Finite Group Databasebeta

← C2×C107×#1458 #41043309

Subgroups — C2×C107×#1458 #41043309

Order 27392.

1390 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C107C211yesmaximal, characteristic
2C2×#431×C107C212yesmaximal, complemented
3C107×#1458C218yesmaximal, direct product factor
4C2×#324×C107C212yesmaximal, complemented
5C2×#323×C107C212yesmaximal
6C24×C4×C107C411yescharacteristic
7C2×#117×C107—22no—
8C2×#117×C107—24no—
9C2×#117×C107—22no—
10C2×#117×C107C414yes—
11C2×#117×C107C2214yes—
12C22×C4⋊C4×C107C411yescharacteristic
13C22×C4⋊C4×C107C2211yescharacteristic
14C22×C22⋊C4×C107C411yescharacteristic
15C22×C22⋊C4×C107C2211yescharacteristic
16C22×C42×C107C411yescharacteristic
17C22×C42×C107C2211yescharacteristic
18#431×C107—24no—
19#431×C107C2218yescomplemented
20C2×C4⋊C8×C107—22no—
21C2×C22⋊C8×C107C2214yes—
22C2×C4×C8×C107—22no—
23#324×C107C2218yescomplemented
24#323×C107C2218yes—
25C25×C107C2×C411yescharacteristic
26C23×C4×C107—22no—
27C23×C4×C107—21no—
28C23×C4×C107—21no—
29C23×C4×C107—24no—
30C23×C4×C107C818yescomplemented
31C23×C4×C107C2×C411yescharacteristic
32C23×C4×C107C2×C414yes—
33C23×C4×C107C2×C411yescharacteristic
34C23×C4×C107C2×C411yescharacteristic
35C23×C4×C107C2×C411yescharacteristic
36C23×C4×C107C2×C411yescharacteristic
37C23×C4×C107C2311yescharacteristic
38C22×C8×C107—24no—
39#117×C107—28no—
40#117×C107—28no—
41#117×C107—28no—
42#117×C107—28no—
43C2×C4⋊C4×C107—22no—
44C2×C4⋊C4×C107—22no—
45C2×C4⋊C4×C107—22no—
46C2×C4⋊C4×C107—22no—
47C2×C4⋊C4×C107C2×C414yes—
48C2×C4⋊C4×C107C2×C412yes—
49C2×C4⋊C4×C107C2312yes—
50C2×C22⋊C4×C107—22no—
51C2×C22⋊C4×C107—22no—
52C2×C22⋊C4×C107—22no—
53C2×C22⋊C4×C107—22no—
54C2×C22⋊C4×C107C2×C414yes—
55C2×C22⋊C4×C107C2×C412yes—
56C2×C22⋊C4×C107C2312yes—
57C2×C42×C107—21no—
58C2×C42×C107—22no—
59C2×C42×C107—21no—
60C2×C42×C107C2×C414yes—
61C2×C42×C107C2×C412yes—
62C2×C42×C107D412yes—
63C2×C42×C107D414yes—
64C2×C42×C107D412yes—
65C2×C42×C107C2312yes—
66C4⋊C8×C107—28no—
67C22⋊C8×C107—24no—
68C22⋊C8×C107C2318yes—
69C4×C8×C107—28no—
70C24×C107—21no—
71C24×C107—21no—
72C24×C107—22no—
73C24×C107—42no—
74C24×C107—42no—
75C24×C107C2×C814yes—
76C24×C107C22×C411yescharacteristic
77C24×C107C22×C412yes—
78C22×C4×C107—21no—
79C22×C4×C107—21no—
80C22×C4×C107—22no—
81C22×C4×C107—216no—
82C22×C4×C107—28no—
83C22×C4×C107—28no—
84C22×C4×C107—24no—
85C22×C4×C107—24no—
86C22×C4×C107—28no—
87C22×C4×C107—21no—
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—42no—
95C22×C4×C107C22⋊C412yes—
96C22×C4×C107C22⋊C412yes—
97C22×C4×C107C22⋊C411yescharacteristic
98C22×C4×C107C22⋊C412yes—
99C22×C4×C107C22⋊C411yescharacteristic
100C22×C4×C107C2×C814yes—
101C22×C4×C107C2×C814yes—
102C22×C4×C107C2×C8116yescomplemented
103C22×C4×C107M1614yes—
104C22×C4×C107C22×C412yes—
105C22×C4×C107C22×C412yes—
106C22×C4×C107C22×C412yes—
107C22×C4×C107C22×C411yescharacteristic
108C22×C4×C107C22×C412yes—
109C22×C4×C107C22×C412yes—
110C22×C4×C107C2×D412yes—
111C22×C4×C107C2×D412yes—
112C22×C4×C107C2411yescharacteristic
113C2×C8×C107—28no—
114C2×C8×C107—48no—
115C4⋊C4×C107—24no—
116C4⋊C4×C107—28no—
117C4⋊C4×C107—24no—
118C22⋊C4×C107—24no—
119C22⋊C4×C107—28no—
120C22⋊C4×C107—24no—
121C42×C107—24no—
122C42×C107—24no—
123C42×C107C22⋊C414yes—
124C42×C107C22⋊C414yes—
125C42×C107C2×D414yes—
126C42×C107C2×D414yes—
127C23×C107—22no—
128C23×C107—22no—
129C23×C107—22no—
130C23×C107—22no—
131C23×C107—24no—
132C23×C107—24no—
133C23×C107—48no—
134C23×C107—42no—
135C23×C107—42no—
136C23×C107—42no—
137C23×C107—42no—
138C23×C107—48no—
139C23×C107—42no—
140C23×C107—42no—
141C23×C107C2×C22⋊C411yescharacteristic
142C23×C107C2×C22⋊C411yescharacteristic
143C23×C107C22×C812yes—
144C23×C107C22×C814yes—
145C23×C107C2×M1612yes—
146C23×C107C23×C411yescharacteristic
147C2×C4×C107—22no—
148C2×C4×C107—22no—
149C2×C4×C107—24no—
150C2×C4×C107—24no—
151C2×C4×C107—24no—
152C2×C4×C107—24no—
153C2×C4×C107—216no—
154C2×C4×C107—216no—
155C2×C4×C107—22no—
156C2×C4×C107—22no—
157C2×C4×C107—42no—
158C2×C4×C107—41no—
159C2×C4×C107—42no—
160C2×C4×C107—42no—
161C2×C4×C107—41no—
162C2×C4×C107—42no—
163C2×C4×C107—42no—
164C2×C4×C107—42no—
165C2×C4×C107—42no—
166C2×C4×C107—42no—
167C2×C4×C107—42no—
168C2×C4×C107C22⋊C818yes—
169C2×C4×C107C22⋊C814yes—
170C2×C4×C107C22⋊C814yes—
171C2×C4×C107C2×C22⋊C412yes—
172C2×C4×C107C2×C22⋊C414yes—
173C2×C4×C107C2×C22⋊C412yes—
174C2×C4×C107C2×C22⋊C412yes—
175C2×C4×C107C22×C814yes—
176C2×C4×C107C22×C814yes—
177C2×C4×C107C2×M1614yes—
178C2×C4×C107C22×D412yes—
179C8×C107—48no—
180C22×C107—21no—
181C22×C107—21no—
182C22×C107—21no—
183C22×C107—21no—
184C22×C107—24no—
185C22×C107—24no—
186C22×C107—24no—
187C22×C107—44no—
188C22×C107—44no—
189C22×C107—48no—
190C22×C107—42no—
191C22×C107—42no—
192C22×C107—48no—
193C22×C107C2×C22⋊C812yes—
194C22×C107C2×C22⋊C812yes—
195C22×C107#41012yes—
196C22×C107#41312yes—
197C22×C107C22×C22⋊C411yescharacteristic
198C22×C107C23×C811yescharacteristic
199C22×C107C22×M1611yescharacteristic
200C4×C107—24no—
201C4×C107—22no—
202C4×C107—22no—
203C4×C107—24no—
204C4×C107—42no—
205C4×C107—42no—
206C4×C107C2×C22⋊C814yes—
207C4×C107C2×C22⋊C814yes—
208C2×#1458C10711yesmaximal, characteristic, direct product factor, Sylow
209C2×C107—21no—
210C2×C107—21no—
211C2×C107—22no—
212C2×C107—44no—
213C2×C107#145814yesdirect product factor
214C2×C107C22×C22⋊C811yescharacteristic
215C2×C107C2×#41011yescharacteristic
216C2×C107C2×#41311yescharacteristic
217C22×#117C2×C10711yescharacteristic
218C2×#431C2×C10712yescomplemented
219#1458C2×C10718yesdirect product factor
220C2×#324C2×C10712yescomplemented
221C2×#323C2×C10712yes—
222C107C2×#145811yescharacteristic, direct product factor, Sylow
223C24×C4C4×C10711yescharacteristic
224C2×#117—22no—
225C2×#117—22no—
226C2×#117—24no—
227C2×#117C4×C10714yes—
228C2×#117C22×C10714yes—
229C22×C4⋊C4C4×C10711yescharacteristic
230C22×C4⋊C4C22×C10711yescharacteristic
231C22×C22⋊C4C4×C10711yescharacteristic
232C22×C22⋊C4C22×C10711yescharacteristic
233C22×C42C4×C10711yescharacteristic
234C22×C42C22×C10711yescharacteristic
235#431—24no—
236#431C22×C10718yescomplemented
237C2×C4⋊C8—22no—
238C2×C22⋊C8C22×C10714yes—
239C2×C4×C8—22no—
240#324C22×C10718yescomplemented
241#323C22×C10718yes—
242C25C2×C4×C10711yescharacteristic
243C23×C4—22no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—24no—
247C23×C4C8×C10718yescomplemented
248C23×C4C2×C4×C10711yescharacteristic
249C23×C4C2×C4×C10714yes—
250C23×C4C2×C4×C10711yescharacteristic
251C23×C4C2×C4×C10711yescharacteristic
252C23×C4C2×C4×C10711yescharacteristic
253C23×C4C2×C4×C10711yescharacteristic
254C23×C4C23×C10711yescharacteristic
255C22×C8—24no—
256#117—28no—
257#117—28no—
258#117—28no—
259#117—28no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4C2×C4×C10714yes—
265C2×C4⋊C4C2×C4×C10712yes—
266C2×C4⋊C4C23×C10712yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4C2×C4×C10714yes—
272C2×C22⋊C4C2×C4×C10712yes—
273C2×C22⋊C4C23×C10712yes—
274C2×C42—22no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42C2×C4×C10714yes—
278C2×C42C2×C4×C10712yes—
279C2×C42D4×C10712yes—
280C2×C42D4×C10712yes—
281C2×C42D4×C10714yes—
282C2×C42C23×C10712yes—
283C4⋊C8—28no—
284C22⋊C8—24no—
285C22⋊C8C23×C10718yes—
286C4×C8—28no—
287C24—21no—
288C24—21no—
289C24—22no—
290C24—42no—
291C24—42no—
292C24C2×C8×C10714yes—
293C24C22×C4×C10711yescharacteristic
294C24C22×C4×C10712yes—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—216no—
299C22×C4—28no—
300C22×C4—28no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—28no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4C22⋊C4×C10712yes—
313C22×C4C22⋊C4×C10712yes—
314C22×C4C22⋊C4×C10712yes—
315C22×C4C22⋊C4×C10711yescharacteristic
316C22×C4C22⋊C4×C10711yescharacteristic
317C22×C4C2×C8×C10714yes—
318C22×C4C2×C8×C10714yes—
319C22×C4C2×C8×C107116yescomplemented
320C22×C4M16×C10714yes—
321C22×C4C22×C4×C10712yes—
322C22×C4C22×C4×C10712yes—
323C22×C4C22×C4×C10712yes—
324C22×C4C22×C4×C10711yescharacteristic
325C22×C4C22×C4×C10712yes—
326C22×C4C22×C4×C10712yes—
327C22×C4C2×D4×C10712yes—
328C22×C4C2×D4×C10712yes—
329C22×C4C24×C10711yescharacteristic
330C2×C8—28no—
331C2×C8—48no—
332C4⋊C4—24no—
333C4⋊C4—28no—
334C4⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—28no—
337C22⋊C4—24no—
338C42—24no—
339C42—24no—
340C42C22⋊C4×C10714yes—
341C42C22⋊C4×C10714yes—
342C42C2×D4×C10714yes—
343C42C2×D4×C10714yes—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—24no—
348C23—22no—
349C23—22no—
350C23—48no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—48no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23C2×C22⋊C4×C10711yescharacteristic
359C23C2×C22⋊C4×C10711yescharacteristic
360C23C22×C8×C10712yes—
361C23C22×C8×C10714yes—
362C23C2×M16×C10712yes—
363C23C23×C4×C10711yescharacteristic
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—216no—
371C2×C4—216no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4C22⋊C8×C10718yes—
386C2×C4C22⋊C8×C10714yes—
387C2×C4C22⋊C8×C10714yes—
388C2×C4C2×C22⋊C4×C10712yes—
389C2×C4C2×C22⋊C4×C10714yes—
390C2×C4C2×C22⋊C4×C10712yes—
391C2×C4C2×C22⋊C4×C10712yes—
392C2×C4C22×C8×C10714yes—
393C2×C4C22×C8×C10714yes—
394C2×C4C2×M16×C10714yes—
395C2×C4C22×D4×C10712yes—
396C8—48no—
397C22—21no—
398C22—21no—
399C22—24no—
400C22—24no—
401C22—21no—
402C22—21no—
403C22—24no—
404C22—44no—
405C22—48no—
406C22—44no—
407C22—42no—
408C22—48no—
409C22—42no—
410C22C2×C22⋊C8×C10712yes—
411C22C2×C22⋊C8×C10712yes—
412C22#410×C10712yes—
413C22#413×C10712yes—
414C22C22×C22⋊C4×C10711yescharacteristic
415C22C23×C8×C10711yescharacteristic
416C22C22×M16×C10711yescharacteristic
417C4—24no—
418C4—24no—
419C4—22no—
420C4—22no—
421C4—42no—
422C4—42no—
423C4C2×C22⋊C8×C10714yes—
424C4C2×C22⋊C8×C10714yes—
425C2—22no—
426C2—21no—
427C2—21no—
428C2—44no—
429C2C107×#145814yesdirect product factor
430C2C22×C22⋊C8×C10711yescharacteristic
431C2C2×#410×C10711yescharacteristic
432C2C2×#413×C10711yescharacteristic
subgroupG/H
centerC22×C4×C107C22⋊C4
commutatorC22C23×C8×C107
Frattini, cosocleC22×C4C24×C107
socleC23×C107C2×C22⋊C4
prime radicalC25×C107C2×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C107 ◁ C22×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#431×C107C2semidirect
3. C107×#1458C2direct (N × H)
4. C2×#324×C107C2semidirect
19. #431×C107C22semidirect
23. #324×C107C22semidirect
30. C23×C4×C107C8semidirect
102. C22×C4×C107C2×C8semidirect
208. C2×#1458C107direct (N × H)
213. C2×C107#1458direct (N × H)
218. C2×#431C2×C107semidirect
219. #1458C2×C107direct (N × H)
220. C2×#324C2×C107semidirect
222. C107C2×#1458direct (N × H)
236. #431C22×C107semidirect
240. #324C22×C107semidirect
247. C23×C4C8×C107semidirect
319. C22×C4C2×C8×C107semidirect
429. C2C107×#1458direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#117×C1072
C2×#431×C1072
C107×#14582
C2×#324×C1072
C2×#323×C1072
C2×#1458107