Finite Group Databasebeta

← C107×#22334 #41048298

Subgroups — C107×#22334 #41048298

Order 27392.

806 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2392C211yesmaximal, characteristic
2C107×#1955C211yesmaximal, characteristic, complemented
3C107×#1954C211yesmaximal, characteristic, complemented
4C107×#1924C211yesmaximal, characteristic, complemented
5C107×#1924C211yesmaximal, characteristic, complemented
6C107×#1917C211yesmaximal, characteristic, complemented
7C107×#1916C211yesmaximal, characteristic, complemented
8C107×#1870C211yesmaximal, characteristic, complemented
9C107×#1870C211yesmaximal, characteristic, complemented
10C107×#1869C211yesmaximal, characteristic, complemented
11C107×#1869C211yesmaximal, characteristic, complemented
12C107×#1818C211yesmaximal, characteristic, complemented
13C107×#1753C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C107C211yesmaximal, characteristic, complemented
15C107×#1750C211yesmaximal, characteristic, complemented
16C22×M16×C107C2211yescharacteristic
17C23×C8×C107C2211yescharacteristic
18C2×C4×D4×C107C2211yescharacteristic
19C2×C4×D4×C107C2211yescharacteristic
20C2×C4×D4×C107C2211yescharacteristic
21C2×#117×C107C2211yescharacteristic
22C2×C4⋊C8×C107C2211yescharacteristic
23C2×C4⋊C8×C107C2211yescharacteristic
24C2×C22⋊C8×C107C2211yescharacteristic
25C2×C22⋊C8×C107C2211yescharacteristic
26C2×C22⋊C8×C107C2211yescharacteristic
27C2×C22⋊C8×C107C2211yescharacteristic
28C2×C22⋊C8×C107C2211yescharacteristic
29C2×C22⋊C8×C107C2211yescharacteristic
30C2×C22⋊C8×C107C2211yescharacteristic
31C2×C22⋊C8×C107C2211yescharacteristic
32C2×C22⋊C8×C107C2211yescharacteristic
33C2×C22⋊C8×C107C2211yescharacteristic
34C2×#97×C107C2211yescharacteristic
35C2×#97×C107C2211yescharacteristic
36C2×C4×C8×C107C2211yescharacteristic
37C2×C4×C8×C107C2211yescharacteristic
38#398×C107C411yescharacteristic
39#397×C107C411yescharacteristic
40#396×C107C411yescharacteristic
41#396×C107C411yescharacteristic
42#394×C107C411yescharacteristic
43#394×C107C411yescharacteristic
44#394×C107C411yescharacteristic
45#392×C107C411yescharacteristic
46C4×C4⋊C4×C107C2211yescharacteristic
47C4×C22⋊C4×C107C2211yescharacteristic
48C4×C22⋊C4×C107C2211yescharacteristic
49#336×C107C2211yescharacteristic
50#336×C107C2211yescharacteristic
51#336×C107C2211yescharacteristic
52#336×C107C2211yescharacteristic
53#336×C107C2211yescharacteristic
54#336×C107C2211yescharacteristic
55#336×C107C2211yescharacteristic
56#336×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59C22×D4×C107C2×C411yescharacteristic
60C22×D4×C107C2×C411yescharacteristic
61C22×D4×C107C2×C411yescharacteristic
62C23×C4×C107C2311yescharacteristic
63C23×C4×C107C2311yescharacteristic
64C23×C4×C107C2311yescharacteristic
65C2×M16×C107—22no—
66C2×M16×C107—41no—
67C2×M16×C107—41no—
68C22×C8×C107—22no—
69C22×C8×C107—41no—
70C22×C8×C107—41no—
71C22×C8×C107C2311yescharacteristic
72C22×C8×C107C2311yescharacteristic
73C22×C8×C107C2311yescharacteristic
74C22×C8×C107C2311yescharacteristic
75C22×C8×C107C2311yescharacteristic
76C22×C8×C107C2311yescharacteristic
77C22×C8×C107C2311yescharacteristic
78C22×C8×C107C2311yescharacteristic
79C4×D4×C107—41no—
80C4×D4×C107—41no—
81C4×D4×C107—41no—
82C4×D4×C107—41no—
83C4×D4×C107—41no—
84C4×D4×C107—41no—
85#117×C107—41no—
86#117×C107—41no—
87C2×C4⋊C4×C107C2×C411yescharacteristic
88C2×C4⋊C4×C107C2×C411yescharacteristic
89C2×C4⋊C4×C107C2×C411yescharacteristic
90C2×C4⋊C4×C107C2×C411yescharacteristic
91C2×C4⋊C4×C107C2×C411yescharacteristic
92C2×C4⋊C4×C107C2×C411yescharacteristic
93C2×C4⋊C4×C107C2×C411yescharacteristic
94C2×C22⋊C4×C107C2×C411yescharacteristic
95C2×C22⋊C4×C107C2×C411yescharacteristic
96C2×C22⋊C4×C107C2×C411yescharacteristic
97C2×C22⋊C4×C107C2×C411yescharacteristic
98C2×C22⋊C4×C107C2×C411yescharacteristic
99C2×C22⋊C4×C107C2×C411yescharacteristic
100C2×C22⋊C4×C107C2×C411yescharacteristic
101C2×C22⋊C4×C107C2×C411yescharacteristic
102C2×C22⋊C4×C107C2×C411yescharacteristic
103C2×C22⋊C4×C107C2×C411yescharacteristic
104C2×C22⋊C4×C107C2×C411yescharacteristic
105C2×C22⋊C4×C107C2×C411yescharacteristic
106C2×C42×C107C2311yescharacteristic
107C2×C42×C107C2311yescharacteristic
108C2×C42×C107C2311yescharacteristic
109C2×C42×C107C2311yescharacteristic
110C4⋊C8×C107—41no—
111C4⋊C8×C107—41no—
112C22⋊C8×C107—22no—
113C22⋊C8×C107—22no—
114C22⋊C8×C107—22no—
115C22⋊C8×C107—22no—
116C22⋊C8×C107—41no—
117C22⋊C8×C107—41no—
118C22⋊C8×C107—41no—
119C22⋊C8×C107—41no—
120C22⋊C8×C107—41no—
121C22⋊C8×C107—41no—
122#97×C107—41no—
123#97×C107—41no—
124C4×C8×C107—41no—
125C4×C8×C107—41no—
126#95×C107C2×C411yescharacteristic
127#95×C107C2×C411yescharacteristic
128#95×C107C2×C411yescharacteristic
129#95×C107C2×C411yescharacteristic
130#95×C107C2×C411yescharacteristic
131#95×C107C2×C411yescharacteristic
132C24×C107C22×C411yescharacteristic
133C24×C107C22×C411yescharacteristic
134C24×C107C22×C411yescharacteristic
135C2×D4×C107—22no—
136C2×D4×C107—22no—
137C2×D4×C107—22no—
138C2×D4×C107—41no—
139C2×D4×C107—41no—
140C2×D4×C107—41no—
141C2×D4×C107—41no—
142C2×D4×C107—41no—
143C2×D4×C107—41no—
144C22×C4×C107—21no—
145C22×C4×C107—21no—
146C22×C4×C107—21no—
147C22×C4×C107—21no—
148C22×C4×C107—21no—
149C22×C4×C107—21no—
150C22×C4×C107—21no—
151C22×C4×C107—21no—
152C22×C4×C107—21no—
153C22×C4×C107—21no—
154C22×C4×C107—21no—
155C22×C4×C107—21no—
156C22×C4×C107—21no—
157C22×C4×C107—21no—
158C22×C4×C107—21no—
159C22×C4×C107—21no—
160C22×C4×C107—21no—
161C22×C4×C107—21no—
162C22×C4×C107C22×C411yescharacteristic
163C22×C4×C107C22×C411yescharacteristic
164C22×C4×C107C22×C411yescharacteristic
165C22×C4×C107C22×C411yescharacteristic
166C22×C4×C107C22×C411yescharacteristic
167C22×C4×C107C22×C411yescharacteristic
168C22×C4×C107C22×C411yescharacteristic
169C22×C4×C107C22×C411yescharacteristic
170C22×C4×C107C22×C411yescharacteristic
171C22×C4×C107C22×C411yescharacteristic
172C22×C4×C107C22×C411yescharacteristic
173C22×C4×C107C2411yescharacteristic
174M16×C107—44no—
175C2×C8×C107—21no—
176C2×C8×C107—21no—
177C2×C8×C107—21no—
178C2×C8×C107—21no—
179C2×C8×C107—21no—
180C2×C8×C107—21no—
181C2×C8×C107—21no—
182C2×C8×C107—21no—
183C2×C8×C107—21no—
184C2×C8×C107—21no—
185C2×C8×C107—21no—
186C2×C8×C107—21no—
187C2×C8×C107—21no—
188C2×C8×C107—21no—
189C2×C8×C107—21no—
190C2×C8×C107—21no—
191C2×C8×C107—21no—
192C2×C8×C107—21no—
193C2×C8×C107—21no—
194C2×C8×C107—21no—
195C2×C8×C107—21no—
196C2×C8×C107—21no—
197C2×C8×C107—44no—
198C2×C8×C107#4112yes—
199C2×C8×C107#4112yes—
200C4⋊C4×C107—22no—
201C4⋊C4×C107—41no—
202C4⋊C4×C107—41no—
203C4⋊C4×C107—41no—
204C4⋊C4×C107—41no—
205C4⋊C4×C107—41no—
206C4⋊C4×C107—41no—
207C22⋊C4×C107—22no—
208C22⋊C4×C107—22no—
209C22⋊C4×C107—41no—
210C22⋊C4×C107—41no—
211C22⋊C4×C107—41no—
212C22⋊C4×C107—41no—
213C22⋊C4×C107—41no—
214C22⋊C4×C107—41no—
215C22⋊C4×C107—41no—
216C22⋊C4×C107—41no—
217C22⋊C4×C107—41no—
218C22⋊C4×C107—41no—
219C42×C107—21no—
220C42×C107—21no—
221C42×C107—21no—
222C42×C107—21no—
223C42×C107—21no—
224C42×C107—21no—
225C42×C107—21no—
226C42×C107—21no—
227C23×C107—21no—
228C23×C107—21no—
229C23×C107—21no—
230C23×C107—21no—
231C23×C107—21no—
232C23×C107—21no—
233C23×C107—21no—
234C23×C107—21no—
235C23×C107—21no—
236C23×C107—21no—
237C23×C107—21no—
238C23×C107—21no—
239C23×C107—21no—
240C23×C107—21no—
241C23×C107—21no—
242C23×C107—21no—
243C23×C107—21no—
244C23×C107—21no—
245C23×C107—21no—
246C23×C107—21no—
247C23×C107#13112yes—
248C23×C107C23×C411yescharacteristic
249D4×C107—44no—
250D4×C107—44no—
251D4×C107—44no—
252C2×C4×C107—21no—
253C2×C4×C107—21no—
254C2×C4×C107—21no—
255C2×C4×C107—21no—
256C2×C4×C107—21no—
257C2×C4×C107—21no—
258C2×C4×C107—21no—
259C2×C4×C107—21no—
260C2×C4×C107—21no—
261C2×C4×C107—21no—
262C2×C4×C107—21no—
263C2×C4×C107—21no—
264C2×C4×C107—21no—
265C2×C4×C107—21no—
266C2×C4×C107—21no—
267C2×C4×C107—21no—
268C2×C4×C107—21no—
269C2×C4×C107—21no—
270C2×C4×C107—21no—
271C2×C4×C107—21no—
272C2×C4×C107—21no—
273C2×C4×C107—21no—
274C2×C4×C107—21no—
275C2×C4×C107—21no—
276C2×C4×C107—21no—
277C2×C4×C107—21no—
278C2×C4×C107—21no—
279C2×C4×C107—21no—
280C2×C4×C107—21no—
281C2×C4×C107—21no—
282C2×C4×C107—21no—
283C2×C4×C107—21no—
284C2×C4×C107—41no—
285C2×C4×C107—41no—
286C2×C4×C107—41no—
287C2×C4×C107—41no—
288C2×C4×C107—41no—
289C2×C4×C107—41no—
290C2×C4×C107—41no—
291C2×C4×C107—41no—
292C2×C4×C107—41no—
293C2×C4×C107—41no—
294C2×C4×C107—41no—
295C2×C4×C107—41no—
296C2×C4×C107#13112yes—
297C2×C4×C107C2×#4111yescharacteristic
298C2×C4×C107C2×#4111yescharacteristic
299C2×C4×C107H(5,𝔽2)11yescharacteristic
300C2×C4×C107H(5,𝔽2)11yescharacteristic
301C2×C4×C107H(5,𝔽2)11yescharacteristic
302C2×C4×C107H(5,𝔽2)11yescharacteristic
303C8×C107—22no—
304C8×C107—22no—
305C8×C107—41no—
306C8×C107—41no—
307C8×C107—41no—
308C8×C107—41no—
309C8×C107—41no—
310C8×C107—41no—
311C22×C107—22no—
312C22×C107—22no—
313C22×C107—22no—
314C22×C107—41no—
315C22×C107—41no—
316C22×C107—41no—
317C22×C107—41no—
318C22×C107—41no—
319C22×C107—41no—
320C22×C107—41no—
321C22×C107—41no—
322C22×C107—41no—
323C22×C107—41no—
324C22×C107—41no—
325C22×C107—41no—
326C22×C107—41no—
327C22×C107—41no—
328C22×C107—41no—
329C22×C107—41no—
330C22×C107—41no—
331C22×C107—41no—
332C22×C107C4×#4111yescharacteristic
333C22×C107#51811yescharacteristic
334C22×C107#51811yescharacteristic
335C22×C107C2×#13111yescharacteristic
336C22×C107C2×#13111yescharacteristic
337C22×C107#56811yescharacteristic
338C22×C107#56811yescharacteristic
339C4×C107—22no—
340C4×C107—41no—
341C4×C107—41no—
342C4×C107—41no—
343C4×C107—41no—
344C4×C107—41no—
345C4×C107—41no—
346C4×C107—41no—
347C4×C107—41no—
348C4×C107—41no—
349C4×C107—41no—
350C4×C107#53811yescharacteristic
351C4×C107#53811yescharacteristic
352C4×C107#54011yescharacteristic
353C4×C107#54011yescharacteristic
354#22334C10711yesmaximal, characteristic, direct product factor, Sylow
355C2×C107—42no—
356C2×C107—81no—
357C2×C107—81no—
358C2×C107#233311yescharacteristic
359C2×C107#296611yescharacteristic
360C2×C107#296711yescharacteristic
361C2×C107#297611yescharacteristic
362C2×C107#297611yescharacteristic
363C2×C107#297611yescharacteristic
364C2×C107#298111yescharacteristic
365#2392C2×C10711yescharacteristic
366#1955C2×C10711yescharacteristic, complemented
367#1954C2×C10711yescharacteristic, complemented
368#1924C2×C10711yescharacteristic, complemented
369#1924C2×C10711yescharacteristic, complemented
370#1917C2×C10711yescharacteristic, complemented
371#1916C2×C10711yescharacteristic, complemented
372#1870C2×C10711yescharacteristic, complemented
373#1870C2×C10711yescharacteristic, complemented
374#1869C2×C10711yescharacteristic, complemented
375#1869C2×C10711yescharacteristic, complemented
376#1818C2×C10711yescharacteristic, complemented
377#1753C2×C10711yescharacteristic, complemented
378C8×C22⋊C4C2×C10711yescharacteristic, complemented
379#1750C2×C10711yescharacteristic, complemented
380C107#2233411yescharacteristic, direct product factor, Sylow
381C22×M16C22×C10711yescharacteristic
382C23×C8C22×C10711yescharacteristic
383C2×C4×D4C22×C10711yescharacteristic
384C2×C4×D4C22×C10711yescharacteristic
385C2×C4×D4C22×C10711yescharacteristic
386C2×#117C22×C10711yescharacteristic
387C2×C4⋊C8C22×C10711yescharacteristic
388C2×C4⋊C8C22×C10711yescharacteristic
389C2×C22⋊C8C22×C10711yescharacteristic
390C2×C22⋊C8C22×C10711yescharacteristic
391C2×C22⋊C8C22×C10711yescharacteristic
392C2×C22⋊C8C22×C10711yescharacteristic
393C2×C22⋊C8C22×C10711yescharacteristic
394C2×C22⋊C8C22×C10711yescharacteristic
395C2×C22⋊C8C22×C10711yescharacteristic
396C2×C22⋊C8C22×C10711yescharacteristic
397C2×C22⋊C8C22×C10711yescharacteristic
398C2×C22⋊C8C22×C10711yescharacteristic
399C2×#97C22×C10711yescharacteristic
400C2×#97C22×C10711yescharacteristic
401C2×C4×C8C22×C10711yescharacteristic
402C2×C4×C8C22×C10711yescharacteristic
403#398C4×C10711yescharacteristic
404#397C4×C10711yescharacteristic
405#396C4×C10711yescharacteristic
406#396C4×C10711yescharacteristic
407#394C4×C10711yescharacteristic
408#394C4×C10711yescharacteristic
409#394C4×C10711yescharacteristic
410#392C4×C10711yescharacteristic
411C4×C4⋊C4C22×C10711yescharacteristic
412C4×C22⋊C4C22×C10711yescharacteristic
413C4×C22⋊C4C22×C10711yescharacteristic
414#336C22×C10711yescharacteristic
415#336C22×C10711yescharacteristic
416#336C22×C10711yescharacteristic
417#336C22×C10711yescharacteristic
418#336C22×C10711yescharacteristic
419#336C22×C10711yescharacteristic
420#336C22×C10711yescharacteristic
421#336C22×C10711yescharacteristic
422#336C22×C10711yescharacteristic
423#336C22×C10711yescharacteristic
424C22×D4C2×C4×C10711yescharacteristic
425C22×D4C2×C4×C10711yescharacteristic
426C22×D4C2×C4×C10711yescharacteristic
427C23×C4C23×C10711yescharacteristic
428C23×C4C23×C10711yescharacteristic
429C23×C4C23×C10711yescharacteristic
430C2×M16—22no—
431C2×M16—41no—
432C2×M16—41no—
433C22×C8—22no—
434C22×C8—41no—
435C22×C8—41no—
436C22×C8C23×C10711yescharacteristic
437C22×C8C23×C10711yescharacteristic
438C22×C8C23×C10711yescharacteristic
439C22×C8C23×C10711yescharacteristic
440C22×C8C23×C10711yescharacteristic
441C22×C8C23×C10711yescharacteristic
442C22×C8C23×C10711yescharacteristic
443C22×C8C23×C10711yescharacteristic
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C4×D4—41no—
450#117—41no—
451#117—41no—
452C2×C4⋊C4C2×C4×C10711yescharacteristic
453C2×C4⋊C4C2×C4×C10711yescharacteristic
454C2×C4⋊C4C2×C4×C10711yescharacteristic
455C2×C4⋊C4C2×C4×C10711yescharacteristic
456C2×C4⋊C4C2×C4×C10711yescharacteristic
457C2×C4⋊C4C2×C4×C10711yescharacteristic
458C2×C4⋊C4C2×C4×C10711yescharacteristic
459C2×C22⋊C4C2×C4×C10711yescharacteristic
460C2×C22⋊C4C2×C4×C10711yescharacteristic
461C2×C22⋊C4C2×C4×C10711yescharacteristic
462C2×C22⋊C4C2×C4×C10711yescharacteristic
463C2×C22⋊C4C2×C4×C10711yescharacteristic
464C2×C22⋊C4C2×C4×C10711yescharacteristic
465C2×C22⋊C4C2×C4×C10711yescharacteristic
466C2×C22⋊C4C2×C4×C10711yescharacteristic
467C2×C22⋊C4C2×C4×C10711yescharacteristic
468C2×C22⋊C4C2×C4×C10711yescharacteristic
469C2×C22⋊C4C2×C4×C10711yescharacteristic
470C2×C22⋊C4C2×C4×C10711yescharacteristic
471C2×C42C23×C10711yescharacteristic
472C2×C42C23×C10711yescharacteristic
473C2×C42C23×C10711yescharacteristic
474C2×C42C23×C10711yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C22⋊C8—22no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487#97—41no—
488#97—41no—
489C4×C8—41no—
490C4×C8—41no—
491#95C2×C4×C10711yescharacteristic
492#95C2×C4×C10711yescharacteristic
493#95C2×C4×C10711yescharacteristic
494#95C2×C4×C10711yescharacteristic
495#95C2×C4×C10711yescharacteristic
496#95C2×C4×C10711yescharacteristic
497C24C22×C4×C10711yescharacteristic
498C24C22×C4×C10711yescharacteristic
499C24C22×C4×C10711yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C22×C4×C10711yescharacteristic
528C22×C4C22×C4×C10711yescharacteristic
529C22×C4C22×C4×C10711yescharacteristic
530C22×C4C22×C4×C10711yescharacteristic
531C22×C4C22×C4×C10711yescharacteristic
532C22×C4C22×C4×C10711yescharacteristic
533C22×C4C22×C4×C10711yescharacteristic
534C22×C4C22×C4×C10711yescharacteristic
535C22×C4C22×C4×C10711yescharacteristic
536C22×C4C22×C4×C10711yescharacteristic
537C22×C4C22×C4×C10711yescharacteristic
538C22×C4C24×C10711yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—44no—
563C2×C8#41×C10712yes—
564C2×C8#41×C10712yes—
565C4⋊C4—22no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23#131×C10712yes—
613C23C23×C4×C10711yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4#131×C10712yes—
662C2×C4C2×#41×C10711yescharacteristic
663C2×C4C2×#41×C10711yescharacteristic
664C2×C4H(5,𝔽2)×C10711yescharacteristic
665C2×C4H(5,𝔽2)×C10711yescharacteristic
666C2×C4H(5,𝔽2)×C10711yescharacteristic
667C2×C4H(5,𝔽2)×C10711yescharacteristic
668C8—22no—
669C8—22no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22C4×#41×C10711yescharacteristic
698C22#518×C10711yescharacteristic
699C22#518×C10711yescharacteristic
700C22C2×#131×C10711yescharacteristic
701C22C2×#131×C10711yescharacteristic
702C22#568×C10711yescharacteristic
703C22#568×C10711yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4#538×C10711yescharacteristic
716C4#538×C10711yescharacteristic
717C4#540×C10711yescharacteristic
718C4#540×C10711yescharacteristic
719C2—42no—
720C2—81no—
721C2—81no—
722C2C107×#233311yescharacteristic
723C2C107×#296611yescharacteristic
724C2C107×#296711yescharacteristic
725C2C107×#297611yescharacteristic
726C2C107×#297611yescharacteristic
727C2C107×#297611yescharacteristic
728C2C107×#298111yescharacteristic
subgroupG/H
centerC22×C4×C107C24
commutatorC23C23×C4×C107
Frattini, cosocleC22×C4C24×C107
socleC23×C107C23×C4
prime radical#392×C107C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1955C2semidirect
3. C107×#1954C2semidirect
4. C107×#1924C2semidirect
5. C107×#1924C2semidirect
6. C107×#1917C2semidirect
7. C107×#1916C2semidirect
8. C107×#1870C2semidirect
9. C107×#1870C2semidirect
10. C107×#1869C2semidirect
11. C107×#1869C2semidirect
12. C107×#1818C2semidirect
13. C107×#1753C2semidirect
14. C8×C22⋊C4×C107C2semidirect
15. C107×#1750C2semidirect
354. #22334C107direct (N × H)
366. #1955C2×C107semidirect
367. #1954C2×C107semidirect
368. #1924C2×C107semidirect
369. #1924C2×C107semidirect
370. #1917C2×C107semidirect
371. #1916C2×C107semidirect
372. #1870C2×C107semidirect
373. #1870C2×C107semidirect
374. #1869C2×C107semidirect
375. #1869C2×C107semidirect
376. #1818C2×C107semidirect
377. #1753C2×C107semidirect
378. C8×C22⋊C4C2×C107semidirect
379. #1750C2×C107semidirect
380. C107#22334direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#23922
C107×#19552
C107×#19542
C107×#19242
C107×#19172
C107×#19162
C107×#18702
C107×#18692
C107×#18182
C107×#17532
C8×C22⋊C4×C1072
C107×#17502
#22334107