Finite Group Databasebeta

← C107×#24428 #41050392

Subgroups — C107×#24428 #41050392

Order 27392.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C107C211yesmaximal, characteristic, complemented
2C2×#466×C107C211yesmaximal, characteristic, complemented
3C2×#449×C107C211yesmaximal, characteristic, complemented
4C2×#447×C107C211yesmaximal, characteristic, complemented
5C2×#416×C107C211yesmaximal, characteristic, complemented
6C107×#2414C211yesmaximal, characteristic, complemented
7C107×#2042C211yesmaximal, characteristic, complemented
8C107×#2036C211yesmaximal, characteristic, complemented
9C107×#2012C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1879C211yesmaximal, characteristic, complemented
12C107×#1875C211yesmaximal, characteristic, complemented
13C107×#1869C211yesmaximal, characteristic, complemented
14C107×#1862C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×D4×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic, complemented
19C22×D8×C107C2211yescharacteristic
20C22×D8×C107C2211yescharacteristic
21C23×C8×C107C2211yescharacteristic, complemented
22#546×C107—24no—
23#546×C107—24no—
24C2×#124×C107C2211yescharacteristic
25C2×#123×C107—21no—
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×#121×C107—21no—
28C2×#121×C107C2211yescharacteristic
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic, complemented
31C2×#120×C107—21no—
32C2×C4×D4×C107C2211yescharacteristic
33C2×C4×D4×C107C2211yescharacteristic
34C2×#117×C107C2211yescharacteristic, complemented
35C22×C22⋊C4×C107—21no—
36#466×C107—24no—
37#449×C107—24no—
38#447×C107—24no—
39C2×#107×C107C2211yescharacteristic, complemented
40#416×C107—24no—
41C2×#103×C107C2211yescharacteristic, complemented
42C2×#103×C107C2211yescharacteristic, complemented
43C2×#103×C107C2211yescharacteristic, complemented
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic, complemented
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54#394×C107—21no—
55#392×C107—21no—
56#390×C107—21no—
57#390×C107C2211yescharacteristic, complemented
58#389×C107C2211yescharacteristic, complemented
59#388×C107—21no—
60#380×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic, complemented
62#340×C107C2211yescharacteristic, complemented
63#336×C107C2211yescharacteristic, complemented
64#336×C107C2211yescharacteristic, complemented
65C25×C107—21no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—41no—
70C2×#41×C107—41no—
71C2×#41×C107D414yescomplemented
72C22×Q8×C107C2311yescharacteristic
73C22×D4×C107—21no—
74C22×D4×C107—21no—
75C22×D4×C107—22no—
76C22×D4×C107—22no—
77C22×D4×C107—22no—
78C22×D4×C107—22no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—41no—
83C22×D4×C107—41no—
84C22×D4×C107D411yescharacteristic
85C22×D4×C107C2311yescharacteristic
86C22×D4×C107C2311yescharacteristic
87C22×D4×C107C2311yescharacteristic
88C23×C4×C107—21no—
89C23×C4×C107—21no—
90C23×C4×C107C2311yescharacteristic
91C23×C4×C107C2311yescharacteristic
92C2×SD16×C107—22no—
93C2×SD16×C107—41no—
94C2×SD16×C107—41no—
95C2×D8×C107—22no—
96C2×D8×C107—22no—
97C2×D8×C107—22no—
98C2×D8×C107—22no—
99C2×D8×C107—22no—
100C2×D8×C107—41no—
101C22×C8×C107—22no—
102C22×C8×C107—22no—
103C22×C8×C107—41no—
104C22×C8×C107C2311yescharacteristic
105C22×C8×C107C2311yescharacteristic
106C22×C8×C107C2311yescharacteristic
107C22×C8×C107C2311yescharacteristic
108#124×C107—22no—
109#124×C107—22no—
110#123×C107—28no—
111C22⋊Q8×C107—22no—
112C22⋊Q8×C107—22no—
113#121×C107—28no—
114#121×C107—22no—
115#121×C107—22no—
116#121×C107—22no—
117#121×C107—22no—
118#121×C107—41no—
119#121×C107D414yescomplemented
120#120×C107—28no—
121C4×D4×C107—22no—
122C4×D4×C107—22no—
123C4×D4×C107—22no—
124C4×D4×C107—22no—
125#117×C107—22no—
126#117×C107—41no—
127C2×C4⋊C4×C107—21no—
128C2×C4⋊C4×C107—21no—
129C2×C4⋊C4×C107D411yescharacteristic
130C2×C4⋊C4×C107C2311yescharacteristic
131C2×C4⋊C4×C107C2311yescharacteristic
132C2×C4⋊C4×C107C2311yescharacteristic
133C2×C4⋊C4×C107C2311yescharacteristic
134C2×C22⋊C4×C107—28no—
135C2×C22⋊C4×C107—21no—
136C2×C22⋊C4×C107—21no—
137C2×C22⋊C4×C107—21no—
138C2×C22⋊C4×C107—21no—
139C2×C22⋊C4×C107—21no—
140C2×C22⋊C4×C107—21no—
141C2×C22⋊C4×C107—21no—
142C2×C22⋊C4×C107—21no—
143C2×C22⋊C4×C107—21no—
144C2×C22⋊C4×C107—21no—
145C2×C22⋊C4×C107—21no—
146C2×C22⋊C4×C107D411yescharacteristic
147C2×C22⋊C4×C107D411yescharacteristic
148C2×C42×C107—21no—
149C2×C42×C107C2311yescharacteristic
150#107×C107—22no—
151#103×C107—22no—
152#103×C107—22no—
153#103×C107—22no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—22no—
157#102×C107—22no—
158#102×C107—22no—
159#102×C107—41no—
160#102×C107D414yescomplemented
161C22⋊C8×C107—22no—
162C22⋊C8×C107—22no—
163C22⋊C8×C107—41no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—21no—
167C24×C107—24no—
168C24×C107—21no—
169C24×C107—21no—
170C24×C107—42no—
171C24×C107—42no—
172C24×C107—42no—
173C24×C107—42no—
174C24×C107—81no—
175C24×C107—81no—
176C24×C107C2×D411yescharacteristic
177C24×C107C2×D411yescharacteristic
178#41×C107—28no—
179#41×C107—44no—
180#41×C107—44no—
181#41×C107—44no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107C2×D412yes—
188C2×D4×C107—24no—
189C2×D4×C107—22no—
190C2×D4×C107—24no—
191C2×D4×C107—22no—
192C2×D4×C107—24no—
193C2×D4×C107—21no—
194C2×D4×C107—21no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—21no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—41no—
208C2×D4×C107—42no—
209C2×D4×C107—42no—
210C2×D4×C107—42no—
211C2×D4×C107—44no—
212C2×D4×C107—44no—
213C2×D4×C107—44no—
214C2×D4×C107—42no—
215C2×D4×C107—42no—
216C2×D4×C107—44no—
217C2×D4×C107—42no—
218C2×D4×C107—42no—
219C2×D4×C107—81no—
220C2×D4×C107—81no—
221C2×D4×C107—81no—
222C2×D4×C107—81no—
223C2×D4×C107—81no—
224C2×D4×C107C2×D412yes—
225C2×D4×C107C2×D412yes—
226C2×D4×C107C2×D412yes—
227C2×D4×C107#4112yes—
228C22×C4×C107—21no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—21no—
232C22×C4×C107—21no—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—24no—
236C22×C4×C107—24no—
237C22×C4×C107—21no—
238C22×C4×C107—21no—
239C22×C4×C107—21no—
240C22×C4×C107—21no—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—42no—
246C22×C4×C107—42no—
247C22×C4×C107—81no—
248C22×C4×C107—81no—
249C22×C4×C107C2×D411yescharacteristic
250C22×C4×C107C2×D411yescharacteristic
251C22×C4×C107C2×D411yescharacteristic
252C22×C4×C107C2×D411yescharacteristic
253C22×C4×C107C2×D412yes—
254C22×C4×C107C2×D412yes—
255C22×C4×C107C2411yescharacteristic
256SD16×C107—44no—
257D8×C107—44no—
258D8×C107—44no—
259C2×C8×C107—21no—
260C2×C8×C107—21no—
261C2×C8×C107—21no—
262C2×C8×C107—21no—
263C2×C8×C107—21no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107—21no—
267C2×C8×C107—21no—
268C2×C8×C107—21no—
269C2×C8×C107—21no—
270C2×C8×C107—44no—
271C2×C8×C107C2×D412yes—
272C4⋊C4×C107—24no—
273C4⋊C4×C107—22no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—21no—
280C4⋊C4×C107—81no—
281C4⋊C4×C107C2×D412yes—
282C4⋊C4×C107C2×D412yes—
283C22⋊C4×C107—24no—
284C22⋊C4×C107—24no—
285C22⋊C4×C107—24no—
286C22⋊C4×C107—24no—
287C22⋊C4×C107—22no—
288C22⋊C4×C107—22no—
289C22⋊C4×C107—24no—
290C22⋊C4×C107—42no—
291C22⋊C4×C107—42no—
292C22⋊C4×C107—42no—
293C22⋊C4×C107—42no—
294C22⋊C4×C107—81no—
295C22⋊C4×C107—81no—
296C42×C107—21no—
297C42×C107—21no—
298C42×C107—42no—
299C23×C107—21no—
300C23×C107—22no—
301C23×C107—21no—
302C23×C107—21no—
303C23×C107—22no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—22no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—21no—
311C23×C107—21no—
312C23×C107—21no—
313C23×C107—21no—
314C23×C107—22no—
315C23×C107—48no—
316C23×C107—48no—
317C23×C107—41no—
318C23×C107—41no—
319C23×C107—41no—
320C23×C107—41no—
321C23×C107—41no—
322C23×C107—41no—
323C23×C107—41no—
324C23×C107—41no—
325C23×C107—41no—
326C23×C107—41no—
327C23×C107—41no—
328C23×C107—41no—
329C23×C107—41no—
330C23×C107—41no—
331C23×C107—41no—
332C23×C107—41no—
333C23×C107—41no—
334C23×C107—84no—
335C23×C107—84no—
336C23×C107—84no—
337C23×C107—84no—
338C23×C107—84no—
339C23×C107#12012yes—
340C23×C107#13512yes—
341C23×C107C22×D411yescharacteristic
342Q8×C107—22no—
343Q8×C107—22no—
344Q8×C107—41no—
345Q8×C107—41no—
346D4×C107—22no—
347D4×C107—22no—
348D4×C107—22no—
349D4×C107—22no—
350D4×C107—22no—
351D4×C107—44no—
352D4×C107—48no—
353D4×C107—48no—
354D4×C107—41no—
355D4×C107—41no—
356D4×C107—41no—
357D4×C107—41no—
358D4×C107—41no—
359D4×C107—41no—
360D4×C107—84no—
361D4×C107—84no—
362D4×C107—84no—
363D4×C107#12114yes—
364C2×C4×C107—21no—
365C2×C4×C107—21no—
366C2×C4×C107—22no—
367C2×C4×C107—22no—
368C2×C4×C107—22no—
369C2×C4×C107—22no—
370C2×C4×C107—21no—
371C2×C4×C107—21no—
372C2×C4×C107—22no—
373C2×C4×C107—22no—
374C2×C4×C107—21no—
375C2×C4×C107—22no—
376C2×C4×C107—21no—
377C2×C4×C107—21no—
378C2×C4×C107—21no—
379C2×C4×C107—21no—
380C2×C4×C107—21no—
381C2×C4×C107—21no—
382C2×C4×C107—48no—
383C2×C4×C107—41no—
384C2×C4×C107—41no—
385C2×C4×C107—41no—
386C2×C4×C107—41no—
387C2×C4×C107—41no—
388C2×C4×C107—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107—41no—
395C2×C4×C107—41no—
396C2×C4×C107—41no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—84no—
400C2×C4×C107#12012yes—
401C2×C4×C107C22×D411yescharacteristic
402C2×C4×C107C22×D411yescharacteristic
403C2×C4×C107C22×D411yescharacteristic
404C2×C4×C107C2×#4111yescharacteristic
405C2×C4×C107H(5,𝔽2)11yescharacteristic
406C2×C4×C107H(5,𝔽2)11yescharacteristic
407C8×C107—22no—
408C8×C107—41no—
409C8×C107—41no—
410C8×C107—41no—
411C22×C107—22no—
412C22×C107—24no—
413C22×C107—22no—
414C22×C107—22no—
415C22×C107—22no—
416C22×C107—22no—
417C22×C107—22no—
418C22×C107—41no—
419C22×C107—42no—
420C22×C107—42no—
421C22×C107—41no—
422C22×C107—41no—
423C22×C107—41no—
424C22×C107—42no—
425C22×C107—41no—
426C22×C107—42no—
427C22×C107—41no—
428C22×C107—42no—
429C22×C107—41no—
430C22×C107—41no—
431C22×C107—42no—
432C22×C107—42no—
433C22×C107—42no—
434C22×C107—42no—
435C22×C107—816no—
436C22×C107—81no—
437C22×C107—81no—
438C22×C107—81no—
439C22×C107—81no—
440C22×C107—81no—
441C22×C107—81no—
442C22×C107—81no—
443C22×C107—81no—
444C22×C107—81no—
445C22×C107—81no—
446C22×C107—81no—
447C22×C107C2×#12011yescharacteristic
448C22×C107D4211yescharacteristic
449C22×C107#54611yescharacteristic
450C22×C107C2×#13511yescharacteristic
451C22×C107#57511yescharacteristic
452C22×C107#57611yescharacteristic
453C22×C107#57611yescharacteristic
454C4×C107—22no—
455C4×C107—41no—
456C4×C107—42no—
457C4×C107—41no—
458C4×C107—41no—
459C4×C107—42no—
460C4×C107—42no—
461C4×C107—81no—
462C4×C107—81no—
463C4×C107C2×#12111yescharacteristic
464C4×C107#53411yescharacteristic
465C4×C107D4211yescharacteristic
466C4×C107#54611yescharacteristic
467#24428C10711yesmaximal, characteristic, direct product factor, Sylow
468C2×C107—42no—
469C2×C107—42no—
470C2×C107—44no—
471C2×C107—82no—
472C2×C107—161no—
473C2×C107#241011yescharacteristic
474C2×C107#300211yescharacteristic
475C2×C107#300811yescharacteristic
476C2×C107#326811yescharacteristic
477C2×C107#328011yescharacteristic
478C2×C107#329711yescharacteristic
479C2×C107#331911yescharacteristic
480C2×#546C2×C10711yescharacteristic, complemented
481C2×#466C2×C10711yescharacteristic, complemented
482C2×#449C2×C10711yescharacteristic, complemented
483C2×#447C2×C10711yescharacteristic, complemented
484C2×#416C2×C10711yescharacteristic, complemented
485#2414C2×C10711yescharacteristic, complemented
486#2042C2×C10711yescharacteristic, complemented
487#2036C2×C10711yescharacteristic, complemented
488#2012C2×C10711yescharacteristic, complemented
489#2000C2×C10711yescharacteristic, complemented
490#1879C2×C10711yescharacteristic, complemented
491#1875C2×C10711yescharacteristic, complemented
492#1869C2×C10711yescharacteristic, complemented
493#1862C2×C10711yescharacteristic, complemented
494#1786C2×C10711yescharacteristic, complemented
495C107#2442811yescharacteristic, direct product factor, Sylow
496C22×#41C22×C10711yescharacteristic
497C23×D4C22×C10711yescharacteristic
498C22×SD16C22×C10711yescharacteristic, complemented
499C22×D8C22×C10711yescharacteristic
500C22×D8C22×C10711yescharacteristic
501C23×C8C22×C10711yescharacteristic, complemented
502#546—24no—
503#546—24no—
504C2×#124C22×C10711yescharacteristic
505C2×#123—21no—
506C2×C22⋊Q8C22×C10711yescharacteristic
507C2×#121—21no—
508C2×#121C22×C10711yescharacteristic
509C2×#121C22×C10711yescharacteristic
510C2×#121C22×C10711yescharacteristic, complemented
511C2×#120—21no—
512C2×C4×D4C22×C10711yescharacteristic
513C2×C4×D4C22×C10711yescharacteristic
514C2×#117C22×C10711yescharacteristic, complemented
515C22×C22⋊C4—21no—
516#466—24no—
517#449—24no—
518#447—24no—
519C2×#107C22×C10711yescharacteristic, complemented
520#416—24no—
521C2×#103C22×C10711yescharacteristic, complemented
522C2×#103C22×C10711yescharacteristic, complemented
523C2×#103C22×C10711yescharacteristic, complemented
524C2×#102C22×C10711yescharacteristic
525C2×#102C22×C10711yescharacteristic
526C2×#102C22×C10711yescharacteristic
527C2×#102C22×C10711yescharacteristic
528C2×#102C22×C10711yescharacteristic
529C2×#102C22×C10711yescharacteristic
530C2×#102C22×C10711yescharacteristic, complemented
531C2×C22⋊C8C22×C10711yescharacteristic
532C2×C22⋊C8C22×C10711yescharacteristic
533C2×C22⋊C8C22×C10711yescharacteristic, complemented
534#394—21no—
535#392—21no—
536#390—21no—
537#390C22×C10711yescharacteristic, complemented
538#389C22×C10711yescharacteristic, complemented
539#388—21no—
540#380C22×C10711yescharacteristic
541#340C22×C10711yescharacteristic, complemented
542#340C22×C10711yescharacteristic, complemented
543#336C22×C10711yescharacteristic, complemented
544#336C22×C10711yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C10714yescomplemented
552C22×Q8C23×C10711yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C10711yescharacteristic
565C22×D4C23×C10711yescharacteristic
566C22×D4C23×C10711yescharacteristic
567C22×D4C23×C10711yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C10711yescharacteristic
571C23×C4C23×C10711yescharacteristic
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C10711yescharacteristic
585C22×C8C23×C10711yescharacteristic
586C22×C8C23×C10711yescharacteristic
587C22×C8C23×C10711yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121D4×C10714yescomplemented
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C10711yescharacteristic
610C2×C4⋊C4C23×C10711yescharacteristic
611C2×C4⋊C4C23×C10711yescharacteristic
612C2×C4⋊C4C23×C10711yescharacteristic
613C2×C4⋊C4C23×C10711yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C10711yescharacteristic
627C2×C22⋊C4D4×C10711yescharacteristic
628C2×C42—21no—
629C2×C42C23×C10711yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102D4×C10714yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C10711yescharacteristic
657C24C2×D4×C10711yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C10712yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C10712yes—
705C2×D4C2×D4×C10712yes—
706C2×D4C2×D4×C10712yes—
707C2×D4#41×C10712yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C10711yescharacteristic
730C22×C4C2×D4×C10711yescharacteristic
731C22×C4C2×D4×C10711yescharacteristic
732C22×C4C2×D4×C10711yescharacteristic
733C22×C4C2×D4×C10712yes—
734C22×C4C2×D4×C10712yes—
735C22×C4C24×C10711yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8C2×D4×C10712yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C10712yes—
762C4⋊C4C2×D4×C10712yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—48no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#120×C10712yes—
820C23#135×C10712yes—
821C23C22×D4×C10711yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C10714yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C10712yes—
881C2×C4C22×D4×C10711yescharacteristic
882C2×C4C22×D4×C10711yescharacteristic
883C2×C4C22×D4×C10711yescharacteristic
884C2×C4C2×#41×C10711yescharacteristic
885C2×C4H(5,𝔽2)×C10711yescharacteristic
886C2×C4H(5,𝔽2)×C10711yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C10711yescharacteristic
928C22D42×C10711yescharacteristic
929C22#546×C10711yescharacteristic
930C22C2×#135×C10711yescharacteristic
931C22#575×C10711yescharacteristic
932C22#576×C10711yescharacteristic
933C22#576×C10711yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C10711yescharacteristic
944C4#534×C10711yescharacteristic
945C4D42×C10711yescharacteristic
946C4#546×C10711yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—161no—
952C2C107×#241011yescharacteristic
953C2C107×#300211yescharacteristic
954C2C107×#300811yescharacteristic
955C2C107×#326811yescharacteristic
956C2C107×#328011yescharacteristic
957C2C107×#329711yescharacteristic
958C2C107×#331911yescharacteristic
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. C2×#546×C107C2semidirect
2. C2×#466×C107C2semidirect
3. C2×#449×C107C2semidirect
4. C2×#447×C107C2semidirect
5. C2×#416×C107C2semidirect
6. C107×#2414C2semidirect
7. C107×#2042C2semidirect
8. C107×#2036C2semidirect
9. C107×#2012C2semidirect
10. C107×#2000C2semidirect
11. C107×#1879C2semidirect
12. C107×#1875C2semidirect
13. C107×#1869C2semidirect
14. C107×#1862C2semidirect
15. C107×#1786C2semidirect
18. C22×SD16×C107C22semidirect
21. C23×C8×C107C22semidirect
30. C2×#121×C107C22semidirect
34. C2×#117×C107C22semidirect
39. C2×#107×C107C22semidirect
41. C2×#103×C107C22semidirect
42. C2×#103×C107C22semidirect
43. C2×#103×C107C22semidirect
50. C2×#102×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
57. #390×C107C22semidirect
58. #389×C107C22semidirect
61. #340×C107C22semidirect
62. #340×C107C22semidirect
63. #336×C107C22semidirect
64. #336×C107C22semidirect
71. C2×#41×C107D4semidirect
119. #121×C107D4semidirect
160. #102×C107D4semidirect
467. #24428C107direct (N × H)
480. C2×#546C2×C107semidirect
481. C2×#466C2×C107semidirect
482. C2×#449C2×C107semidirect
483. C2×#447C2×C107semidirect
484. C2×#416C2×C107semidirect
485. #2414C2×C107semidirect
486. #2042C2×C107semidirect
487. #2036C2×C107semidirect
488. #2012C2×C107semidirect
489. #2000C2×C107semidirect
490. #1879C2×C107semidirect
491. #1875C2×C107semidirect
492. #1869C2×C107semidirect
493. #1862C2×C107semidirect
494. #1786C2×C107semidirect
495. C107#24428direct (N × H)
498. C22×SD16C22×C107semidirect
501. C23×C8C22×C107semidirect
510. C2×#121C22×C107semidirect
514. C2×#117C22×C107semidirect
519. C2×#107C22×C107semidirect
521. C2×#103C22×C107semidirect
522. C2×#103C22×C107semidirect
523. C2×#103C22×C107semidirect
530. C2×#102C22×C107semidirect
533. C2×C22⋊C8C22×C107semidirect
537. #390C22×C107semidirect
538. #389C22×C107semidirect
541. #340C22×C107semidirect
542. #340C22×C107semidirect
543. #336C22×C107semidirect
544. #336C22×C107semidirect
551. C2×#41D4×C107semidirect
599. #121D4×C107semidirect
640. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1072
C2×#466×C1072
C2×#449×C1072
C2×#447×C1072
C2×#416×C1072
C107×#24142
C107×#20422
C107×#20362
C107×#20122
C107×#20002
C107×#18792
C107×#18752
C107×#18692
C107×#18622
C107×#17862
#24428107