Finite Group Databasebeta

← C107×#22056 #41048020

Subgroups — C107×#22056 #41048020

Order 27392.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C107C211yesmaximal, characteristic
2C107×#2324C211yesmaximal, characteristic, complemented
3C107×#2309C211yesmaximal, characteristic, complemented
4C107×#1972C211yesmaximal, characteristic, complemented
5C107×#1970C211yesmaximal, characteristic, complemented
6C107×#1936C211yesmaximal, characteristic, complemented
7C107×#1934C211yesmaximal, characteristic, complemented
8C107×#1926C211yesmaximal, characteristic, complemented
9C107×#1925C211yesmaximal, characteristic, complemented
10C107×#1879C211yesmaximal, characteristic, complemented
11C107×#1879C211yesmaximal, characteristic, complemented
12C107×#1875C211yesmaximal, characteristic, complemented
13C107×#1854C211yesmaximal, characteristic, complemented
14C107×#1786C211yesmaximal, characteristic, complemented
15C107×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C2×#121×C107C2211yescharacteristic
20C2×C4×D4×C107C2211yescharacteristic, complemented
21C2×#117×C107C2211yescharacteristic
22C2×#117×C107C2211yescharacteristic
23#447×C107C418yescomplemented
24C2×#107×C107C2211yescharacteristic, complemented
25C2×#106×C107C2211yescharacteristic, complemented
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×#102×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic, complemented
33C2×#102×C107C2211yescharacteristic, complemented
34C2×C22⋊C8×C107C2211yescharacteristic
35C2×C22⋊C8×C107C2211yescharacteristic
36C2×#97×C107C2211yescharacteristic, complemented
37C2×C4×C8×C107C2211yescharacteristic, complemented
38#390×C107—21no—
39#390×C107—21no—
40#390×C107—21no—
41#390×C107C2211yescharacteristic
42#390×C107C2211yescharacteristic
43#390×C107C2211yescharacteristic
44#390×C107C2211yescharacteristic
45#390×C107C2211yescharacteristic, complemented
46#389×C107C2211yescharacteristic, complemented
47#388×C107—21no—
48#386×C107—21no—
49#385×C107—21no—
50#380×C107C2211yescharacteristic
51#379×C107—21no—
52#379×C107—21no—
53C4×C4⋊C4×C107C2211yescharacteristic, complemented
54#340×C107C2211yescharacteristic, complemented
55#340×C107C2211yescharacteristic, complemented
56#340×C107C2211yescharacteristic, complemented
57#340×C107C2211yescharacteristic, complemented
58#336×C107C2211yescharacteristic, complemented
59#336×C107C2211yescharacteristic, complemented
60C25×C107—21no—
61C22×D4×C107—21no—
62C22×D4×C107—21no—
63C22×D4×C107—22no—
64C22×D4×C107—41no—
65C22×D4×C107—41no—
66C22×D4×C107—41no—
67C22×D4×C107—41no—
68C22×D4×C107C2×C414yescomplemented
69C22×D4×C107C2311yescharacteristic
70C22×D4×C107C2311yescharacteristic
71C22×D4×C107C2311yescharacteristic
72C23×C4×C107—21no—
73C23×C4×C107C2311yescharacteristic
74C2×D8×C107—41no—
75C2×D8×C107—41no—
76C2×D8×C107—41no—
77C2×D8×C107—41no—
78C2×D8×C107C2×C414yes—
79C2×D8×C107C2×C414yes—
80C22×C8×C107C2311yescharacteristic
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83C22×C8×C107C2311yescharacteristic
84#121×C107—22no—
85#121×C107C2×C414yes—
86C4×D4×C107—41no—
87C4×D4×C107—41no—
88#117×C107—41no—
89#117×C107—41no—
90#117×C107—41no—
91#117×C107—41no—
92C2×C4⋊C4×C107—21no—
93C2×C4⋊C4×C107D411yescharacteristic
94C2×C4⋊C4×C107D411yescharacteristic
95C2×C4⋊C4×C107C2311yescharacteristic
96C2×C4⋊C4×C107C2311yescharacteristic
97C2×C4⋊C4×C107C2311yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C22⋊C4×C107—21no—
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—21no—
105C2×C22⋊C4×C107—21no—
106C2×C22⋊C4×C107—21no—
107C2×C22⋊C4×C107—21no—
108C2×C22⋊C4×C107—21no—
109C2×C22⋊C4×C107—21no—
110C2×C22⋊C4×C107—21no—
111C2×C22⋊C4×C107—21no—
112C2×C22⋊C4×C107—21no—
113C2×C22⋊C4×C107—21no—
114C2×C22⋊C4×C107D411yescharacteristic
115C2×C22⋊C4×C107D411yescharacteristic
116C2×C42×C107—21no—
117C2×C42×C107—21no—
118C2×C42×C107C2311yescharacteristic
119C2×C42×C107C2311yescharacteristic
120#107×C107—41no—
121#106×C107—41no—
122#102×C107—41no—
123#102×C107—41no—
124#102×C107—41no—
125#102×C107—41no—
126#102×C107—41no—
127#102×C107—41no—
128#102×C107C2×C414yescomplemented
129#102×C107C2×C414yescomplemented
130C22⋊C8×C107—22no—
131C22⋊C8×C107C2×C414yescomplemented
132#97×C107—41no—
133C4×C8×C107—41no—
134#95×C107—21no—
135#95×C107—21no—
136#95×C107—21no—
137C24×C107—21no—
138C24×C107—21no—
139C24×C107—21no—
140C24×C107—24no—
141C24×C107—42no—
142C24×C107—42no—
143C24×C107—81no—
144C24×C107—81no—
145C24×C107—81no—
146C24×C107—81no—
147C24×C107C2×D411yescharacteristic
148C2×D4×C107—24no—
149C2×D4×C107—24no—
150C2×D4×C107—21no—
151C2×D4×C107—21no—
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—21no—
156C2×D4×C107—21no—
157C2×D4×C107—21no—
158C2×D4×C107—21no—
159C2×D4×C107—21no—
160C2×D4×C107—21no—
161C2×D4×C107—21no—
162C2×D4×C107—21no—
163C2×D4×C107—21no—
164C2×D4×C107—21no—
165C2×D4×C107—44no—
166C2×D4×C107—44no—
167C2×D4×C107—42no—
168C2×D4×C107—42no—
169C2×D4×C107—44no—
170C2×D4×C107—44no—
171C2×D4×C107—81no—
172C2×D4×C107—81no—
173C2×D4×C107C22×C412yes—
174C2×D4×C107C22×C412yes—
175C2×D4×C107C22×C412yes—
176C22×C4×C107—21no—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—42no—
186C22×C4×C107—81no—
187C22×C4×C107—81no—
188C22×C4×C107C22×C412yes—
189C22×C4×C107C2×D411yescharacteristic
190C22×C4×C107C2×D411yescharacteristic
191C22×C4×C107C2×D411yescharacteristic
192C22×C4×C107C2×D411yescharacteristic
193C22×C4×C107C2×D411yescharacteristic
194C22×C4×C107#4112yes—
195C22×C4×C107C2411yescharacteristic
196D8×C107—44no—
197D8×C107—44no—
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—21no—
207C2×C8×C107—21no—
208C2×C8×C107C22×C412yes—
209C2×C8×C107C22×C412yes—
210C4⋊C4×C107—21no—
211C4⋊C4×C107—21no—
212C4⋊C4×C107—21no—
213C4⋊C4×C107—21no—
214C4⋊C4×C107—21no—
215C4⋊C4×C107—21no—
216C4⋊C4×C107—21no—
217C4⋊C4×C107—21no—
218C4⋊C4×C107—21no—
219C4⋊C4×C107—41no—
220C4⋊C4×C107—41no—
221C4⋊C4×C107—81no—
222C4⋊C4×C107C22×C412yes—
223C22⋊C4×C107—24no—
224C22⋊C4×C107—41no—
225C22⋊C4×C107—41no—
226C22⋊C4×C107—42no—
227C22⋊C4×C107—42no—
228C22⋊C4×C107—81no—
229C22⋊C4×C107—81no—
230C22⋊C4×C107—81no—
231C22⋊C4×C107—81no—
232C22⋊C4×C107—81no—
233C22⋊C4×C107—81no—
234C22⋊C4×C107—81no—
235C22⋊C4×C107—81no—
236C22⋊C4×C107—81no—
237C22⋊C4×C107—81no—
238C22⋊C4×C107—81no—
239C42×C107—21no—
240C42×C107—21no—
241C42×C107—21no—
242C42×C107—21no—
243C42×C107—42no—
244C42×C107—81no—
245C23×C107—21no—
246C23×C107—21no—
247C23×C107—21no—
248C23×C107—21no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107—22no—
252C23×C107—22no—
253C23×C107—22no—
254C23×C107—48no—
255C23×C107—41no—
256C23×C107—41no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107—41no—
260C23×C107—41no—
261C23×C107—41no—
262C23×C107—41no—
263C23×C107—41no—
264C23×C107—41no—
265C23×C107—41no—
266C23×C107—41no—
267C23×C107—41no—
268C23×C107—41no—
269C23×C107—41no—
270C23×C107—41no—
271C23×C107—41no—
272C23×C107—41no—
273C23×C107—84no—
274C23×C107—84no—
275C23×C107—84no—
276C23×C107—84no—
277C23×C107—84no—
278C23×C107—84no—
279C23×C107C4×D412yes—
280C23×C107C22×D411yescharacteristic
281D4×C107—22no—
282D4×C107—22no—
283D4×C107—22no—
284D4×C107—22no—
285D4×C107—22no—
286D4×C107—22no—
287D4×C107—48no—
288D4×C107—41no—
289D4×C107—41no—
290D4×C107—41no—
291D4×C107—41no—
292D4×C107—41no—
293D4×C107—41no—
294D4×C107—84no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—22no—
298C2×C4×C107—22no—
299C2×C4×C107—22no—
300C2×C4×C107—22no—
301C2×C4×C107—22no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—21no—
313C2×C4×C107—21no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—84no—
329C2×C4×C107C4×D412yes—
330C2×C4×C107C23×C411yescharacteristic
331C2×C4×C107C2×#4111yescharacteristic
332C2×C4×C107H(5,𝔽2)11yescharacteristic
333C2×C4×C107H(5,𝔽2)11yescharacteristic
334C2×C4×C107H(5,𝔽2)11yescharacteristic
335C2×C4×C107H(5,𝔽2)11yescharacteristic
336C8×C107—22no—
337C8×C107—22no—
338C8×C107—41no—
339C8×C107—41no—
340C22×C107—22no—
341C22×C107—22no—
342C22×C107—22no—
343C22×C107—41no—
344C22×C107—41no—
345C22×C107—41no—
346C22×C107—41no—
347C22×C107—42no—
348C22×C107—42no—
349C22×C107—42no—
350C22×C107—42no—
351C22×C107—42no—
352C22×C107—42no—
353C22×C107—42no—
354C22×C107—42no—
355C22×C107—42no—
356C22×C107—816no—
357C22×C107—81no—
358C22×C107—81no—
359C22×C107—81no—
360C22×C107—81no—
361C22×C107—81no—
362C22×C107—81no—
363C22×C107—81no—
364C22×C107—81no—
365C22×C107—81no—
366C22×C107—81no—
367C22×C107—81no—
368C22×C107—81no—
369C22×C107C2×C4×D411yescharacteristic
370C22×C107#53411yescharacteristic
371C22×C107#53511yescharacteristic
372C22×C107#57611yescharacteristic
373C22×C107#57611yescharacteristic
374C22×C107#57611yescharacteristic
375C22×C107#57711yescharacteristic
376C4×C107—22no—
377C4×C107—41no—
378C4×C107—41no—
379C4×C107—41no—
380C4×C107—41no—
381C4×C107—42no—
382C4×C107—81no—
383C4×C107—81no—
384C4×C107—81no—
385C4×C107—81no—
386C4×C107#51811yescharacteristic
387C4×C107#51811yescharacteristic
388C4×C107#53811yescharacteristic
389C4×C107#53811yescharacteristic
390#22056C10711yesmaximal, characteristic, direct product factor, Sylow
391C2×C107—42no—
392C2×C107—82no—
393C2×C107—82no—
394C2×C107—82no—
395C2×C107#232111yescharacteristic
396C2×C107#294611yescharacteristic
397C2×C107#294811yescharacteristic
398C2×C107#319811yescharacteristic
399C2×C107#319911yescharacteristic
400C2×C107#322011yescharacteristic
401C2×C107#322411yescharacteristic
402C2×#447C2×C10711yescharacteristic
403#2324C2×C10711yescharacteristic, complemented
404#2309C2×C10711yescharacteristic, complemented
405#1972C2×C10711yescharacteristic, complemented
406#1970C2×C10711yescharacteristic, complemented
407#1936C2×C10711yescharacteristic, complemented
408#1934C2×C10711yescharacteristic, complemented
409#1926C2×C10711yescharacteristic, complemented
410#1925C2×C10711yescharacteristic, complemented
411#1879C2×C10711yescharacteristic, complemented
412#1879C2×C10711yescharacteristic, complemented
413#1875C2×C10711yescharacteristic, complemented
414#1854C2×C10711yescharacteristic, complemented
415#1786C2×C10711yescharacteristic, complemented
416#1750C2×C10711yescharacteristic, complemented
417C107#2205611yescharacteristic, direct product factor, Sylow
418C23×D4C22×C10711yescharacteristic
419C22×D8C22×C10711yescharacteristic
420C22×D8C22×C10711yescharacteristic
421C2×#121C22×C10711yescharacteristic
422C2×C4×D4C22×C10711yescharacteristic, complemented
423C2×#117C22×C10711yescharacteristic
424C2×#117C22×C10711yescharacteristic
425#447C4×C10718yescomplemented
426C2×#107C22×C10711yescharacteristic, complemented
427C2×#106C22×C10711yescharacteristic, complemented
428C2×#102C22×C10711yescharacteristic
429C2×#102C22×C10711yescharacteristic
430C2×#102C22×C10711yescharacteristic
431C2×#102C22×C10711yescharacteristic
432C2×#102C22×C10711yescharacteristic
433C2×#102C22×C10711yescharacteristic
434C2×#102C22×C10711yescharacteristic, complemented
435C2×#102C22×C10711yescharacteristic, complemented
436C2×C22⋊C8C22×C10711yescharacteristic
437C2×C22⋊C8C22×C10711yescharacteristic
438C2×#97C22×C10711yescharacteristic, complemented
439C2×C4×C8C22×C10711yescharacteristic, complemented
440#390—21no—
441#390—21no—
442#390—21no—
443#390C22×C10711yescharacteristic
444#390C22×C10711yescharacteristic
445#390C22×C10711yescharacteristic
446#390C22×C10711yescharacteristic
447#390C22×C10711yescharacteristic, complemented
448#389C22×C10711yescharacteristic, complemented
449#388—21no—
450#386—21no—
451#385—21no—
452#380C22×C10711yescharacteristic
453#379—21no—
454#379—21no—
455C4×C4⋊C4C22×C10711yescharacteristic, complemented
456#340C22×C10711yescharacteristic, complemented
457#340C22×C10711yescharacteristic, complemented
458#340C22×C10711yescharacteristic, complemented
459#340C22×C10711yescharacteristic, complemented
460#336C22×C10711yescharacteristic, complemented
461#336C22×C10711yescharacteristic, complemented
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×C4×C10714yescomplemented
471C22×D4C23×C10711yescharacteristic
472C22×D4C23×C10711yescharacteristic
473C22×D4C23×C10711yescharacteristic
474C23×C4—21no—
475C23×C4C23×C10711yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×C4×C10714yes—
481C2×D8C2×C4×C10714yes—
482C22×C8C23×C10711yescharacteristic
483C22×C8C23×C10711yescharacteristic
484C22×C8C23×C10711yescharacteristic
485C22×C8C23×C10711yescharacteristic
486#121—22no—
487#121C2×C4×C10714yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4D4×C10711yescharacteristic
496C2×C4⋊C4D4×C10711yescharacteristic
497C2×C4⋊C4C23×C10711yescharacteristic
498C2×C4⋊C4C23×C10711yescharacteristic
499C2×C4⋊C4C23×C10711yescharacteristic
500C2×C4⋊C4C23×C10711yescharacteristic
501C2×C4⋊C4C23×C10711yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C10711yescharacteristic
517C2×C22⋊C4D4×C10711yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C10711yescharacteristic
521C2×C42C23×C10711yescharacteristic
522#107—41no—
523#106—41no—
524#102—41no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102C2×C4×C10714yescomplemented
531#102C2×C4×C10714yescomplemented
532C22⋊C8—22no—
533C22⋊C8C2×C4×C10714yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24C2×D4×C10711yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×C4×C10712yes—
576C2×D4C22×C4×C10712yes—
577C2×D4C22×C4×C10712yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×C4×C10712yes—
591C22×C4C2×D4×C10711yescharacteristic
592C22×C4C2×D4×C10711yescharacteristic
593C22×C4C2×D4×C10711yescharacteristic
594C22×C4C2×D4×C10711yescharacteristic
595C22×C4C2×D4×C10711yescharacteristic
596C22×C4#41×C10712yes—
597C22×C4C24×C10711yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C22×C4×C10712yes—
611C2×C8C22×C4×C10712yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—81no—
624C4⋊C4C22×C4×C10712yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C4×D4×C10712yes—
682C23C22×D4×C10711yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4C4×D4×C10712yes—
732C2×C4C23×C4×C10711yescharacteristic
733C2×C4C2×#41×C10711yescharacteristic
734C2×C4H(5,𝔽2)×C10711yescharacteristic
735C2×C4H(5,𝔽2)×C10711yescharacteristic
736C2×C4H(5,𝔽2)×C10711yescharacteristic
737C2×C4H(5,𝔽2)×C10711yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C4×D4×C10711yescharacteristic
772C22#534×C10711yescharacteristic
773C22#535×C10711yescharacteristic
774C22#576×C10711yescharacteristic
775C22#576×C10711yescharacteristic
776C22#576×C10711yescharacteristic
777C22#577×C10711yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4#518×C10711yescharacteristic
789C4#518×C10711yescharacteristic
790C4#538×C10711yescharacteristic
791C4#538×C10711yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2C107×#232111yescharacteristic
797C2C107×#294611yescharacteristic
798C2C107×#294811yescharacteristic
799C2C107×#319811yescharacteristic
800C2C107×#319911yescharacteristic
801C2C107×#322011yescharacteristic
802C2C107×#322411yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC2×#447×C107C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×#117×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2324C2semidirect
3. C107×#2309C2semidirect
4. C107×#1972C2semidirect
5. C107×#1970C2semidirect
6. C107×#1936C2semidirect
7. C107×#1934C2semidirect
8. C107×#1926C2semidirect
9. C107×#1925C2semidirect
10. C107×#1879C2semidirect
11. C107×#1879C2semidirect
12. C107×#1875C2semidirect
13. C107×#1854C2semidirect
14. C107×#1786C2semidirect
15. C107×#1750C2semidirect
20. C2×C4×D4×C107C22semidirect
23. #447×C107C4semidirect
24. C2×#107×C107C22semidirect
25. C2×#106×C107C22semidirect
32. C2×#102×C107C22semidirect
33. C2×#102×C107C22semidirect
36. C2×#97×C107C22semidirect
37. C2×C4×C8×C107C22semidirect
45. #390×C107C22semidirect
46. #389×C107C22semidirect
53. C4×C4⋊C4×C107C22semidirect
54. #340×C107C22semidirect
55. #340×C107C22semidirect
56. #340×C107C22semidirect
57. #340×C107C22semidirect
58. #336×C107C22semidirect
59. #336×C107C22semidirect
68. C22×D4×C107C2×C4semidirect
128. #102×C107C2×C4semidirect
129. #102×C107C2×C4semidirect
131. C22⋊C8×C107C2×C4semidirect
390. #22056C107direct (N × H)
403. #2324C2×C107semidirect
404. #2309C2×C107semidirect
405. #1972C2×C107semidirect
406. #1970C2×C107semidirect
407. #1936C2×C107semidirect
408. #1934C2×C107semidirect
409. #1926C2×C107semidirect
410. #1925C2×C107semidirect
411. #1879C2×C107semidirect
412. #1879C2×C107semidirect
413. #1875C2×C107semidirect
414. #1854C2×C107semidirect
415. #1786C2×C107semidirect
416. #1750C2×C107semidirect
417. C107#22056direct (N × H)
422. C2×C4×D4C22×C107semidirect
425. #447C4×C107semidirect
426. C2×#107C22×C107semidirect
427. C2×#106C22×C107semidirect
434. C2×#102C22×C107semidirect
435. C2×#102C22×C107semidirect
438. C2×#97C22×C107semidirect
439. C2×C4×C8C22×C107semidirect
447. #390C22×C107semidirect
448. #389C22×C107semidirect
455. C4×C4⋊C4C22×C107semidirect
456. #340C22×C107semidirect
457. #340C22×C107semidirect
458. #340C22×C107semidirect
459. #340C22×C107semidirect
460. #336C22×C107semidirect
461. #336C22×C107semidirect
470. C22×D4C2×C4×C107semidirect
530. #102C2×C4×C107semidirect
531. #102C2×C4×C107semidirect
533. C22⋊C8C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1072
C107×#23242
C107×#23092
C107×#19722
C107×#19702
C107×#19362
C107×#19342
C107×#19262
C107×#19252
C107×#18792
C107×#18752
C107×#18542
C107×#17862
C107×#17502
#22056107