Finite Group Databasebeta

← C107×#23857 #41049821

Subgroups — C107×#23857 #41049821

Order 27392.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C107C211yesmaximal, characteristic, complemented
2C2×#550×C107C211yesmaximal, characteristic, complemented
3C2×#452×C107C211yesmaximal, characteristic, complemented
4C2×#449×C107C211yesmaximal, characteristic, complemented
5C2×#449×C107C211yesmaximal, characteristic, complemented
6C107×#2407C211yesmaximal, characteristic, complemented
7C107×#2014C211yesmaximal, characteristic, complemented
8C107×#2011C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1893C211yesmaximal, characteristic, complemented
12C107×#1880C211yesmaximal, characteristic, complemented
13C107×#1878C211yesmaximal, characteristic, complemented
14C107×#1869C211yesmaximal, characteristic, complemented
15C107×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C22×#41×C107C2211yescharacteristic
19C2×#135×C107—24no—
20C2×#135×C107—24no—
21C2×#135×C107—24no—
22C22×Q16×C107C2211yescharacteristic
23C22×SD16×C107C2211yescharacteristic
24C22×SD16×C107C2211yescharacteristic
25C22×SD16×C107C2211yescharacteristic
26C22×D8×C107C2211yescharacteristic
27C22×D8×C107C2211yescharacteristic
28C23×C8×C107C2211yescharacteristic
29#550×C107—24no—
30#550×C107—24no—
31C2×#127×C107—21no—
32C2×#127×C107C2211yescharacteristic
33C2×C22⋊Q8×C107C2211yescharacteristic
34C2×#121×C107—21no—
35C2×#121×C107—21no—
36C2×#121×C107C2211yescharacteristic
37C2×#121×C107C2211yescharacteristic
38C2×#121×C107C2211yescharacteristic
39C2×C4×Q8×C107C2211yescharacteristic
40C2×C4×D4×C107—21no—
41C2×C4×D4×C107C2211yescharacteristic
42#452×C107—24no—
43#449×C107—24no—
44#449×C107—24no—
45C2×#103×C107C2211yescharacteristic
46C2×#103×C107C2211yescharacteristic
47C2×#103×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic
51C2×#102×C107C2211yescharacteristic
52C2×#102×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic
54C2×C22⋊C8×C107C2211yescharacteristic
55C2×C22⋊C8×C107C2211yescharacteristic
56#394×C107—21no—
57#392×C107—21no—
58#391×C107C2211yescharacteristic
59#390×C107C2211yescharacteristic
60#386×C107—21no—
61#385×C107—21no—
62#380×C107C2211yescharacteristic
63#340×C107C2211yescharacteristic
64#340×C107C2211yescharacteristic
65#336×C107C2211yescharacteristic
66#336×C107C2211yescharacteristic
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—22no—
71C2×#41×C107—22no—
72C2×#41×C107—22no—
73C2×#41×C107—22no—
74C2×#41×C107—22no—
75C2×#41×C107—22no—
76C2×#41×C107—22no—
77C2×#41×C107—22no—
78C2×#41×C107—41no—
79C2×#41×C107—41no—
80C2×#41×C107—41no—
81C2×#41×C107—41no—
82C2×#41×C107—41no—
83C2×#41×C107—41no—
84C2×#41×C107D414yescomplemented
85C22×Q8×C107C2311yescharacteristic
86C22×Q8×C107C2311yescharacteristic
87C22×D4×C107—21no—
88C22×D4×C107—21no—
89C22×D4×C107—21no—
90C22×D4×C107—21no—
91C22×D4×C107—21no—
92C22×D4×C107—21no—
93C22×D4×C107—21no—
94C22×D4×C107—21no—
95C22×D4×C107D411yescharacteristic
96C22×D4×C107C2311yescharacteristic
97C22×D4×C107C2311yescharacteristic
98C22×D4×C107C2311yescharacteristic
99C23×C4×C107—21no—
100C23×C4×C107—21no—
101C23×C4×C107—21no—
102C23×C4×C107C2311yescharacteristic
103C23×C4×C107C2311yescharacteristic
104#135×C107—232no—
105C2×Q16×C107—22no—
106C2×Q16×C107—22no—
107C2×Q16×C107D414yescomplemented
108C2×SD16×C107—22no—
109C2×SD16×C107—22no—
110C2×SD16×C107—22no—
111C2×SD16×C107—22no—
112C2×SD16×C107—22no—
113C2×SD16×C107—22no—
114C2×SD16×C107—22no—
115C2×SD16×C107—41no—
116C2×SD16×C107D414yescomplemented
117C2×D8×C107—22no—
118C2×D8×C107—22no—
119C2×D8×C107—22no—
120C2×D8×C107—22no—
121C2×D8×C107—22no—
122C2×D8×C107—41no—
123C22×C8×C107—22no—
124C22×C8×C107—22no—
125C22×C8×C107—22no—
126C22×C8×C107C2311yescharacteristic
127C22×C8×C107C2311yescharacteristic
128C22×C8×C107C2311yescharacteristic
129C22×C8×C107C2311yescharacteristic
130#127×C107—28no—
131#127×C107—22no—
132#127×C107—22no—
133C22⋊Q8×C107—22no—
134C22⋊Q8×C107—41no—
135#121×C107—28no—
136#121×C107—28no—
137#121×C107—22no—
138#121×C107—22no—
139#121×C107—22no—
140#121×C107—22no—
141#121×C107—41no—
142#121×C107D414yescomplemented
143C4×Q8×C107—22no—
144C4×Q8×C107—22no—
145C4×D4×C107—28no—
146C4×D4×C107—22no—
147C4×D4×C107—22no—
148C2×C4⋊C4×C107—21no—
149C2×C4⋊C4×C107—21no—
150C2×C4⋊C4×C107D411yescharacteristic
151C2×C4⋊C4×C107C2311yescharacteristic
152C2×C4⋊C4×C107C2311yescharacteristic
153C2×C4⋊C4×C107C2311yescharacteristic
154C2×C22⋊C4×C107—21no—
155C2×C22⋊C4×C107—21no—
156C2×C22⋊C4×C107—21no—
157C2×C22⋊C4×C107—21no—
158C2×C22⋊C4×C107—21no—
159C2×C22⋊C4×C107—21no—
160C2×C22⋊C4×C107—21no—
161C2×C22⋊C4×C107D411yescharacteristic
162C2×C22⋊C4×C107D411yescharacteristic
163C2×C42×C107—21no—
164C2×C42×C107C2311yescharacteristic
165#103×C107—22no—
166#103×C107—22no—
167#103×C107—22no—
168#102×C107—22no—
169#102×C107—22no—
170#102×C107—22no—
171#102×C107—41no—
172#102×C107—41no—
173C22⋊C8×C107—22no—
174C22⋊C8×C107—22no—
175C22⋊C8×C107—22no—
176#95×C107—21no—
177#95×C107—21no—
178#95×C107—21no—
179C24×C107—21no—
180C24×C107—21no—
181C24×C107—21no—
182C24×C107C2×D411yescharacteristic
183C24×C107C2×D411yescharacteristic
184#41×C107—28no—
185#41×C107—28no—
186#41×C107—44no—
187#41×C107—44no—
188#41×C107—44no—
189#41×C107—44no—
190#41×C107—44no—
191#41×C107—44no—
192#41×C107—44no—
193#41×C107—44no—
194#41×C107—44no—
195#41×C107—44no—
196C2×Q8×C107—21no—
197C2×Q8×C107—21no—
198C2×Q8×C107—21no—
199C2×Q8×C107—21no—
200C2×Q8×C107—21no—
201C2×Q8×C107—21no—
202C2×Q8×C107—21no—
203C2×Q8×C107—21no—
204C2×Q8×C107C2×D412yes—
205C2×Q8×C107C2×D412yes—
206C2×Q8×C107C2×D412yes—
207C2×Q8×C107C2×D412yes—
208C2×D4×C107—24no—
209C2×D4×C107—24no—
210C2×D4×C107—22no—
211C2×D4×C107—24no—
212C2×D4×C107—24no—
213C2×D4×C107—24no—
214C2×D4×C107—24no—
215C2×D4×C107—22no—
216C2×D4×C107—21no—
217C2×D4×C107—21no—
218C2×D4×C107—21no—
219C2×D4×C107—21no—
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—21no—
223C2×D4×C107—21no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—21no—
229C2×D4×C107—21no—
230C2×D4×C107—21no—
231C2×D4×C107—41no—
232C2×D4×C107—42no—
233C2×D4×C107—42no—
234C2×D4×C107—42no—
235C2×D4×C107—42no—
236C2×D4×C107—42no—
237C2×D4×C107—42no—
238C2×D4×C107—42no—
239C2×D4×C107—42no—
240C2×D4×C107—42no—
241C2×D4×C107—42no—
242C2×D4×C107—42no—
243C2×D4×C107—81no—
244C2×D4×C107—81no—
245C2×D4×C107—81no—
246C2×D4×C107—81no—
247C2×D4×C107—81no—
248C2×D4×C107—81no—
249C2×D4×C107—81no—
250C2×D4×C107C2×D412yes—
251C2×D4×C107C2×D412yes—
252C2×D4×C107C2×D412yes—
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—24no—
259C22×C4×C107—21no—
260C22×C4×C107—21no—
261C22×C4×C107—24no—
262C22×C4×C107—21no—
263C22×C4×C107—21no—
264C22×C4×C107—21no—
265C22×C4×C107—21no—
266C22×C4×C107—21no—
267C22×C4×C107—21no—
268C22×C4×C107—21no—
269C22×C4×C107—21no—
270C22×C4×C107—42no—
271C22×C4×C107—42no—
272C22×C4×C107—42no—
273C22×C4×C107—42no—
274C22×C4×C107—42no—
275C22×C4×C107—42no—
276C22×C4×C107—42no—
277C22×C4×C107C2×D411yescharacteristic
278C22×C4×C107C2×D411yescharacteristic
279C22×C4×C107C2×D411yescharacteristic
280C22×C4×C107C2×D412yes—
281C22×C4×C107C2×D412yes—
282C22×C4×C107C2×D411yescharacteristic
283C22×C4×C107C2411yescharacteristic
284Q16×C107—28no—
285SD16×C107—28no—
286SD16×C107—28no—
287SD16×C107—44no—
288D8×C107—28no—
289D8×C107—44no—
290C2×C8×C107—28no—
291C2×C8×C107—21no—
292C2×C8×C107—21no—
293C2×C8×C107—21no—
294C2×C8×C107—21no—
295C2×C8×C107—21no—
296C2×C8×C107—21no—
297C2×C8×C107—21no—
298C2×C8×C107—21no—
299C2×C8×C107—21no—
300C2×C8×C107—21no—
301C2×C8×C107C2×D412yes—
302C2×C8×C107C2×D412yes—
303C4⋊C4×C107—24no—
304C4⋊C4×C107—22no—
305C4⋊C4×C107—21no—
306C4⋊C4×C107—21no—
307C4⋊C4×C107—21no—
308C4⋊C4×C107—21no—
309C4⋊C4×C107—21no—
310C4⋊C4×C107—42no—
311C4⋊C4×C107C2×D412yes—
312C22⋊C4×C107—24no—
313C22⋊C4×C107—22no—
314C22⋊C4×C107—24no—
315C22⋊C4×C107—22no—
316C22⋊C4×C107—42no—
317C22⋊C4×C107—42no—
318C22⋊C4×C107—42no—
319C22⋊C4×C107—81no—
320C22⋊C4×C107—81no—
321C42×C107—24no—
322C42×C107—21no—
323C42×C107—21no—
324C23×C107—21no—
325C23×C107—21no—
326C23×C107—21no—
327C23×C107—21no—
328C23×C107—21no—
329C23×C107—21no—
330C23×C107—21no—
331C23×C107—22no—
332C23×C107—22no—
333C23×C107—21no—
334C23×C107—22no—
335C23×C107—21no—
336C23×C107—21no—
337C23×C107—21no—
338C23×C107—21no—
339C23×C107—21no—
340C23×C107—41no—
341C23×C107—41no—
342C23×C107—41no—
343C23×C107—41no—
344C23×C107—41no—
345C23×C107—41no—
346C23×C107—41no—
347C23×C107—41no—
348C23×C107—41no—
349C23×C107—41no—
350C23×C107—41no—
351C23×C107—41no—
352C23×C107—41no—
353C23×C107—41no—
354C23×C107—41no—
355C23×C107—41no—
356C23×C107—41no—
357C23×C107—41no—
358C23×C107#12012yes—
359C23×C107C22×D411yescharacteristic
360Q8×C107—22no—
361Q8×C107—22no—
362Q8×C107—22no—
363Q8×C107—22no—
364Q8×C107—22no—
365Q8×C107—41no—
366Q8×C107—41no—
367Q8×C107#12014yes—
368D4×C107—22no—
369D4×C107—22no—
370D4×C107—22no—
371D4×C107—22no—
372D4×C107—22no—
373D4×C107—22no—
374D4×C107—44no—
375D4×C107—48no—
376D4×C107—48no—
377D4×C107—48no—
378D4×C107—48no—
379D4×C107—41no—
380D4×C107—41no—
381D4×C107—41no—
382D4×C107—41no—
383D4×C107—41no—
384D4×C107—41no—
385D4×C107—84no—
386D4×C107—84no—
387D4×C107—84no—
388D4×C107—84no—
389C2×C4×C107—21no—
390C2×C4×C107—22no—
391C2×C4×C107—21no—
392C2×C4×C107—21no—
393C2×C4×C107—22no—
394C2×C4×C107—22no—
395C2×C4×C107—21no—
396C2×C4×C107—22no—
397C2×C4×C107—22no—
398C2×C4×C107—22no—
399C2×C4×C107—22no—
400C2×C4×C107—21no—
401C2×C4×C107—22no—
402C2×C4×C107—21no—
403C2×C4×C107—21no—
404C2×C4×C107—22no—
405C2×C4×C107—21no—
406C2×C4×C107—21no—
407C2×C4×C107—21no—
408C2×C4×C107—48no—
409C2×C4×C107—48no—
410C2×C4×C107—48no—
411C2×C4×C107—41no—
412C2×C4×C107—41no—
413C2×C4×C107—41no—
414C2×C4×C107—41no—
415C2×C4×C107—41no—
416C2×C4×C107—41no—
417C2×C4×C107—41no—
418C2×C4×C107—41no—
419C2×C4×C107—41no—
420C2×C4×C107—41no—
421C2×C4×C107—41no—
422C2×C4×C107—41no—
423C2×C4×C107—41no—
424C2×C4×C107—41no—
425C2×C4×C107#12012yes—
426C2×C4×C107#13512yescomplemented
427C2×C4×C107C22×D411yescharacteristic
428C2×C4×C107C22×D411yescharacteristic
429C2×C4×C107C22×D411yescharacteristic
430C2×C4×C107C22×D411yescharacteristic
431C2×C4×C107H(5,𝔽2)11yescharacteristic
432C2×C4×C107H(5,𝔽2)11yescharacteristic
433C8×C107—22no—
434C8×C107—22no—
435C8×C107—41no—
436C8×C107—41no—
437C22×C107—22no—
438C22×C107—22no—
439C22×C107—22no—
440C22×C107—41no—
441C22×C107—41no—
442C22×C107—41no—
443C22×C107—41no—
444C22×C107—42no—
445C22×C107—42no—
446C22×C107—42no—
447C22×C107—41no—
448C22×C107—41no—
449C22×C107—42no—
450C22×C107—42no—
451C22×C107—41no—
452C22×C107—42no—
453C22×C107—42no—
454C22×C107—41no—
455C22×C107—42no—
456C22×C107—41no—
457C22×C107—41no—
458C22×C107—42no—
459C22×C107—41no—
460C22×C107—81no—
461C22×C107—81no—
462C22×C107—81no—
463C22×C107—81no—
464C22×C107—81no—
465C22×C107—81no—
466C22×C107—81no—
467C22×C107—81no—
468C22×C107—81no—
469C22×C107—81no—
470C22×C107—81no—
471C22×C107—81no—
472C22×C107C2×#12011yescharacteristic
473C22×C107D4211yescharacteristic
474C22×C107D4211yescharacteristic
475C22×C107C2×#13511yescharacteristic
476C22×C107#57511yescharacteristic
477C22×C107#57611yescharacteristic
478C22×C107#57711yescharacteristic
479C4×C107—22no—
480C4×C107—24no—
481C4×C107—22no—
482C4×C107—41no—
483C4×C107—42no—
484C4×C107—41no—
485C4×C107—42no—
486C4×C107—81no—
487C4×C107—81no—
488C4×C107C2×#12011yescharacteristic
489C4×C107#53411yescharacteristic
490C4×C107D4211yescharacteristic
491C4×C107D4211yescharacteristic
492#23857C10711yesmaximal, characteristic, direct product factor, Sylow
493C2×C107—42no—
494C2×C107—81no—
495C2×C107—82no—
496C2×C107—82no—
497C2×C107—82no—
498C2×C107#240311yescharacteristic
499C2×C107#300211yescharacteristic
500C2×C107#301211yescharacteristic
501C2×C107#326811yescharacteristic
502C2×C107#327111yescharacteristic
503C2×C107#328411yescharacteristic
504C2×C107#328711yescharacteristic
505C22×#135C2×C10711yescharacteristic, complemented
506C2×#550C2×C10711yescharacteristic, complemented
507C2×#452C2×C10711yescharacteristic, complemented
508C2×#449C2×C10711yescharacteristic, complemented
509C2×#449C2×C10711yescharacteristic, complemented
510#2407C2×C10711yescharacteristic, complemented
511#2014C2×C10711yescharacteristic, complemented
512#2011C2×C10711yescharacteristic, complemented
513#2000C2×C10711yescharacteristic, complemented
514#1999C2×C10711yescharacteristic, complemented
515#1893C2×C10711yescharacteristic, complemented
516#1880C2×C10711yescharacteristic, complemented
517#1878C2×C10711yescharacteristic, complemented
518#1869C2×C10711yescharacteristic, complemented
519#1788C2×C10711yescharacteristic, complemented
520C107#2385711yescharacteristic, direct product factor, Sylow
521C22×#41C22×C10711yescharacteristic
522C22×#41C22×C10711yescharacteristic
523C22×#41C22×C10711yescharacteristic
524C2×#135—24no—
525C2×#135—24no—
526C2×#135—24no—
527C22×Q16C22×C10711yescharacteristic
528C22×SD16C22×C10711yescharacteristic
529C22×SD16C22×C10711yescharacteristic
530C22×SD16C22×C10711yescharacteristic
531C22×D8C22×C10711yescharacteristic
532C22×D8C22×C10711yescharacteristic
533C23×C8C22×C10711yescharacteristic
534#550—24no—
535#550—24no—
536C2×#127—21no—
537C2×#127C22×C10711yescharacteristic
538C2×C22⋊Q8C22×C10711yescharacteristic
539C2×#121—21no—
540C2×#121—21no—
541C2×#121C22×C10711yescharacteristic
542C2×#121C22×C10711yescharacteristic
543C2×#121C22×C10711yescharacteristic
544C2×C4×Q8C22×C10711yescharacteristic
545C2×C4×D4—21no—
546C2×C4×D4C22×C10711yescharacteristic
547#452—24no—
548#449—24no—
549#449—24no—
550C2×#103C22×C10711yescharacteristic
551C2×#103C22×C10711yescharacteristic
552C2×#103C22×C10711yescharacteristic
553C2×#102C22×C10711yescharacteristic
554C2×#102C22×C10711yescharacteristic
555C2×#102C22×C10711yescharacteristic
556C2×#102C22×C10711yescharacteristic
557C2×#102C22×C10711yescharacteristic
558C2×C22⋊C8C22×C10711yescharacteristic
559C2×C22⋊C8C22×C10711yescharacteristic
560C2×C22⋊C8C22×C10711yescharacteristic
561#394—21no—
562#392—21no—
563#391C22×C10711yescharacteristic
564#390C22×C10711yescharacteristic
565#386—21no—
566#385—21no—
567#380C22×C10711yescharacteristic
568#340C22×C10711yescharacteristic
569#340C22×C10711yescharacteristic
570#336C22×C10711yescharacteristic
571#336C22×C10711yescharacteristic
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—41no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C10714yescomplemented
590C22×Q8C23×C10711yescharacteristic
591C22×Q8C23×C10711yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4D4×C10711yescharacteristic
601C22×D4C23×C10711yescharacteristic
602C22×D4C23×C10711yescharacteristic
603C22×D4C23×C10711yescharacteristic
604C23×C4—21no—
605C23×C4—21no—
606C23×C4—21no—
607C23×C4C23×C10711yescharacteristic
608C23×C4C23×C10711yescharacteristic
609#135—232no—
610C2×Q16—22no—
611C2×Q16—22no—
612C2×Q16D4×C10714yescomplemented
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—41no—
621C2×SD16D4×C10714yescomplemented
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—41no—
628C22×C8—22no—
629C22×C8—22no—
630C22×C8—22no—
631C22×C8C23×C10711yescharacteristic
632C22×C8C23×C10711yescharacteristic
633C22×C8C23×C10711yescharacteristic
634C22×C8C23×C10711yescharacteristic
635#127—28no—
636#127—22no—
637#127—22no—
638C22⋊Q8—22no—
639C22⋊Q8—41no—
640#121—28no—
641#121—28no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121—22no—
646#121—41no—
647#121D4×C10714yescomplemented
648C4×Q8—22no—
649C4×Q8—22no—
650C4×D4—28no—
651C4×D4—22no—
652C4×D4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4D4×C10711yescharacteristic
656C2×C4⋊C4C23×C10711yescharacteristic
657C2×C4⋊C4C23×C10711yescharacteristic
658C2×C4⋊C4C23×C10711yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4D4×C10711yescharacteristic
667C2×C22⋊C4D4×C10711yescharacteristic
668C2×C42—21no—
669C2×C42C23×C10711yescharacteristic
670#103—22no—
671#103—22no—
672#103—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681#95—21no—
682#95—21no—
683#95—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×D4×C10711yescharacteristic
688C24C2×D4×C10711yescharacteristic
689#41—28no—
690#41—28no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700#41—44no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8C2×D4×C10712yes—
710C2×Q8C2×D4×C10712yes—
711C2×Q8C2×D4×C10712yes—
712C2×Q8C2×D4×C10712yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×D4×C10712yes—
756C2×D4C2×D4×C10712yes—
757C2×D4C2×D4×C10712yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2×D4×C10711yescharacteristic
783C22×C4C2×D4×C10711yescharacteristic
784C22×C4C2×D4×C10711yescharacteristic
785C22×C4C2×D4×C10712yes—
786C22×C4C2×D4×C10712yes—
787C22×C4C2×D4×C10711yescharacteristic
788C22×C4C24×C10711yescharacteristic
789Q16—28no—
790SD16—28no—
791SD16—28no—
792SD16—44no—
793D8—28no—
794D8—44no—
795C2×C8—28no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×D4×C10712yes—
807C2×C8C2×D4×C10712yes—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4C2×D4×C10712yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C42—24no—
827C42—21no—
828C42—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23#120×C10712yes—
864C23C22×D4×C10711yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8#120×C10714yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4#120×C10712yes—
931C2×C4#135×C10712yescomplemented
932C2×C4C22×D4×C10711yescharacteristic
933C2×C4C22×D4×C10711yescharacteristic
934C2×C4C22×D4×C10711yescharacteristic
935C2×C4C22×D4×C10711yescharacteristic
936C2×C4H(5,𝔽2)×C10711yescharacteristic
937C2×C4H(5,𝔽2)×C10711yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×#120×C10711yescharacteristic
978C22D42×C10711yescharacteristic
979C22D42×C10711yescharacteristic
980C22C2×#135×C10711yescharacteristic
981C22#575×C10711yescharacteristic
982C22#576×C10711yescharacteristic
983C22#577×C10711yescharacteristic
984C4—22no—
985C4—24no—
986C4—22no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×#120×C10711yescharacteristic
994C4#534×C10711yescharacteristic
995C4D42×C10711yescharacteristic
996C4D42×C10711yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2C107×#240311yescharacteristic
1003C2C107×#300211yescharacteristic
1004C2C107×#301211yescharacteristic
1005C2C107×#326811yescharacteristic
1006C2C107×#327111yescharacteristic
1007C2C107×#328411yescharacteristic
1008C2C107×#328711yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C107C2semidirect
2. C2×#550×C107C2semidirect
3. C2×#452×C107C2semidirect
4. C2×#449×C107C2semidirect
5. C2×#449×C107C2semidirect
6. C107×#2407C2semidirect
7. C107×#2014C2semidirect
8. C107×#2011C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1893C2semidirect
12. C107×#1880C2semidirect
13. C107×#1878C2semidirect
14. C107×#1869C2semidirect
15. C107×#1788C2semidirect
84. C2×#41×C107D4semidirect
107. C2×Q16×C107D4semidirect
116. C2×SD16×C107D4semidirect
142. #121×C107D4semidirect
426. C2×C4×C107#135semidirect
492. #23857C107direct (N × H)
505. C22×#135C2×C107semidirect
506. C2×#550C2×C107semidirect
507. C2×#452C2×C107semidirect
508. C2×#449C2×C107semidirect
509. C2×#449C2×C107semidirect
510. #2407C2×C107semidirect
511. #2014C2×C107semidirect
512. #2011C2×C107semidirect
513. #2000C2×C107semidirect
514. #1999C2×C107semidirect
515. #1893C2×C107semidirect
516. #1880C2×C107semidirect
517. #1878C2×C107semidirect
518. #1869C2×C107semidirect
519. #1788C2×C107semidirect
520. C107#23857direct (N × H)
589. C2×#41D4×C107semidirect
612. C2×Q16D4×C107semidirect
621. C2×SD16D4×C107semidirect
647. #121D4×C107semidirect
931. C2×C4#135×C107semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1072
C2×#550×C1072
C2×#452×C1072
C2×#449×C1072
C107×#24072
C107×#20142
C107×#20112
C107×#20002
C107×#19992
C107×#18932
C107×#18802
C107×#18782
C107×#18692
C107×#17882
#23857107