Finite Group Databasebeta

← C107×#8559 #41034523

Subgroups — C107×#8559 #41034523

Order 27392.

898 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
1C2×C4×C22⋊C4×C107C211yesmaximal, characteristic
2C107×#1797C212yesmaximal, complemented
3C2×#323×C107C212yesmaximal
4C107×#1280C212yesmaximal, complemented
5C24×C4×C107C411yescharacteristic
6C22×C22⋊C4×C107C411yescharacteristic
7C22×C22⋊C4×C107C2211yescharacteristic
8C22×C42×C107C411yescharacteristic
9C22×C42×C107C2211yescharacteristic
10C2×C4⋊C8×C107—22no—
11C2×C22⋊C8×C107C2214yes—
12C4×C22⋊C4×C107—22no—
13C4×C22⋊C4×C107—22no—
14C2×#95×C107C411yescharacteristic
15C2×#95×C107C2211yescharacteristic
16#336×C107—22no—
17#323×C107—24no—
18C25×C107C2×C411yescharacteristic
19C23×C4×C107—22no—
20C23×C4×C107—21no—
21C23×C4×C107—21no—
22C23×C4×C107—22no—
23C23×C4×C107—42no—
24C23×C4×C107—42no—
25C23×C4×C107C2×C411yescharacteristic
26C23×C4×C107C2×C411yescharacteristic
27C23×C4×C107C2×C411yescharacteristic
28C23×C4×C107C2×C411yescharacteristic
29C23×C4×C107C2×C411yescharacteristic
30C23×C4×C107C2311yescharacteristic
31C22×C8×C107—24no—
32C2×C22⋊C4×C107—22no—
33C2×C22⋊C4×C107—22no—
34C2×C22⋊C4×C107—22no—
35C2×C22⋊C4×C107—22no—
36C2×C22⋊C4×C107C814yescomplemented
37C2×C22⋊C4×C107D412yes—
38C2×C22⋊C4×C107Q812yes—
39C2×C42×C107—21no—
40C2×C42×C107—21no—
41C2×C42×C107—42no—
42C2×C42×C107—42no—
43C2×C42×C107D412yes—
44C2×C42×C107D412yes—
45C4⋊C8×C107—44no—
46C22⋊C8×C107—24no—
47C22⋊C8×C107—24no—
48#95×C107—22no—
49#95×C107—22no—
50C24×C107—21no—
51C24×C107—21no—
52C24×C107—21no—
53C24×C107—21no—
54C24×C107—41no—
55C24×C107—41no—
56C24×C107—41no—
57C24×C107—41no—
58C24×C107C4⋊C412yes—
59C24×C107C2×C812yes—
60C24×C107M1612yes—
61C24×C107C22×C411yescharacteristic
62C22×C4×C107—21no—
63C22×C4×C107—21no—
64C22×C4×C107—22no—
65C22×C4×C107—22no—
66C22×C4×C107—24no—
67C22×C4×C107—24no—
68C22×C4×C107—21no—
69C22×C4×C107—21no—
70C22×C4×C107—21no—
71C22×C4×C107—21no—
72C22×C4×C107—21no—
73C22×C4×C107—21no—
74C22×C4×C107—41no—
75C22×C4×C107—41no—
76C22×C4×C107—41no—
77C22×C4×C107—41no—
78C22×C4×C107—48no—
79C22×C4×C107—48no—
80C22×C4×C107—42no—
81C22×C4×C107—42no—
82C22×C4×C107—42no—
83C22×C4×C107—42no—
84C22×C4×C107—41no—
85C22×C4×C107—41no—
86C22×C4×C107—41no—
87C22×C4×C107—41no—
88C22×C4×C107—41no—
89C22×C4×C107—41no—
90C22×C4×C107C22⋊C412yes—
91C22×C4×C107C22⋊C411yescharacteristic
92C22×C4×C107C22⋊C411yescharacteristic
93C22×C4×C107C4⋊C412yes—
94C22×C4×C107C2×C812yes—
95C22×C4×C107C2×C812yes—
96C22×C4×C107M1612yes—
97C22×C4×C107M1612yes—
98C22×C4×C107C2×D412yes—
99C22×C4×C107C2×D411yescharacteristic
100C22×C4×C107C2×Q811yescharacteristic
101C22×C4×C107#4112yes—
102C2×C8×C107—44no—
103C2×C8×C107—44no—
104C2×C8×C107—44no—
105C22⋊C4×C107—28no—
106C22⋊C4×C107—24no—
107C22⋊C4×C107—24no—
108C42×C107—24no—
109C42×C107—42no—
110C42×C107—42no—
111C42×C107—42no—
112C23×C107—21no—
113C23×C107—21no—
114C23×C107—21no—
115C23×C107—21no—
116C23×C107—22no—
117C23×C107—22no—
118C23×C107—22no—
119C23×C107—22no—
120C23×C107—22no—
121C23×C107—22no—
122C23×C107—42no—
123C23×C107—42no—
124C23×C107—42no—
125C23×C107—42no—
126C23×C107—42no—
127C23×C107—42no—
128C23×C107—42no—
129C23×C107—42no—
130C23×C107—42no—
131C23×C107—42no—
132C23×C107—42no—
133C23×C107—42no—
134C23×C107—41no—
135C23×C107—41no—
136C23×C107—41no—
137C23×C107—41no—
138C23×C107C4⋊C814yescomplemented
139C23×C107C2×C22⋊C411yescharacteristic
140C23×C107C2×C4⋊C411yescharacteristic
141C23×C107#11711yescharacteristic
142C23×C107C22×C811yescharacteristic
143C23×C107C2×M1611yescharacteristic
144C23×C107C2×M1611yescharacteristic
145C23×C107C2×M1611yescharacteristic
146C2×C4×C107—24no—
147C2×C4×C107—24no—
148C2×C4×C107—21no—
149C2×C4×C107—21no—
150C2×C4×C107—22no—
151C2×C4×C107—22no—
152C2×C4×C107—21no—
153C2×C4×C107—22no—
154C2×C4×C107—21no—
155C2×C4×C107—22no—
156C2×C4×C107—22no—
157C2×C4×C107—22no—
158C2×C4×C107—22no—
159C2×C4×C107—42no—
160C2×C4×C107—42no—
161C2×C4×C107—41no—
162C2×C4×C107—41no—
163C2×C4×C107—42no—
164C2×C4×C107—48no—
165C2×C4×C107—48no—
166C2×C4×C107—42no—
167C2×C4×C107—42no—
168C2×C4×C107—42no—
169C2×C4×C107—41no—
170C2×C4×C107—41no—
171C2×C4×C107—41no—
172C2×C4×C107—41no—
173C2×C4×C107—41no—
174C2×C4×C107—41no—
175C2×C4×C107—42no—
176C2×C4×C107—42no—
177C2×C4×C107—42no—
178C2×C4×C107C22⋊C814yes—
179C2×C4×C107#9912yes—
180C2×C4×C107#10012yes—
181C2×C4×C107#12112yes—
182C2×C4×C107C22⋊Q812yes—
183C8×C107—84no—
184C22×C107—21no—
185C22×C107—21no—
186C22×C107—21no—
187C22×C107—21no—
188C22×C107—21no—
189C22×C107—21no—
190C22×C107—21no—
191C22×C107—21no—
192C22×C107—21no—
193C22×C107—21no—
194C22×C107—21no—
195C22×C107—21no—
196C22×C107—24no—
197C22×C107—44no—
198C22×C107—44no—
199C22×C107—44no—
200C22×C107—44no—
201C22×C107—42no—
202C22×C107—42no—
203C22×C107—42no—
204C22×C107—42no—
205C22×C107—42no—
206C22×C107—42no—
207C22×C107#38011yescharacteristic
208C22×C107C2×C22⋊C811yescharacteristic
209C22×C107#40711yescharacteristic
210C22×C107C2×#9911yescharacteristic
211C22×C107#41011yescharacteristic
212C22×C107C2×#10011yescharacteristic
213C22×C107#41311yescharacteristic
214C22×C107C2×C4⋊C811yescharacteristic
215C22×C107#42311yescharacteristic
216C22×C107#43111yescharacteristic
217C22×C107#43211yescharacteristic
218C4×C107—22no—
219C4×C107—22no—
220C4×C107—24no—
221C4×C107—22no—
222C4×C107—22no—
223C4×C107—42no—
224C4×C107—42no—
225C4×C107—42no—
226#8559C10711yesmaximal, characteristic, direct product factor, Sylow
227C2×C107—21no—
228C2×C107—21no—
229C2×C107—21no—
230C2×C107—21no—
231C2×C107—44no—
232C2×C107#145911yescharacteristic
233C2×C107#146011yescharacteristic
234C2×C107#146211yescharacteristic
235C2×C107#146411yescharacteristic
236C2×C107#179711yescharacteristic
237C2×C107#179911yescharacteristic
238C2×C107#180011yescharacteristic
239C2×C4×C22⋊C4C2×C10711yescharacteristic
240#1797C2×C10712yescomplemented
241C2×#323C2×C10712yes—
242#1280C2×C10712yescomplemented
243C107#855911yescharacteristic, direct product factor, Sylow
244C24×C4C4×C10711yescharacteristic
245C22×C22⋊C4C4×C10711yescharacteristic
246C22×C22⋊C4C22×C10711yescharacteristic
247C22×C42C4×C10711yescharacteristic
248C22×C42C22×C10711yescharacteristic
249C2×C4⋊C8—22no—
250C2×C22⋊C8C22×C10714yes—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C2×#95C4×C10711yescharacteristic
254C2×#95C22×C10711yescharacteristic
255#336—22no—
256#323—24no—
257C25C2×C4×C10711yescharacteristic
258C23×C4—22no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—22no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4C2×C4×C10711yescharacteristic
265C23×C4C2×C4×C10711yescharacteristic
266C23×C4C2×C4×C10711yescharacteristic
267C23×C4C2×C4×C10711yescharacteristic
268C23×C4C2×C4×C10711yescharacteristic
269C23×C4C23×C10711yescharacteristic
270C22×C8—24no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4C8×C10714yescomplemented
276C2×C22⋊C4D4×C10712yes—
277C2×C22⋊C4Q8×C10712yes—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—42no—
281C2×C42—42no—
282C2×C42D4×C10712yes—
283C2×C42D4×C10712yes—
284C4⋊C8—44no—
285C22⋊C8—24no—
286C22⋊C8—24no—
287#95—22no—
288#95—22no—
289C24—21no—
290C24—21no—
291C24—21no—
292C24—21no—
293C24—41no—
294C24—41no—
295C24—41no—
296C24—41no—
297C24C4⋊C4×C10712yes—
298C24C2×C8×C10712yes—
299C24M16×C10712yes—
300C24C22×C4×C10711yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—48no—
318C22×C4—48no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4C22⋊C4×C10712yes—
330C22×C4C22⋊C4×C10711yescharacteristic
331C22×C4C22⋊C4×C10711yescharacteristic
332C22×C4C4⋊C4×C10712yes—
333C22×C4C2×C8×C10712yes—
334C22×C4C2×C8×C10712yes—
335C22×C4M16×C10712yes—
336C22×C4M16×C10712yes—
337C22×C4C2×D4×C10712yes—
338C22×C4C2×D4×C10711yescharacteristic
339C22×C4C2×Q8×C10711yescharacteristic
340C22×C4#41×C10712yes—
341C2×C8—44no—
342C2×C8—44no—
343C2×C8—44no—
344C22⋊C4—28no—
345C22⋊C4—24no—
346C22⋊C4—24no—
347C42—24no—
348C42—42no—
349C42—42no—
350C42—42no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23C4⋊C8×C10714yescomplemented
378C23C2×C22⋊C4×C10711yescharacteristic
379C23C2×C4⋊C4×C10711yescharacteristic
380C23#117×C10711yescharacteristic
381C23C22×C8×C10711yescharacteristic
382C23C2×M16×C10711yescharacteristic
383C23C2×M16×C10711yescharacteristic
384C23C2×M16×C10711yescharacteristic
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—48no—
404C2×C4—48no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4C22⋊C8×C10714yes—
418C2×C4#99×C10712yes—
419C2×C4#100×C10712yes—
420C2×C4#121×C10712yes—
421C2×C4C22⋊Q8×C10712yes—
422C8—84no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—44no—
437C22—44no—
438C22—44no—
439C22—44no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22#380×C10711yescharacteristic
447C22C2×C22⋊C8×C10711yescharacteristic
448C22#407×C10711yescharacteristic
449C22C2×#99×C10711yescharacteristic
450C22#410×C10711yescharacteristic
451C22C2×#100×C10711yescharacteristic
452C22#413×C10711yescharacteristic
453C22C2×C4⋊C8×C10711yescharacteristic
454C22#423×C10711yescharacteristic
455C22#431×C10711yescharacteristic
456C22#432×C10711yescharacteristic
457C4—24no—
458C4—22no—
459C4—22no—
460C4—22no—
461C4—22no—
462C4—42no—
463C4—42no—
464C4—42no—
465C2—21no—
466C2—21no—
467C2—21no—
468C2—21no—
469C2—44no—
470C2C107×#145911yescharacteristic
471C2C107×#146011yescharacteristic
472C2C107×#146211yescharacteristic
473C2C107×#146411yescharacteristic
474C2C107×#179711yescharacteristic
475C2C107×#179911yescharacteristic
476C2C107×#180011yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC23C22×C8×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC25×C107C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1797C2semidirect
4. C107×#1280C2semidirect
36. C2×C22⋊C4×C107C8semidirect
138. C23×C107C4⋊C8semidirect
226. #8559C107direct (N × H)
240. #1797C2×C107semidirect
242. #1280C2×C107semidirect
243. C107#8559direct (N × H)
275. C2×C22⋊C4C8×C107semidirect
377. C23C4⋊C8×C107semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊C4×C1072
C107×#17972
C2×#323×C1072
C107×#12802
#8559107