C2×Q16—21no—
261C2×SD16—22no—
262C2×M16—21no—
263C22×C8—22no—
264C22×C8—21no—
265C22×C8D4×C10711yescharacteristic
266C22×C8D4×C10711yescharacteristic
267C4⋊Q8C23×C10712yes—
268C4⋊Q8C23×C10712yes—
269#126—21no—
270#125—22no—
271#125D4×C10711yescharacteristic
272#124D4×C10711yescharacteristic
273#123—21no—
274C22⋊Q8—22no—
275C22⋊Q8—22no—
276C22⋊Q8D4×C10711yescharacteristic
277#121D4×C10711yescharacteristic
278C4×Q8—22no—
279C4×Q8—22no—
280C4×Q8C23×C10711yescharacteristic
281C4×D4—21no—
282C4×D4C23×C10711yescharacteristic
283#117—21no—
284#117—22no—
285C2×C42C23×C10711yescharacteristic
286#107—21no—
287#107—21no—
288#107—22no—
289#106—22no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—22no—
293C4⋊C8C23×C10711yescharacteristic
294C4⋊C8C23×C10711yescharacteristic
295C4⋊C8C23×C10712yes—
296C4⋊C8C23×C10712yes—
297#103—22no—
298#103—22no—
299#103—22no—
300#103—22no—
301#103—22no—
302#102—22no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306#97—21no—
307#97—21no—
308C4×C8—21no—
309C4×C8D4×C10711yescharacteristic
310C4×C8D4×C10711yescharacteristic
311C4×C8C23×C10711yescharacteristic
312C4×C8C23×C10711yescharacteristic
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8C2×D4×C10711yescharacteristic
316C2×D4—21no—
317C2×D4C2×D4×C10711yescharacteristic
318C22×C4—21no—
319C22×C4C2×D4×C10711yescharacteristic
320C22×C4C2×D4×C10711yescharacteristic
321C22×C4#41×C10711yescharacteristic
322Q16—42no—
323Q16—42no—
324Q16—82no—
325SD16—82no—
326M16—42no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—42no—
334C2×C8—82no—
335C2×C8C2×D4×C10711yescharacteristic
336C2×C8C2×D4×C10711yescharacteristic
337C2×C8C2×D4×C10711yescharacteristic
338C2×C8C2×D4×C10711yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4C2×D4×C10711yescharacteristic
350C4⋊C4C2×D4×C10711yescharacteristic
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—42no—
357C42—21no—
358C42—42no—
359C42C2×D4×C10711yescharacteristic
360C42C2×D4×C10711yescharacteristic
361C42#41×C10711yescharacteristic
362C42C24×C10711yescharacteristic
363C23—21no—
364C23#121×C10711yescharacteristic
365Q8—22no—
366Q8—42no—
367Q8—42no—
368Q8—42no—
369Q8—42no—
370D4—22no—
371D4—42no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4#121×C10711yescharacteristic
384C2×C4#121×C10711yescharacteristic
385C2×C4#121×C10711yescharacteristic
386C2×C4C22×D4×C10711yescharacteristic
387C2×C4C22×D4×C10711yescharacteristic
388C2×C4C2×#41×C10711yescharacteristic
389C8—21no—
390C8—21no—
391C8—21no—
392C8—41no—
393C8—41no—
394C8—42no—
395C8—42no—
396C8#135×C10712yes—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22#473×C10712yes—
403C22C2×#121×C10711yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—82no—
412C4—82no—
413C4C2×#135×C10711yescharacteristic
414C4#575×C10711yescharacteristic
415C4#577×C10712yes—
416C2—22no—
417C2—81no—
418C2C107×#303511yescharacteristic
419C2C107×#306011yescharacteristic
420C2C2×#473×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#121
commutator, Frattini, cosocleC42C24×C107
prime radical#121×C107D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3170C2semidirect
4. C107×#1694C2semidirect
5. C107×#1693C2semidirect
6. C107×#1690C2semidirect
7. C107×#1689C2semidirect
8. C107×#1680C2semidirect
9. C107×#1679C2semidirect
10. C2×#334×C107C2semidirect
11. C107×#1552C2semidirect
205. #19228C107direct (N × H)
212. #3170C2×C107semidirect
214. #1694C2×C107semidirect
215. #1693C2×C107semidirect
216. #1690C2×C107semidirect
217. #1689C2×C107semidirect
218. #1680C2×C107semidirect
219. #1679C2×C107semidirect
220. C2×#334C2×C107semidirect
221. #1552C2×C107semidirect
222. C107#19228direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32482
C107×#31702
C107×#29662
C107×#16942
C107×#16932
C107×#16902
C107×#16892
C107×#16802
C107×#16792
C2×#334×C1072
C107×#15522
#19228107