Finite Group Databasebeta

← C107×#24017 #41049981

Subgroups — C107×#24017 #41049981

Order 27392.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C107C211yesmaximal, characteristic
2C2×#485×C107C211yesmaximal, characteristic, complemented
3C2×#482×C107C211yesmaximal, characteristic, complemented
4C107×#2311C211yesmaximal, characteristic, complemented
5C107×#2036C211yesmaximal, characteristic, complemented
6C107×#2035C211yesmaximal, characteristic, complemented
7C107×#2034C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#1874C211yesmaximal, characteristic, complemented
10C107×#1872C211yesmaximal, characteristic, complemented
11C107×#1853C211yesmaximal, characteristic, complemented
12C107×#1852C211yesmaximal, characteristic, complemented
13C107×#1788C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18#537×C107—24no—
19#537×C107—24no—
20C2×C22⋊Q8×C107—21no—
21C2×C22⋊Q8×C107C2211yescharacteristic
22C2×C22⋊Q8×C107C2211yescharacteristic
23C2×#121×C107—21no—
24C2×#121×C107—21no—
25C2×#121×C107—21no—
26C2×#121×C107C2211yescharacteristic
27C2×#121×C107C2211yescharacteristic
28C2×#117×C107C2211yescharacteristic
29C22×C4⋊C4×C107C2211yescharacteristic
30C22×C4⋊C4×C107C2211yescharacteristic
31#485×C107—24no—
32#482×C107—24no—
33C2×#107×C107C2211yescharacteristic
34C2×#107×C107C2211yescharacteristic
35C2×#106×C107C2211yescharacteristic
36C2×#106×C107C2211yescharacteristic
37C2×#103×C107C2211yescharacteristic
38C2×#103×C107C2211yescharacteristic
39C2×#103×C107C2211yescharacteristic
40C2×#103×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×C22⋊C8×C107C2211yescharacteristic
46C2×C22⋊C8×C107C2211yescharacteristic
47C2×C22⋊C8×C107C2211yescharacteristic
48C2×C22⋊C8×C107C2211yescharacteristic
49C2×C22⋊C8×C107C2211yescharacteristic
50C2×C22⋊C8×C107C2211yescharacteristic
51#391×C107—21no—
52#390×C107—21no—
53#386×C107—21no—
54#386×C107—21no—
55#380×C107C2211yescharacteristic
56#380×C107C2211yescharacteristic
57#380×C107C2211yescharacteristic
58#380×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63C2×#41×C107—22no—
64C2×#41×C107—22no—
65C2×#41×C107—22no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—22no—
71C2×#41×C107—41no—
72C2×#41×C107—41no—
73C2×#41×C107—41no—
74C2×#41×C107—41no—
75C22×Q8×C107D411yescharacteristic
76C22×Q8×C107C2311yescharacteristic
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107D411yescharacteristic
81C22×D4×C107D411yescharacteristic
82C22×D4×C107D411yescharacteristic
83C22×D4×C107C2311yescharacteristic
84C23×C4×C107—21no—
85C23×C4×C107—21no—
86C23×C4×C107—21no—
87C23×C4×C107C2311yescharacteristic
88C23×C4×C107C2311yescharacteristic
89C23×C4×C107C2311yescharacteristic
90C22×C8×C107C2311yescharacteristic
91C22×C8×C107C2311yescharacteristic
92C22×C8×C107C2311yescharacteristic
93C22×C8×C107C2311yescharacteristic
94C22⋊Q8×C107—28no—
95C22⋊Q8×C107—22no—
96C22⋊Q8×C107—22no—
97C22⋊Q8×C107—22no—
98C22⋊Q8×C107D414yes—
99#121×C107—28no—
100#121×C107—28no—
101#121×C107—28no—
102#121×C107—22no—
103#121×C107—22no—
104#121×C107—22no—
105#121×C107D414yes—
106#117×C107—22no—
107#117×C107—22no—
108C2×C4⋊C4×C107—21no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107—22no—
112C2×C4⋊C4×C107—22no—
113C2×C4⋊C4×C107—21no—
114C2×C4⋊C4×C107—41no—
115C2×C4⋊C4×C107—41no—
116C2×C4⋊C4×C107C2311yescharacteristic
117C2×C4⋊C4×C107C2311yescharacteristic
118C2×C4⋊C4×C107C2311yescharacteristic
119C2×C4⋊C4×C107C2311yescharacteristic
120C2×C4⋊C4×C107C2311yescharacteristic
121C2×C4⋊C4×C107C2311yescharacteristic
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107—21no—
130C2×C22⋊C4×C107—21no—
131C2×C42×C107—21no—
132#107×C107—22no—
133#107×C107—22no—
134#106×C107—22no—
135#106×C107—22no—
136#103×C107—22no—
137#103×C107—22no—
138#103×C107—41no—
139#103×C107—41no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107—41no—
143#102×C107—41no—
144C22⋊C8×C107—22no—
145C22⋊C8×C107—22no—
146C22⋊C8×C107—22no—
147C22⋊C8×C107—22no—
148C22⋊C8×C107—41no—
149C22⋊C8×C107—41no—
150#95×C107—21no—
151#95×C107—21no—
152#95×C107—21no—
153#95×C107—21no—
154C24×C107—21no—
155C24×C107C2×D411yescharacteristic
156C24×C107C2×D411yescharacteristic
157C24×C107C2×D411yescharacteristic
158#41×C107—44no—
159#41×C107—44no—
160#41×C107—44no—
161#41×C107—44no—
162#41×C107—44no—
163#41×C107—44no—
164#41×C107—44no—
165#41×C107—44no—
166C2×Q8×C107—22no—
167C2×Q8×C107—22no—
168C2×Q8×C107—21no—
169C2×Q8×C107—21no—
170C2×Q8×C107—21no—
171C2×Q8×C107—21no—
172C2×Q8×C107—21no—
173C2×Q8×C107—41no—
174C2×Q8×C107C2×D412yes—
175C2×D4×C107—24no—
176C2×D4×C107—22no—
177C2×D4×C107—22no—
178C2×D4×C107—22no—
179C2×D4×C107—22no—
180C2×D4×C107—24no—
181C2×D4×C107—24no—
182C2×D4×C107—22no—
183C2×D4×C107—22no—
184C2×D4×C107—21no—
185C2×D4×C107—21no—
186C2×D4×C107—21no—
187C2×D4×C107—21no—
188C2×D4×C107—21no—
189C2×D4×C107—41no—
190C2×D4×C107—41no—
191C2×D4×C107—41no—
192C2×D4×C107—42no—
193C2×D4×C107—42no—
194C2×D4×C107—81no—
195C2×D4×C107—81no—
196C2×D4×C107—81no—
197C2×D4×C107—81no—
198C2×D4×C107C2×D412yes—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—21no—
206C22×C4×C107—21no—
207C22×C4×C107—24no—
208C22×C4×C107—21no—
209C22×C4×C107—21no—
210C22×C4×C107—21no—
211C22×C4×C107—24no—
212C22×C4×C107—21no—
213C22×C4×C107—21no—
214C22×C4×C107—21no—
215C22×C4×C107—21no—
216C22×C4×C107—21no—
217C22×C4×C107—21no—
218C22×C4×C107—21no—
219C22×C4×C107—21no—
220C22×C4×C107—21no—
221C22×C4×C107—21no—
222C22×C4×C107—42no—
223C22×C4×C107—42no—
224C22×C4×C107—42no—
225C22×C4×C107—81no—
226C22×C4×C107—81no—
227C22×C4×C107—81no—
228C22×C4×C107—81no—
229C22×C4×C107C2×D411yescharacteristic
230C22×C4×C107C2×D411yescharacteristic
231C22×C4×C107C2×D412yes—
232C22×C4×C107C2×D412yes—
233C22×C4×C107C2×D411yescharacteristic
234C22×C4×C107#4112yes—
235C22×C4×C107#4112yes—
236C22×C4×C107C2411yescharacteristic
237C2×C8×C107—21no—
238C2×C8×C107—21no—
239C2×C8×C107—21no—
240C2×C8×C107—21no—
241C2×C8×C107—21no—
242C2×C8×C107—21no—
243C2×C8×C107—21no—
244C2×C8×C107—21no—
245C2×C8×C107—21no—
246C2×C8×C107—21no—
247C2×C8×C107—21no—
248C2×C8×C107—21no—
249C4⋊C4×C107—24no—
250C4⋊C4×C107—24no—
251C4⋊C4×C107—24no—
252C4⋊C4×C107—21no—
253C4⋊C4×C107—21no—
254C4⋊C4×C107—21no—
255C4⋊C4×C107—21no—
256C4⋊C4×C107—21no—
257C4⋊C4×C107—21no—
258C4⋊C4×C107—21no—
259C4⋊C4×C107—21no—
260C4⋊C4×C107—21no—
261C4⋊C4×C107—21no—
262C4⋊C4×C107—42no—
263C4⋊C4×C107C2×D412yes—
264C4⋊C4×C107C2×D412yes—
265C22⋊C4×C107—24no—
266C22⋊C4×C107—24no—
267C22⋊C4×C107—24no—
268C22⋊C4×C107—24no—
269C22⋊C4×C107—42no—
270C22⋊C4×C107—81no—
271C22⋊C4×C107—81no—
272C22⋊C4×C107—81no—
273C22⋊C4×C107—81no—
274C42×C107—42no—
275C23×C107—21no—
276C23×C107—21no—
277C23×C107—21no—
278C23×C107—21no—
279C23×C107—21no—
280C23×C107—21no—
281C23×C107—21no—
282C23×C107—21no—
283C23×C107—21no—
284C23×C107—21no—
285C23×C107—21no—
286C23×C107—21no—
287C23×C107—21no—
288C23×C107—22no—
289C23×C107—21no—
290C23×C107—21no—
291C23×C107—21no—
292C23×C107—21no—
293C23×C107—21no—
294C23×C107—21no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—41no—
298C23×C107—41no—
299C23×C107—41no—
300C23×C107—41no—
301C23×C107#12012yes—
302C23×C107#12312yes—
303C23×C107C22×D411yescharacteristic
304Q8×C107—22no—
305Q8×C107—22no—
306Q8×C107—44no—
307Q8×C107—41no—
308Q8×C107—41no—
309D4×C107—22no—
310D4×C107—22no—
311D4×C107—44no—
312D4×C107—44no—
313D4×C107—44no—
314D4×C107—48no—
315D4×C107—41no—
316D4×C107—41no—
317D4×C107—84no—
318D4×C107—84no—
319C2×C4×C107—21no—
320C2×C4×C107—21no—
321C2×C4×C107—21no—
322C2×C4×C107—21no—
323C2×C4×C107—22no—
324C2×C4×C107—22no—
325C2×C4×C107—22no—
326C2×C4×C107—22no—
327C2×C4×C107—22no—
328C2×C4×C107—22no—
329C2×C4×C107—22no—
330C2×C4×C107—22no—
331C2×C4×C107—22no—
332C2×C4×C107—22no—
333C2×C4×C107—22no—
334C2×C4×C107—21no—
335C2×C4×C107—21no—
336C2×C4×C107—21no—
337C2×C4×C107—48no—
338C2×C4×C107—41no—
339C2×C4×C107—41no—
340C2×C4×C107—41no—
341C2×C4×C107—41no—
342C2×C4×C107—41no—
343C2×C4×C107—41no—
344C2×C4×C107—41no—
345C2×C4×C107—41no—
346C2×C4×C107—41no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—41no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—41no—
354C2×C4×C107—41no—
355C2×C4×C107—41no—
356C2×C4×C107—41no—
357C2×C4×C107—41no—
358C2×C4×C107—41no—
359C2×C4×C107—41no—
360C2×C4×C107—84no—
361C2×C4×C107—84no—
362C2×C4×C107#12012yes—
363C2×C4×C107#12312yes—
364C2×C4×C107C22×D411yescharacteristic
365C2×C4×C107C22×D411yescharacteristic
366C2×C4×C107C2×#4111yescharacteristic
367C2×C4×C107C2×#4111yescharacteristic
368C2×C4×C107H(5,𝔽2)11yescharacteristic
369C2×C4×C107H(5,𝔽2)11yescharacteristic
370C8×C107—41no—
371C8×C107—41no—
372C8×C107—41no—
373C8×C107—41no—
374C22×C107—22no—
375C22×C107—22no—
376C22×C107—22no—
377C22×C107—22no—
378C22×C107—22no—
379C22×C107—22no—
380C22×C107—41no—
381C22×C107—41no—
382C22×C107—41no—
383C22×C107—41no—
384C22×C107—41no—
385C22×C107—41no—
386C22×C107—41no—
387C22×C107—41no—
388C22×C107—41no—
389C22×C107—41no—
390C22×C107—42no—
391C22×C107—41no—
392C22×C107—41no—
393C22×C107—41no—
394C22×C107—41no—
395C22×C107—42no—
396C22×C107—41no—
397C22×C107—42no—
398C22×C107—81no—
399C22×C107—81no—
400C22×C107—81no—
401C22×C107—81no—
402C22×C107C2×#12011yescharacteristic
403C22×C107C2×#12311yescharacteristic
404C22×C107#53411yescharacteristic
405C22×C107#57611yescharacteristic
406C22×C107#57711yescharacteristic
407C22×C107#57711yescharacteristic
408C22×C107#57811yescharacteristic
409C4×C107—22no—
410C4×C107—22no—
411C4×C107—41no—
412C4×C107—42no—
413C4×C107—42no—
414C4×C107—42no—
415C4×C107—81no—
416C4×C107—81no—
417C4×C107—81no—
418C4×C107—81no—
419C4×C107#54611yescharacteristic
420C4×C107#54611yescharacteristic
421C4×C107#54611yescharacteristic
422C4×C107#54611yescharacteristic
423#24017C10711yesmaximal, characteristic, direct product factor, Sylow
424C2×C107—42no—
425C2×C107—42no—
426C2×C107—81no—
427C2×C107—82no—
428C2×C107#240511yescharacteristic
429C2×C107#301211yescharacteristic
430C2×C107#301311yescharacteristic
431C2×C107#309811yescharacteristic
432C2×C107#309911yescharacteristic
433C2×C107#319811yescharacteristic
434C2×C107#320111yescharacteristic
435C2×#537C2×C10711yescharacteristic
436C2×#485C2×C10711yescharacteristic, complemented
437C2×#482C2×C10711yescharacteristic, complemented
438#2311C2×C10711yescharacteristic, complemented
439#2036C2×C10711yescharacteristic, complemented
440#2035C2×C10711yescharacteristic, complemented
441#2034C2×C10711yescharacteristic, complemented
442#2033C2×C10711yescharacteristic, complemented
443#1874C2×C10711yescharacteristic, complemented
444#1872C2×C10711yescharacteristic, complemented
445#1853C2×C10711yescharacteristic, complemented
446#1852C2×C10711yescharacteristic, complemented
447#1788C2×C10711yescharacteristic, complemented
448#1788C2×C10711yescharacteristic, complemented
449#1780C2×C10711yescharacteristic, complemented
450C107#2401711yescharacteristic, direct product factor, Sylow
451C22×#41C22×C10711yescharacteristic
452C22×#41C22×C10711yescharacteristic
453#537—24no—
454#537—24no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8C22×C10711yescharacteristic
457C2×C22⋊Q8C22×C10711yescharacteristic
458C2×#121—21no—
459C2×#121—21no—
460C2×#121—21no—
461C2×#121C22×C10711yescharacteristic
462C2×#121C22×C10711yescharacteristic
463C2×#117C22×C10711yescharacteristic
464C22×C4⋊C4C22×C10711yescharacteristic
465C22×C4⋊C4C22×C10711yescharacteristic
466#485—24no—
467#482—24no—
468C2×#107C22×C10711yescharacteristic
469C2×#107C22×C10711yescharacteristic
470C2×#106C22×C10711yescharacteristic
471C2×#106C22×C10711yescharacteristic
472C2×#103C22×C10711yescharacteristic
473C2×#103C22×C10711yescharacteristic
474C2×#103C22×C10711yescharacteristic
475C2×#103C22×C10711yescharacteristic
476C2×#102C22×C10711yescharacteristic
477C2×#102C22×C10711yescharacteristic
478C2×#102C22×C10711yescharacteristic
479C2×#102C22×C10711yescharacteristic
480C2×C22⋊C8C22×C10711yescharacteristic
481C2×C22⋊C8C22×C10711yescharacteristic
482C2×C22⋊C8C22×C10711yescharacteristic
483C2×C22⋊C8C22×C10711yescharacteristic
484C2×C22⋊C8C22×C10711yescharacteristic
485C2×C22⋊C8C22×C10711yescharacteristic
486#391—21no—
487#390—21no—
488#386—21no—
489#386—21no—
490#380C22×C10711yescharacteristic
491#380C22×C10711yescharacteristic
492#380C22×C10711yescharacteristic
493#380C22×C10711yescharacteristic
494#340C22×C10711yescharacteristic
495#340C22×C10711yescharacteristic
496#340C22×C10711yescharacteristic
497#340C22×C10711yescharacteristic
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C10711yescharacteristic
511C22×Q8C23×C10711yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C10711yescharacteristic
516C22×D4D4×C10711yescharacteristic
517C22×D4D4×C10711yescharacteristic
518C22×D4C23×C10711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C10711yescharacteristic
523C23×C4C23×C10711yescharacteristic
524C23×C4C23×C10711yescharacteristic
525C22×C8C23×C10711yescharacteristic
526C22×C8C23×C10711yescharacteristic
527C22×C8C23×C10711yescharacteristic
528C22×C8C23×C10711yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C10714yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C10714yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C10711yescharacteristic
552C2×C4⋊C4C23×C10711yescharacteristic
553C2×C4⋊C4C23×C10711yescharacteristic
554C2×C4⋊C4C23×C10711yescharacteristic
555C2×C4⋊C4C23×C10711yescharacteristic
556C2×C4⋊C4C23×C10711yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C10711yescharacteristic
591C24C2×D4×C10711yescharacteristic
592C24C2×D4×C10711yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C10712yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C10712yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C10711yescharacteristic
665C22×C4C2×D4×C10711yescharacteristic
666C22×C4C2×D4×C10712yes—
667C22×C4C2×D4×C10712yes—
668C22×C4C2×D4×C10711yescharacteristic
669C22×C4#41×C10712yes—
670C22×C4#41×C10712yes—
671C22×C4C24×C10711yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4C2×D4×C10712yes—
699C4⋊C4C2×D4×C10712yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C10712yes—
737C23#123×C10712yes—
738C23C22×D4×C10711yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4#120×C10712yes—
798C2×C4#123×C10712yes—
799C2×C4C22×D4×C10711yescharacteristic
800C2×C4C22×D4×C10711yescharacteristic
801C2×C4C2×#41×C10711yescharacteristic
802C2×C4C2×#41×C10711yescharacteristic
803C2×C4H(5,𝔽2)×C10711yescharacteristic
804C2×C4H(5,𝔽2)×C10711yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C10711yescharacteristic
838C22C2×#123×C10711yescharacteristic
839C22#534×C10711yescharacteristic
840C22#576×C10711yescharacteristic
841C22#577×C10711yescharacteristic
842C22#577×C10711yescharacteristic
843C22#578×C10711yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4#546×C10711yescharacteristic
855C4#546×C10711yescharacteristic
856C4#546×C10711yescharacteristic
857C4#546×C10711yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C107×#240511yescharacteristic
863C2C107×#301211yescharacteristic
864C2C107×#301311yescharacteristic
865C2C107×#309811yescharacteristic
866C2C107×#309911yescharacteristic
867C2C107×#319811yescharacteristic
868C2C107×#320111yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#537×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×#41×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C107C2semidirect
3. C2×#482×C107C2semidirect
4. C107×#2311C2semidirect
5. C107×#2036C2semidirect
6. C107×#2035C2semidirect
7. C107×#2034C2semidirect
8. C107×#2033C2semidirect
9. C107×#1874C2semidirect
10. C107×#1872C2semidirect
11. C107×#1853C2semidirect
12. C107×#1852C2semidirect
13. C107×#1788C2semidirect
14. C107×#1788C2semidirect
15. C107×#1780C2semidirect
423. #24017C107direct (N × H)
436. C2×#485C2×C107semidirect
437. C2×#482C2×C107semidirect
438. #2311C2×C107semidirect
439. #2036C2×C107semidirect
440. #2035C2×C107semidirect
441. #2034C2×C107semidirect
442. #2033C2×C107semidirect
443. #1874C2×C107semidirect
444. #1872C2×C107semidirect
445. #1853C2×C107semidirect
446. #1852C2×C107semidirect
447. #1788C2×C107semidirect
448. #1788C2×C107semidirect
449. #1780C2×C107semidirect
450. C107#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#537×C1072
C2×#485×C1072
C2×#482×C1072
C107×#23112
C107×#20362
C107×#20352
C107×#20342
C107×#20332
C107×#18742
C107×#18722
C107×#18532
C107×#18522
C107×#17882
C107×#17802
#24017107