Finite Group Databasebeta

← C107×#23854 #41049818

Subgroups — C107×#23854 #41049818

Order 27392.

1794 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C107C211yesmaximal, characteristic, complemented
2C2×#548×C107C211yesmaximal, characteristic, complemented
3C2×#452×C107C211yesmaximal, characteristic, complemented
4C2×#451×C107C211yesmaximal, characteristic, complemented
5C2×#448×C107C211yesmaximal, characteristic, complemented
6C107×#2407C211yesmaximal, characteristic, complemented
7C107×#2015C211yesmaximal, characteristic, complemented
8C107×#2012C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1892C211yesmaximal, characteristic, complemented
12C107×#1880C211yesmaximal, characteristic, complemented
13C107×#1878C211yesmaximal, characteristic, complemented
14C107×#1869C211yesmaximal, characteristic, complemented
15C107×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C23×Q8×C107C2211yescharacteristic
19C2×#135×C107—24no—
20C2×#135×C107—24no—
21C2×#135×C107—24no—
22C22×Q16×C107C2211yescharacteristic
23C22×Q16×C107C2211yescharacteristic
24C22×SD16×C107C2211yescharacteristic
25C22×SD16×C107C2211yescharacteristic
26C22×SD16×C107C2211yescharacteristic
27C22×D8×C107C2211yescharacteristic
28C23×C8×C107C2211yescharacteristic
29#548×C107—24no—
30#548×C107—24no—
31C2×#124×C107—21no—
32C2×#124×C107C2211yescharacteristic
33C2×C22⋊Q8×C107—21no—
34C2×C22⋊Q8×C107C2211yescharacteristic
35C2×C22⋊Q8×C107C2211yescharacteristic
36C2×#121×C107—21no—
37C2×#121×C107C2211yescharacteristic
38C2×#121×C107C2211yescharacteristic
39C2×C4×Q8×C107C2211yescharacteristic
40C2×C4×D4×C107—21no—
41C2×C4×D4×C107C2211yescharacteristic
42#452×C107—24no—
43#451×C107—24no—
44#448×C107—24no—
45C2×#103×C107C2211yescharacteristic
46C2×#103×C107C2211yescharacteristic
47C2×#103×C107C2211yescharacteristic
48C2×#103×C107C2211yescharacteristic
49C2×#103×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—41no—
75C2×#41×C107—41no—
76C2×#41×C107—41no—
77C2×#41×C107—41no—
78C2×#41×C107D414yescomplemented
79C22×Q8×C107—22no—
80C22×Q8×C107—22no—
81C22×Q8×C107—21no—
82C22×Q8×C107—22no—
83C22×Q8×C107—22no—
84C22×Q8×C107—41no—
85C22×Q8×C107—41no—
86C22×Q8×C107C2311yescharacteristic
87C22×Q8×C107C2311yescharacteristic
88C22×Q8×C107C2311yescharacteristic
89C22×D4×C107—21no—
90C22×D4×C107—21no—
91C22×D4×C107—21no—
92C22×D4×C107—21no—
93C22×D4×C107D411yescharacteristic
94C22×D4×C107C2311yescharacteristic
95C22×D4×C107C2311yescharacteristic
96C23×C4×C107—21no—
97C23×C4×C107—21no—
98C23×C4×C107—21no—
99C23×C4×C107C2311yescharacteristic
100C23×C4×C107C2311yescharacteristic
101#135×C107—232no—
102C2×Q16×C107—22no—
103C2×Q16×C107—22no—
104C2×Q16×C107—22no—
105C2×Q16×C107—22no—
106C2×Q16×C107—41no—
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—
120C22×C8×C107—22no—
121C22×C8×C107—22no—
122C22×C8×C107—22no—
123C22×C8×C107C2311yescharacteristic
124C22×C8×C107C2311yescharacteristic
125C22×C8×C107C2311yescharacteristic
126C22×C8×C107C2311yescharacteristic
127#124×C107—28no—
128#124×C107—22no—
129#124×C107—22no—
130C22⋊Q8×C107—28no—
131C22⋊Q8×C107—22no—
132C22⋊Q8×C107—22no—
133C22⋊Q8×C107—41no—
134C22⋊Q8×C107D414yescomplemented
135#121×C107—28no—
136#121×C107—22no—
137#121×C107—22no—
138#121×C107—22no—
139#121×C107—41no—
140C4×Q8×C107—22no—
141C4×Q8×C107—22no—
142C4×D4×C107—28no—
143C4×D4×C107—22no—
144C4×D4×C107—22no—
145C2×C4⋊C4×C107—21no—
146C2×C4⋊C4×C107—21no—
147C2×C4⋊C4×C107—21no—
148C2×C4⋊C4×C107D411yescharacteristic
149C2×C4⋊C4×C107C2311yescharacteristic
150C2×C4⋊C4×C107C2311yescharacteristic
151C2×C4⋊C4×C107C2311yescharacteristic
152C2×C22⋊C4×C107—21no—
153C2×C22⋊C4×C107—21no—
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#103×C107—22no—
169#103×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×C107C2×D411yescharacteristic
182C24×C107C2×D411yescharacteristic
183#41×C107—28no—
184#41×C107—28no—
185#41×C107—44no—
186#41×C107—44no—
187#41×C107—44no—
188#41×C107—44no—
189#41×C107—44no—
190#41×C107—44no—
191C2×Q8×C107—24no—
192C2×Q8×C107—21no—
193C2×Q8×C107—21no—
194C2×Q8×C107—21no—
195C2×Q8×C107—21no—
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×C107—21no—
205C2×Q8×C107—42no—
206C2×Q8×C107—42no—
207C2×Q8×C107—44no—
208C2×Q8×C107—44no—
209C2×Q8×C107—44no—
210C2×Q8×C107—44no—
211C2×Q8×C107C2×D412yes—
212C2×Q8×C107C2×D412yes—
213C2×Q8×C107C2×D412yes—
214C2×Q8×C107C2×D412yes—
215C2×Q8×C107C2×D412yes—
216C2×D4×C107—24no—
217C2×D4×C107—22no—
218C2×D4×C107—24no—
219C2×D4×C107—22no—
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—41no—
231C2×D4×C107—42no—
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—81no—
241C2×D4×C107C2×D412yes—
242C2×D4×C107C2×D412yes—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—24no—
249C22×C4×C107—21no—
250C22×C4×C107—21no—
251C22×C4×C107—21no—
252C22×C4×C107—24no—
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—21no—
259C22×C4×C107—21no—
260C22×C4×C107—21no—
261C22×C4×C107—42no—
262C22×C4×C107—42no—
263C22×C4×C107—42no—
264C22×C4×C107—42no—
265C22×C4×C107—42no—
266C22×C4×C107—42no—
267C22×C4×C107—42no—
268C22×C4×C107C2×D411yescharacteristic
269C22×C4×C107C2×D411yescharacteristic
270C22×C4×C107C2×D411yescharacteristic
271C22×C4×C107C2×D411yescharacteristic
272C22×C4×C107C2×D412yes—
273C22×C4×C107C2×D412yes—
274C22×C4×C107C2411yescharacteristic
275Q16×C107—28no—
276Q16×C107—44no—
277SD16×C107—28no—
278SD16×C107—28no—
279SD16×C107—44no—
280D8×C107—28no—
281C2×C8×C107—28no—
282C2×C8×C107—21no—
283C2×C8×C107—21no—
284C2×C8×C107—21no—
285C2×C8×C107—21no—
286C2×C8×C107—21no—
287C2×C8×C107—21no—
288C2×C8×C107—21no—
289C2×C8×C107—21no—
290C2×C8×C107—21no—
291C2×C8×C107—21no—
292C2×C8×C107C2×D412yes—
293C2×C8×C107C2×D412yes—
294C4⋊C4×C107—24no—
295C4⋊C4×C107—24no—
296C4⋊C4×C107—22no—
297C4⋊C4×C107—21no—
298C4⋊C4×C107—21no—
299C4⋊C4×C107—21no—
300C4⋊C4×C107—21no—
301C4⋊C4×C107—21no—
302C4⋊C4×C107—42no—
303C4⋊C4×C107C2×D412yes—
304C22⋊C4×C107—24no—
305C22⋊C4×C107—24no—
306C22⋊C4×C107—24no—
307C22⋊C4×C107—24no—
308C22⋊C4×C107—22no—
309C22⋊C4×C107—22no—
310C22⋊C4×C107—42no—
311C22⋊C4×C107—42no—
312C22⋊C4×C107—42no—
313C22⋊C4×C107—81no—
314C22⋊C4×C107—81no—
315C42×C107—24no—
316C42×C107—21no—
317C42×C107—21no—
318C23×C107—21no—
319C23×C107—21no—
320C23×C107—21no—
321C23×C107—21no—
322C23×C107—21no—
323C23×C107—21no—
324C23×C107—21no—
325C23×C107—21no—
326C23×C107—21no—
327C23×C107—21no—
328C23×C107—21no—
329C23×C107—21no—
330C23×C107—22no—
331C23×C107—22no—
332C23×C107—41no—
333C23×C107—41no—
334C23×C107—41no—
335C23×C107—41no—
336C23×C107—41no—
337C23×C107—41no—
338C23×C107—41no—
339C23×C107—41no—
340C23×C107—41no—
341C23×C107—41no—
342C23×C107—41no—
343C23×C107—41no—
344C23×C107#12012yes—
345C23×C107#13512yescomplemented
346C23×C107C22×D411yescharacteristic
347Q8×C107—22no—
348Q8×C107—22no—
349Q8×C107—22no—
350Q8×C107—22no—
351Q8×C107—22no—
352Q8×C107—22no—
353Q8×C107—22no—
354Q8×C107—48no—
355Q8×C107—41no—
356Q8×C107—41no—
357Q8×C107—41no—
358Q8×C107—41no—
359Q8×C107#12014yes—
360D4×C107—22no—
361D4×C107—22no—
362D4×C107—22no—
363D4×C107—22no—
364D4×C107—48no—
365D4×C107—44no—
366D4×C107—48no—
367D4×C107—48no—
368D4×C107—41no—
369D4×C107—41no—
370D4×C107—41no—
371D4×C107—41no—
372D4×C107—84no—
373C2×C4×C107—22no—
374C2×C4×C107—21no—
375C2×C4×C107—21no—
376C2×C4×C107—22no—
377C2×C4×C107—22no—
378C2×C4×C107—22no—
379C2×C4×C107—22no—
380C2×C4×C107—22no—
381C2×C4×C107—22no—
382C2×C4×C107—21no—
383C2×C4×C107—21no—
384C2×C4×C107—22no—
385C2×C4×C107—22no—
386C2×C4×C107—21no—
387C2×C4×C107—21no—
388C2×C4×C107—22no—
389C2×C4×C107—21no—
390C2×C4×C107—21no—
391C2×C4×C107—21no—
392C2×C4×C107—21no—
393C2×C4×C107—21no—
394C2×C4×C107—48no—
395C2×C4×C107—48no—
396C2×C4×C107—48no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—41no—
402C2×C4×C107—41no—
403C2×C4×C107—41no—
404C2×C4×C107—41no—
405C2×C4×C107—41no—
406C2×C4×C107—41no—
407C2×C4×C107—41no—
408C2×C4×C107—41no—
409C2×C4×C107—41no—
410C2×C4×C107—41no—
411C2×C4×C107—41no—
412C2×C4×C107—41no—
413C2×C4×C107#12012yes—
414C2×C4×C107C22×D411yescharacteristic
415C2×C4×C107C22×D411yescharacteristic
416C2×C4×C107C22×D411yescharacteristic
417C2×C4×C107C22×D411yescharacteristic
418C2×C4×C107H(5,𝔽2)11yescharacteristic
419C2×C4×C107H(5,𝔽2)11yescharacteristic
420C8×C107—22no—
421C8×C107—22no—
422C8×C107—41no—
423C8×C107—41no—
424C22×C107—22no—
425C22×C107—22no—
426C22×C107—22no—
427C22×C107—22no—
428C22×C107—22no—
429C22×C107—22no—
430C22×C107—41no—
431C22×C107—41no—
432C22×C107—41no—
433C22×C107—41no—
434C22×C107—41no—
435C22×C107—41no—
436C22×C107—41no—
437C22×C107—41no—
438C22×C107—42no—
439C22×C107—42no—
440C22×C107—42no—
441C22×C107—42no—
442C22×C107—42no—
443C22×C107—42no—
444C22×C107—81no—
445C22×C107—81no—
446C22×C107—81no—
447C22×C107—81no—
448C22×C107—81no—
449C22×C107—81no—
450C22×C107—81no—
451C22×C107—81no—
452C22×C107C2×#12011yescharacteristic
453C22×C107D4211yescharacteristic
454C22×C107D4211yescharacteristic
455C22×C107C2×#13511yescharacteristic
456C22×C107#57511yescharacteristic
457C22×C107#57711yescharacteristic
458C22×C107#57811yescharacteristic
459C4×C107—22no—
460C4×C107—24no—
461C4×C107—41no—
462C4×C107—42no—
463C4×C107—42no—
464C4×C107—41no—
465C4×C107—42no—
466C4×C107—41no—
467C4×C107—81no—
468C4×C107—81no—
469C4×C107C2×#12011yescharacteristic
470C4×C107#53411yescharacteristic
471C4×C107D4211yescharacteristic
472C4×C107D4211yescharacteristic
473#23854C10711yesmaximal, characteristic, direct product factor, Sylow
474C2×C107—42no—
475C2×C107—42no—
476C2×C107—82no—
477C2×C107—82no—
478C2×C107#240311yescharacteristic
479C2×C107#300211yescharacteristic
480C2×C107#301311yescharacteristic
481C2×C107#326911yescharacteristic
482C2×C107#327111yescharacteristic
483C2×C107#328211yescharacteristic
484C2×C107#328511yescharacteristic
485C22×#135C2×C10711yescharacteristic, complemented
486C2×#548C2×C10711yescharacteristic, complemented
487C2×#452C2×C10711yescharacteristic, complemented
488C2×#451C2×C10711yescharacteristic, complemented
489C2×#448C2×C10711yescharacteristic, complemented
490#2407C2×C10711yescharacteristic, complemented
491#2015C2×C10711yescharacteristic, complemented
492#2012C2×C10711yescharacteristic, complemented
493#2000C2×C10711yescharacteristic, complemented
494#1999C2×C10711yescharacteristic, complemented
495#1892C2×C10711yescharacteristic, complemented
496#1880C2×C10711yescharacteristic, complemented
497#1878C2×C10711yescharacteristic, complemented
498#1869C2×C10711yescharacteristic, complemented
499#1788C2×C10711yescharacteristic, complemented
500C107#2385411yescharacteristic, direct product factor, Sylow
501C22×#41C22×C10711yescharacteristic
502C22×#41C22×C10711yescharacteristic
503C23×Q8C22×C10711yescharacteristic
504C2×#135—24no—
505C2×#135—24no—
506C2×#135—24no—
507C22×Q16C22×C10711yescharacteristic
508C22×Q16C22×C10711yescharacteristic
509C22×SD16C22×C10711yescharacteristic
510C22×SD16C22×C10711yescharacteristic
511C22×SD16C22×C10711yescharacteristic
512C22×D8C22×C10711yescharacteristic
513C23×C8C22×C10711yescharacteristic
514#548—24no—
515#548—24no—
516C2×#124—21no—
517C2×#124C22×C10711yescharacteristic
518C2×C22⋊Q8—21no—
519C2×C22⋊Q8C22×C10711yescharacteristic
520C2×C22⋊Q8C22×C10711yescharacteristic
521C2×#121—21no—
522C2×#121C22×C10711yescharacteristic
523C2×#121C22×C10711yescharacteristic
524C2×C4×Q8C22×C10711yescharacteristic
525C2×C4×D4—21no—
526C2×C4×D4C22×C10711yescharacteristic
527#452—24no—
528#451—24no—
529#448—24no—
530C2×#103C22×C10711yescharacteristic
531C2×#103C22×C10711yescharacteristic
532C2×#103C22×C10711yescharacteristic
533C2×#103C22×C10711yescharacteristic
534C2×#103C22×C10711yescharacteristic
535C2×#102C22×C10711yescharacteristic
536C2×#102C22×C10711yescharacteristic
537C2×#102C22×C10711yescharacteristic
538C2×C22⋊C8C22×C10711yescharacteristic
539C2×C22⋊C8C22×C10711yescharacteristic
540C2×C22⋊C8C22×C10711yescharacteristic
541#394—21no—
542#392—21no—
543#391C22×C10711yescharacteristic
544#390C22×C10711yescharacteristic
545#386—21no—
546#385—21no—
547#380C22×C10711yescharacteristic
548#340C22×C10711yescharacteristic
549#340C22×C10711yescharacteristic
550#336C22×C10711yescharacteristic
551#336C22×C10711yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—41no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41—41no—
563C2×#41D4×C10714yescomplemented
564C22×Q8—22no—
565C22×Q8—22no—
566C22×Q8—21no—
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—41no—
570C22×Q8—41no—
571C22×Q8C23×C10711yescharacteristic
572C22×Q8C23×C10711yescharacteristic
573C22×Q8C23×C10711yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C10711yescharacteristic
579C22×D4C23×C10711yescharacteristic
580C22×D4C23×C10711yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C10711yescharacteristic
585C23×C4C23×C10711yescharacteristic
586#135—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—41no—
592C2×Q16D4×C10714yescomplemented
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C10714yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—22no—
605C22×C8—22no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8C23×C10711yescharacteristic
609C22×C8C23×C10711yescharacteristic
610C22×C8C23×C10711yescharacteristic
611C22×C8C23×C10711yescharacteristic
612#124—28no—
613#124—22no—
614#124—22no—
615C22⋊Q8—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—41no—
619C22⋊Q8D4×C10714yescomplemented
620#121—28no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—41no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×D4—28no—
628C4×D4—22no—
629C4×D4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4D4×C10711yescharacteristic
634C2×C4⋊C4C23×C10711yescharacteristic
635C2×C4⋊C4C23×C10711yescharacteristic
636C2×C4⋊C4C23×C10711yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4D4×C10711yescharacteristic
647C2×C22⋊C4D4×C10711yescharacteristic
648C2×C42—21no—
649C2×C42C23×C10711yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#102—22no—
656#102—41no—
657#102—41no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C10711yescharacteristic
667C24C2×D4×C10711yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676C2×Q8—24no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8C2×D4×C10712yes—
697C2×Q8C2×D4×C10712yes—
698C2×Q8C2×D4×C10712yes—
699C2×Q8C2×D4×C10712yes—
700C2×Q8C2×D4×C10712yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—81no—
726C2×D4C2×D4×C10712yes—
727C2×D4C2×D4×C10712yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—24no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—24no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C10711yescharacteristic
754C22×C4C2×D4×C10711yescharacteristic
755C22×C4C2×D4×C10711yescharacteristic
756C22×C4C2×D4×C10711yescharacteristic
757C22×C4C2×D4×C10712yes—
758C22×C4C2×D4×C10712yes—
759C22×C4C24×C10711yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C10712yes—
778C2×C8C2×D4×C10712yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—42no—
788C4⋊C4C2×D4×C10712yes—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C42—24no—
801C42—21no—
802C42—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—22no—
816C23—22no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23#120×C10712yes—
830C23#135×C10712yescomplemented
831C23C22×D4×C10711yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—22no—
839Q8—48no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8#120×C10714yes—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—48no—
850D4—44no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—84no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4#120×C10712yes—
899C2×C4C22×D4×C10711yescharacteristic
900C2×C4C22×D4×C10711yescharacteristic
901C2×C4C22×D4×C10711yescharacteristic
902C2×C4C22×D4×C10711yescharacteristic
903C2×C4H(5,𝔽2)×C10711yescharacteristic
904C2×C4H(5,𝔽2)×C10711yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C10711yescharacteristic
938C22D42×C10711yescharacteristic
939C22D42×C10711yescharacteristic
940C22C2×#135×C10711yescharacteristic
941C22#575×C10711yescharacteristic
942C22#577×C10711yescharacteristic
943C22#578×C10711yescharacteristic
944C4—22no—
945C4—24no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×#120×C10711yescharacteristic
955C4#534×C10711yescharacteristic
956C4D42×C10711yescharacteristic
957C4D42×C10711yescharacteristic
958C2—42no—
959C2—42no—
960C2—82no—
961C2—82no—
962C2C107×#240311yescharacteristic
963C2C107×#300211yescharacteristic
964C2C107×#301311yescharacteristic
965C2C107×#326911yescharacteristic
966C2C107×#327111yescharacteristic
967C2C107×#328211yescharacteristic
968C2C107×#328511yescharacteristic
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×#548×C107C2semidirect
3. C2×#452×C107C2semidirect
4. C2×#451×C107C2semidirect
5. C2×#448×C107C2semidirect
6. C107×#2407C2semidirect
7. C107×#2015C2semidirect
8. C107×#2012C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1892C2semidirect
12. C107×#1880C2semidirect
13. C107×#1878C2semidirect
14. C107×#1869C2semidirect
15. C107×#1788C2semidirect
78. C2×#41×C107D4semidirect
107. C2×Q16×C107D4semidirect
116. C2×SD16×C107D4semidirect
134. C22⋊Q8×C107D4semidirect
345. C23×C107#135semidirect
473. #23854C107direct (N × H)
485. C22×#135C2×C107semidirect
486. C2×#548C2×C107semidirect
487. C2×#452C2×C107semidirect
488. C2×#451C2×C107semidirect
489. C2×#448C2×C107semidirect
490. #2407C2×C107semidirect
491. #2015C2×C107semidirect
492. #2012C2×C107semidirect
493. #2000C2×C107semidirect
494. #1999C2×C107semidirect
495. #1892C2×C107semidirect
496. #1880C2×C107semidirect
497. #1878C2×C107semidirect
498. #1869C2×C107semidirect
499. #1788C2×C107semidirect
500. C107#23854direct (N × H)
563. C2×#41D4×C107semidirect
592. C2×Q16D4×C107semidirect
601. C2×SD16D4×C107semidirect
619. C22⋊Q8D4×C107semidirect
830. C23#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×#548×C1072
C2×#452×C1072
C2×#451×C1072
C2×#448×C1072
C107×#24072
C107×#20152
C107×#20122
C107×#20002
C107×#19992
C107×#18922
C107×#18802
C107×#18782
C107×#18692
C107×#17882
#23854107