Finite Group Databasebeta

← C107×#23331 #41049295

Subgroups — C107×#23331 #41049295

Order 27392.

854 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C107C211yesmaximal, characteristic
2C107×#1955C211yesmaximal, characteristic, complemented
3C107×#1954C211yesmaximal, characteristic, complemented
4C107×#1924C211yesmaximal, characteristic, complemented
5C107×#1923C211yesmaximal, 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×#1851C211yesmaximal, characteristic, complemented
13C107×#1850C211yesmaximal, characteristic, complemented
14C107×#1817C211yesmaximal, characteristic, complemented
15C107×#1797C211yesmaximal, characteristic, complemented
16C22×M16×C107C2211yescharacteristic
17C23×C8×C107C2211yescharacteristic
18C2×#121×C107C411yescharacteristic
19C2×C4×D4×C107C2211yescharacteristic
20C2×C4×D4×C107C2211yescharacteristic
21C2×C4×D4×C107C2211yescharacteristic
22C22×C42×C107C2211yescharacteristic
23C2×C4⋊C8×C107C2211yescharacteristic
24C2×C4⋊C8×C107C2211yescharacteristic
25C2×C4⋊C8×C107C2211yescharacteristic
26C2×C4⋊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×C22⋊C8×C107C2211yescharacteristic
35C2×C22⋊C8×C107C2211yescharacteristic
36C2×C22⋊C8×C107C2211yescharacteristic
37C2×#97×C107C2211yescharacteristic
38C2×C4×C8×C107C2211yescharacteristic
39#390×C107C411yescharacteristic
40#389×C107C411yescharacteristic
41#388×C107C411yescharacteristic
42#388×C107C411yescharacteristic
43#386×C107C411yescharacteristic
44#386×C107C411yescharacteristic
45#380×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×C107C2×C411yescharacteristic
63C23×C4×C107C2×C411yescharacteristic
64C23×C4×C107C2311yescharacteristic
65C23×C4×C107C2311yescharacteristic
66C23×C4×C107C2311yescharacteristic
67C2×M16×C107—41no—
68C2×M16×C107—41no—
69C2×M16×C107—41no—
70C22×C8×C107—41no—
71C22×C8×C107—41no—
72C22×C8×C107—41no—
73C22×C8×C107C2311yescharacteristic
74C22×C8×C107C2311yescharacteristic
75C22×C8×C107C2311yescharacteristic
76C22×C8×C107C2311yescharacteristic
77C22×C8×C107C2311yescharacteristic
78C22×C8×C107C2311yescharacteristic
79C22×C8×C107C2311yescharacteristic
80C22×C8×C107C2311yescharacteristic
81#121×C107—24no—
82C4×D4×C107—41no—
83C4×D4×C107—41no—
84C4×D4×C107—41no—
85C4×D4×C107—41no—
86C4×D4×C107—41no—
87C4×D4×C107—41no—
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×C22⋊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×C42×C107—41no—
104C2×C42×C107—41no—
105C2×C42×C107C2×C411yescharacteristic
106C2×C42×C107C2×C411yescharacteristic
107C2×C42×C107C2311yescharacteristic
108C2×C42×C107C2311yescharacteristic
109C2×C42×C107C2311yescharacteristic
110C2×C42×C107C2311yescharacteristic
111C4⋊C8×C107—41no—
112C4⋊C8×C107—41no—
113C4⋊C8×C107—41no—
114C4⋊C8×C107—41no—
115C22⋊C8×C107—41no—
116C22⋊C8×C107—41no—
117C22⋊C8×C107—41no—
118C22⋊C8×C107—41no—
119C22⋊C8×C107—41no—
120C22⋊C8×C107—41no—
121C22⋊C8×C107—41no—
122C22⋊C8×C107—41no—
123C22⋊C8×C107—41no—
124C22⋊C8×C107—41no—
125#97×C107—41no—
126C4×C8×C107—41no—
127#95×C107C2×C411yescharacteristic
128#95×C107C2×C411yescharacteristic
129#95×C107C2×C411yescharacteristic
130#95×C107C2×C411yescharacteristic
131#95×C107C2×C411yescharacteristic
132#95×C107C2×C411yescharacteristic
133C24×C107C22×C411yescharacteristic
134C24×C107C22×C411yescharacteristic
135C24×C107C22×C411yescharacteristic
136C2×D4×C107—22no—
137C2×D4×C107—22no—
138C2×D4×C107—22no—
139C2×D4×C107—41no—
140C2×D4×C107—41no—
141C2×D4×C107—41no—
142C2×D4×C107—41no—
143C2×D4×C107—41no—
144C2×D4×C107M1614yescomplemented
145C22×C4×C107—22no—
146C22×C4×C107—22no—
147C22×C4×C107—22no—
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×C107—21no—
163C22×C4×C107—21no—
164C22×C4×C107—21no—
165C22×C4×C107—21no—
166C22×C4×C107—41no—
167C22×C4×C107—41no—
168C22×C4×C107—41no—
169C22×C4×C107C22×C411yescharacteristic
170C22×C4×C107C22×C411yescharacteristic
171C22×C4×C107C22×C411yescharacteristic
172C22×C4×C107C22×C411yescharacteristic
173C22×C4×C107C22×C411yescharacteristic
174C22×C4×C107C22×C411yescharacteristic
175C22×C4×C107C22×C411yescharacteristic
176C22×C4×C107C22×C411yescharacteristic
177C22×C4×C107C22×C411yescharacteristic
178C22×C4×C107C22×C411yescharacteristic
179C22×C4×C107C22×C411yescharacteristic
180C22×C4×C107C2411yescharacteristic
181M16×C107—44no—
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—21no—
198C2×C8×C107—21no—
199C2×C8×C107—21no—
200C2×C8×C107—21no—
201C2×C8×C107—21no—
202C2×C8×C107—21no—
203C2×C8×C107—21no—
204C2×C8×C107—21no—
205C2×C8×C107—21no—
206C2×C8×C107—44no—
207C4⋊C4×C107—22no—
208C4⋊C4×C107—22no—
209C4⋊C4×C107—41no—
210C4⋊C4×C107—41no—
211C4⋊C4×C107—41no—
212C22⋊C4×C107—22no—
213C22⋊C4×C107—22no—
214C22⋊C4×C107—22no—
215C22⋊C4×C107—22no—
216C22⋊C4×C107—41no—
217C22⋊C4×C107—41no—
218C22⋊C4×C107—41no—
219C22⋊C4×C107—41no—
220C22⋊C4×C107—41no—
221C22⋊C4×C107—41no—
222C42×C107—21no—
223C42×C107—21no—
224C42×C107—21no—
225C42×C107—21no—
226C42×C107—21no—
227C42×C107—21no—
228C42×C107—21no—
229C42×C107—21no—
230C42×C107—41no—
231C42×C107—41no—
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—21no—
248C23×C107—21no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107C2×M1612yes—
252C23×C107C2×M1612yes—
253C23×C107C23×C411yescharacteristic
254D4×C107—44no—
255D4×C107—44no—
256D4×C107—44no—
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—21no—
285C2×C4×C107—21no—
286C2×C4×C107—21no—
287C2×C4×C107—44no—
288C2×C4×C107—44no—
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—41no—
297C2×C4×C107—41no—
298C2×C4×C107—41no—
299C2×C4×C107—41no—
300C2×C4×C107—41no—
301C2×C4×C107C2×M1612yes—
302C2×C4×C107#13112yes—
303C2×C4×C107#13112yes—
304C2×C4×C107H(5,𝔽2)11yescharacteristic
305C2×C4×C107H(5,𝔽2)11yescharacteristic
306C2×C4×C107H(5,𝔽2)11yescharacteristic
307C2×C4×C107H(5,𝔽2)11yescharacteristic
308C2×C4×C107H(5,𝔽2)11yescharacteristic
309C2×C4×C1072−1+411yescharacteristic
310C8×C107—41no—
311C8×C107—41no—
312C8×C107—41no—
313C8×C107—41no—
314C8×C107—41no—
315C8×C107—41no—
316C8×C107—41no—
317C8×C107—41no—
318C22×C107—22no—
319C22×C107—22no—
320C22×C107—22no—
321C22×C107—22no—
322C22×C107—22no—
323C22×C107—22no—
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×C107—41no—
333C22×C107—41no—
334C22×C107—41no—
335C22×C107—41no—
336C22×C107—41no—
337C22×C107—41no—
338C22×C107—41no—
339C22×C107#51811yescharacteristic
340C22×C107#51811yescharacteristic
341C22×C107#52011yescharacteristic
342C22×C107C22×M1611yescharacteristic
343C22×C107C2×#13111yescharacteristic
344C22×C107C2×#13111yescharacteristic
345C22×C107#56811yescharacteristic
346C4×C107—22no—
347C4×C107—22no—
348C4×C107—22no—
349C4×C107—41no—
350C4×C107—41no—
351C4×C107—41no—
352C4×C107—41no—
353C4×C107—41no—
354C4×C107—41no—
355C4×C107—41no—
356C4×C107—41no—
357C4×C107#56011yescharacteristic
358C4×C107#56011yescharacteristic
359C4×C107#56211yescharacteristic
360C4×C107#56211yescharacteristic
361#23331C10711yesmaximal, characteristic, direct product factor, Sylow
362C2×C107—42no—
363C2×C107—42no—
364C2×C107—81no—
365C2×C107#237711yescharacteristic
366C2×C107#297311yescharacteristic
367C2×C107#297411yescharacteristic
368C2×C107#297611yescharacteristic
369C2×C107#297911yescharacteristic
370C2×C107#299011yescharacteristic
371C2×C107#299311yescharacteristic
372C4×#121C2×C10711yescharacteristic
373#1955C2×C10711yescharacteristic, complemented
374#1954C2×C10711yescharacteristic, complemented
375#1924C2×C10711yescharacteristic, complemented
376#1923C2×C10711yescharacteristic, complemented
377#1917C2×C10711yescharacteristic, complemented
378#1916C2×C10711yescharacteristic, complemented
379#1870C2×C10711yescharacteristic, complemented
380#1870C2×C10711yescharacteristic, complemented
381#1869C2×C10711yescharacteristic, complemented
382#1869C2×C10711yescharacteristic, complemented
383#1851C2×C10711yescharacteristic, complemented
384#1850C2×C10711yescharacteristic, complemented
385#1817C2×C10711yescharacteristic, complemented
386#1797C2×C10711yescharacteristic, complemented
387C107#2333111yescharacteristic, direct product factor, Sylow
388C22×M16C22×C10711yescharacteristic
389C23×C8C22×C10711yescharacteristic
390C2×#121C4×C10711yescharacteristic
391C2×C4×D4C22×C10711yescharacteristic
392C2×C4×D4C22×C10711yescharacteristic
393C2×C4×D4C22×C10711yescharacteristic
394C22×C42C22×C10711yescharacteristic
395C2×C4⋊C8C22×C10711yescharacteristic
396C2×C4⋊C8C22×C10711yescharacteristic
397C2×C4⋊C8C22×C10711yescharacteristic
398C2×C4⋊C8C22×C10711yescharacteristic
399C2×C22⋊C8C22×C10711yescharacteristic
400C2×C22⋊C8C22×C10711yescharacteristic
401C2×C22⋊C8C22×C10711yescharacteristic
402C2×C22⋊C8C22×C10711yescharacteristic
403C2×C22⋊C8C22×C10711yescharacteristic
404C2×C22⋊C8C22×C10711yescharacteristic
405C2×C22⋊C8C22×C10711yescharacteristic
406C2×C22⋊C8C22×C10711yescharacteristic
407C2×C22⋊C8C22×C10711yescharacteristic
408C2×C22⋊C8C22×C10711yescharacteristic
409C2×#97C22×C10711yescharacteristic
410C2×C4×C8C22×C10711yescharacteristic
411#390C4×C10711yescharacteristic
412#389C4×C10711yescharacteristic
413#388C4×C10711yescharacteristic
414#388C4×C10711yescharacteristic
415#386C4×C10711yescharacteristic
416#386C4×C10711yescharacteristic
417#380C4×C10711yescharacteristic
418C4×C4⋊C4C22×C10711yescharacteristic
419C4×C22⋊C4C22×C10711yescharacteristic
420C4×C22⋊C4C22×C10711yescharacteristic
421#336C22×C10711yescharacteristic
422#336C22×C10711yescharacteristic
423#336C22×C10711yescharacteristic
424#336C22×C10711yescharacteristic
425#336C22×C10711yescharacteristic
426#336C22×C10711yescharacteristic
427#336C22×C10711yescharacteristic
428#336C22×C10711yescharacteristic
429#336C22×C10711yescharacteristic
430#336C22×C10711yescharacteristic
431C22×D4C2×C4×C10711yescharacteristic
432C22×D4C2×C4×C10711yescharacteristic
433C22×D4C2×C4×C10711yescharacteristic
434C23×C4C2×C4×C10711yescharacteristic
435C23×C4C2×C4×C10711yescharacteristic
436C23×C4C23×C10711yescharacteristic
437C23×C4C23×C10711yescharacteristic
438C23×C4C23×C10711yescharacteristic
439C2×M16—41no—
440C2×M16—41no—
441C2×M16—41no—
442C22×C8—41no—
443C22×C8—41no—
444C22×C8—41no—
445C22×C8C23×C10711yescharacteristic
446C22×C8C23×C10711yescharacteristic
447C22×C8C23×C10711yescharacteristic
448C22×C8C23×C10711yescharacteristic
449C22×C8C23×C10711yescharacteristic
450C22×C8C23×C10711yescharacteristic
451C22×C8C23×C10711yescharacteristic
452C22×C8C23×C10711yescharacteristic
453#121—24no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458C4×D4—41no—
459C4×D4—41no—
460C2×C4⋊C4C2×C4×C10711yescharacteristic
461C2×C4⋊C4C2×C4×C10711yescharacteristic
462C2×C4⋊C4C2×C4×C10711yescharacteristic
463C2×C4⋊C4C2×C4×C10711yescharacteristic
464C2×C4⋊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×C22⋊C4C2×C4×C10711yescharacteristic
472C2×C22⋊C4C2×C4×C10711yescharacteristic
473C2×C22⋊C4C2×C4×C10711yescharacteristic
474C2×C22⋊C4C2×C4×C10711yescharacteristic
475C2×C42—41no—
476C2×C42—41no—
477C2×C42C2×C4×C10711yescharacteristic
478C2×C42C2×C4×C10711yescharacteristic
479C2×C42C23×C10711yescharacteristic
480C2×C42C23×C10711yescharacteristic
481C2×C42C23×C10711yescharacteristic
482C2×C42C23×C10711yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—41no—
485C4⋊C8—41no—
486C4⋊C8—41no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496C22⋊C8—41no—
497#97—41no—
498C4×C8—41no—
499#95C2×C4×C10711yescharacteristic
500#95C2×C4×C10711yescharacteristic
501#95C2×C4×C10711yescharacteristic
502#95C2×C4×C10711yescharacteristic
503#95C2×C4×C10711yescharacteristic
504#95C2×C4×C10711yescharacteristic
505C24C22×C4×C10711yescharacteristic
506C24C22×C4×C10711yescharacteristic
507C24C22×C4×C10711yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4M16×C10714yescomplemented
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4C22×C4×C10711yescharacteristic
542C22×C4C22×C4×C10711yescharacteristic
543C22×C4C22×C4×C10711yescharacteristic
544C22×C4C22×C4×C10711yescharacteristic
545C22×C4C22×C4×C10711yescharacteristic
546C22×C4C22×C4×C10711yescharacteristic
547C22×C4C22×C4×C10711yescharacteristic
548C22×C4C22×C4×C10711yescharacteristic
549C22×C4C22×C4×C10711yescharacteristic
550C22×C4C22×C4×C10711yescharacteristic
551C22×C4C22×C4×C10711yescharacteristic
552C22×C4C24×C10711yescharacteristic
553M16—44no—
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—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—44no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—41no—
603C42—41no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×M16×C10712yes—
624C23C2×M16×C10712yes—
625C23C23×C4×C10711yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
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—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4C2×M16×C10712yes—
674C2×C4#131×C10712yes—
675C2×C4#131×C10712yes—
676C2×C4H(5,𝔽2)×C10711yescharacteristic
677C2×C4H(5,𝔽2)×C10711yescharacteristic
678C2×C4H(5,𝔽2)×C10711yescharacteristic
679C2×C4H(5,𝔽2)×C10711yescharacteristic
680C2×C4H(5,𝔽2)×C10711yescharacteristic
681C2×C42−1+4×C10711yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22#518×C10711yescharacteristic
712C22#518×C10711yescharacteristic
713C22#520×C10711yescharacteristic
714C22C22×M16×C10711yescharacteristic
715C22C2×#131×C10711yescharacteristic
716C22C2×#131×C10711yescharacteristic
717C22#568×C10711yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4#560×C10711yescharacteristic
730C4#560×C10711yescharacteristic
731C4#562×C10711yescharacteristic
732C4#562×C10711yescharacteristic
733C2—42no—
734C2—42no—
735C2—81no—
736C2C107×#237711yescharacteristic
737C2C107×#297311yescharacteristic
738C2C107×#297411yescharacteristic
739C2C107×#297611yescharacteristic
740C2C107×#297911yescharacteristic
741C2C107×#299011yescharacteristic
742C2C107×#299311yescharacteristic
subgroupG/H
centerC22×C4×C107C24
commutatorC23C23×C4×C107
Frattini, cosocleC22×C4C24×C107
socleC23×C107C23×C4
prime radicalC2×#121×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×#1923C2semidirect
6. C107×#1917C2semidirect
7. C107×#1916C2semidirect
8. C107×#1870C2semidirect
9. C107×#1870C2semidirect
10. C107×#1869C2semidirect
11. C107×#1869C2semidirect
12. C107×#1851C2semidirect
13. C107×#1850C2semidirect
14. C107×#1817C2semidirect
15. C107×#1797C2semidirect
144. C2×D4×C107M16semidirect
361. #23331C107direct (N × H)
373. #1955C2×C107semidirect
374. #1954C2×C107semidirect
375. #1924C2×C107semidirect
376. #1923C2×C107semidirect
377. #1917C2×C107semidirect
378. #1916C2×C107semidirect
379. #1870C2×C107semidirect
380. #1870C2×C107semidirect
381. #1869C2×C107semidirect
382. #1869C2×C107semidirect
383. #1851C2×C107semidirect
384. #1850C2×C107semidirect
385. #1817C2×C107semidirect
386. #1797C2×C107semidirect
387. C107#23331direct (N × H)
516. C2×D4M16×C107semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1072
C107×#19552
C107×#19542
C107×#19242
C107×#19232
C107×#19172
C107×#19162
C107×#18702
C107×#18692
C107×#18512
C107×#18502
C107×#18172
C107×#17972
#23331107