Finite Group Databasebeta

← C107×#24443 #41050407

Subgroups — C107×#24443 #41050407

Order 27392.

1510 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C107C211yesmaximal, characteristic
2C2×#468×C107C211yesmaximal, characteristic, complemented
3C2×#452×C107C211yesmaximal, characteristic, complemented
4C2×#452×C107C211yesmaximal, characteristic, complemented
5C2×#417×C107C211yesmaximal, characteristic, complemented
6C107×#2417C211yesmaximal, characteristic, complemented
7C107×#2041C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#2014C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1878C211yesmaximal, characteristic, complemented
12C107×#1874C211yesmaximal, characteristic, complemented
13C107×#1870C211yesmaximal, characteristic, complemented
14C107×#1863C211yesmaximal, characteristic, complemented
15C107×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C22×Q16×C107C2211yescharacteristic
19C22×SD16×C107C2211yescharacteristic
20C22×SD16×C107C2211yescharacteristic
21C22×M16×C107C2211yescharacteristic
22#550×C107—24no—
23#550×C107—24no—
24C2×#127×C107—21no—
25C2×#127×C107C2211yescharacteristic
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×C22⋊Q8×C107C2211yescharacteristic
28C2×#121×C107—21no—
29C2×#121×C107—21no—
30C2×#121×C107C2211yescharacteristic
31C2×#121×C107C2211yescharacteristic
32C2×C4×Q8×C107C2211yescharacteristic
33C2×C4×D4×C107—21no—
34C2×C4×D4×C107C2211yescharacteristic
35C22×C4⋊C4×C107C2211yescharacteristic
36#468×C107—24no—
37#452×C107—24no—
38#452×C107—24no—
39C2×#107×C107C2211yescharacteristic
40#417×C107—24no—
41C2×#103×C107C2211yescharacteristic
42C2×#103×C107C2211yescharacteristic
43C2×#103×C107C2211yescharacteristic
44C2×#103×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic
54#398×C107—21no—
55#396×C107—21no—
56#391×C107C2211yescharacteristic
57#389×C107C2211yescharacteristic
58#386×C107—21no—
59#380×C107—21no—
60#380×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63#336×C107C2211yescharacteristic
64#336×C107C2211yescharacteristic
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—22no—
72C2×#41×C107—41no—
73C2×#41×C107—41no—
74C2×#41×C107—41no—
75C2×#41×C107—41no—
76C2×#41×C107D414yes—
77C22×Q8×C107C2311yescharacteristic
78C22×Q8×C107C2311yescharacteristic
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—21no—
83C22×D4×C107—21no—
84C22×D4×C107—21no—
85C22×D4×C107D411yescharacteristic
86C22×D4×C107C2311yescharacteristic
87C22×D4×C107C2311yescharacteristic
88C23×C4×C107—21no—
89C23×C4×C107—21no—
90C23×C4×C107—21no—
91C23×C4×C107C2311yescharacteristic
92C23×C4×C107C2311yescharacteristic
93C2×Q16×C107—22no—
94C2×Q16×C107—22no—
95C2×Q16×C107—22no—
96C2×SD16×C107—22no—
97C2×SD16×C107—22no—
98C2×SD16×C107—22no—
99C2×SD16×C107—41no—
100C2×SD16×C107—41no—
101C2×SD16×C107—41no—
102C2×M16×C107—22no—
103C2×M16×C107—22no—
104C2×M16×C107—41no—
105C22×C8×C107C2311yescharacteristic
106C22×C8×C107C2311yescharacteristic
107C22×C8×C107C2311yescharacteristic
108C22×C8×C107C2311yescharacteristic
109#127×C107—28no—
110#127×C107—22no—
111#127×C107—22no—
112C22⋊Q8×C107—22no—
113C22⋊Q8×C107—22no—
114C22⋊Q8×C107—22no—
115C22⋊Q8×C107—41no—
116#121×C107—28no—
117#121×C107—28no—
118#121×C107—22no—
119#121×C107—22no—
120#121×C107—22no—
121#121×C107D414yes—
122C4×Q8×C107—22no—
123C4×Q8×C107—22no—
124C4×D4×C107—28no—
125C4×D4×C107—22no—
126C4×D4×C107—22no—
127C2×C4⋊C4×C107—21no—
128C2×C4⋊C4×C107—22no—
129C2×C4⋊C4×C107—21no—
130C2×C4⋊C4×C107—21no—
131C2×C4⋊C4×C107—21no—
132C2×C4⋊C4×C107—21no—
133C2×C4⋊C4×C107—41no—
134C2×C4⋊C4×C107D411yescharacteristic
135C2×C4⋊C4×C107C2311yescharacteristic
136C2×C4⋊C4×C107C2311yescharacteristic
137C2×C4⋊C4×C107C2311yescharacteristic
138C2×C4⋊C4×C107C2311yescharacteristic
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×C107D411yescharacteristic
145C2×C22⋊C4×C107D411yescharacteristic
146C2×C42×C107—21no—
147C2×C42×C107C2311yescharacteristic
148#107×C107—22no—
149#103×C107—22no—
150#103×C107—22no—
151#103×C107—22no—
152#103×C107D414yescomplemented
153#102×C107—22no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—22no—
157#102×C107—22no—
158#102×C107—41no—
159C22⋊C8×C107—22no—
160C22⋊C8×C107—22no—
161C22⋊C8×C107—41no—
162#95×C107—21no—
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—21no—
167C24×C107—21no—
168C24×C107C2×D411yescharacteristic
169C24×C107C2×D411yescharacteristic
170#41×C107—28no—
171#41×C107—44no—
172#41×C107—44no—
173#41×C107—44no—
174#41×C107—44no—
175#41×C107—44no—
176#41×C107—44no—
177#41×C107—44no—
178C2×Q8×C107—21no—
179C2×Q8×C107—21no—
180C2×Q8×C107—21no—
181C2×Q8×C107—21no—
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×Q8×C107C2×D412yes—
189C2×Q8×C107#4112yes—
190C2×D4×C107—24no—
191C2×D4×C107—24no—
192C2×D4×C107—22no—
193C2×D4×C107—24no—
194C2×D4×C107—24no—
195C2×D4×C107—24no—
196C2×D4×C107—24no—
197C2×D4×C107—22no—
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—21no—
208C2×D4×C107—41no—
209C2×D4×C107—42no—
210C2×D4×C107—42no—
211C2×D4×C107—42no—
212C2×D4×C107—42no—
213C2×D4×C107—42no—
214C2×D4×C107—42no—
215C2×D4×C107—81no—
216C2×D4×C107—81no—
217C2×D4×C107—81no—
218C2×D4×C107—81no—
219C2×D4×C107—81no—
220C2×D4×C107—81no—
221C2×D4×C107C2×D412yes—
222C2×D4×C107C2×D412yes—
223C22×C4×C107—21no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—24no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—24no—
232C22×C4×C107—21no—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—21no—
236C22×C4×C107—21no—
237C22×C4×C107—21no—
238C22×C4×C107—21no—
239C22×C4×C107—21no—
240C22×C4×C107—21no—
241C22×C4×C107—42no—
242C22×C4×C107—42no—
243C22×C4×C107—42no—
244C22×C4×C107—42no—
245C22×C4×C107—42no—
246C22×C4×C107—42no—
247C22×C4×C107—81no—
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2×D411yescharacteristic
250C22×C4×C107C2×D411yescharacteristic
251C22×C4×C107C2×D412yes—
252C22×C4×C107C2×D412yes—
253C22×C4×C107C2×D411yescharacteristic
254C22×C4×C107C2411yescharacteristic
255Q16×C107—44no—
256SD16×C107—44no—
257SD16×C107—44no—
258M16×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×C107C2×D412yes—
271C4⋊C4×C107—24no—
272C4⋊C4×C107—22no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—42no—
280C4⋊C4×C107—42no—
281C4⋊C4×C107—42no—
282C4⋊C4×C107—81no—
283C4⋊C4×C107C2×D412yes—
284C4⋊C4×C107C2×D412yes—
285C22⋊C4×C107—24no—
286C22⋊C4×C107—22no—
287C22⋊C4×C107—24no—
288C22⋊C4×C107—22no—
289C22⋊C4×C107—42no—
290C22⋊C4×C107—42no—
291C22⋊C4×C107—81no—
292C42×C107—24no—
293C42×C107—21no—
294C42×C107—21no—
295C23×C107—21no—
296C23×C107—21no—
297C23×C107—21no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—22no—
303C23×C107—22no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—41no—
311C23×C107—41no—
312C23×C107—41no—
313C23×C107—41no—
314C23×C107—41no—
315C23×C107—41no—
316C23×C107—41no—
317C23×C107—41no—
318C23×C107—41no—
319C23×C107—41no—
320C23×C107—41no—
321C23×C107—41no—
322C23×C107#12012yes—
323C23×C107C22×D411yescharacteristic
324Q8×C107—22no—
325Q8×C107—22no—
326Q8×C107—22no—
327Q8×C107—41no—
328Q8×C107—41no—
329Q8×C107—41no—
330Q8×C107—41no—
331Q8×C107#12114yes—
332D4×C107—22no—
333D4×C107—22no—
334D4×C107—22no—
335D4×C107—22no—
336D4×C107—44no—
337D4×C107—48no—
338D4×C107—48no—
339D4×C107—48no—
340D4×C107—41no—
341D4×C107—41no—
342D4×C107—41no—
343D4×C107—41no—
344D4×C107—84no—
345D4×C107—84no—
346D4×C107—84no—
347C2×C4×C107—21no—
348C2×C4×C107—22no—
349C2×C4×C107—21no—
350C2×C4×C107—22no—
351C2×C4×C107—21no—
352C2×C4×C107—22no—
353C2×C4×C107—21no—
354C2×C4×C107—22no—
355C2×C4×C107—22no—
356C2×C4×C107—22no—
357C2×C4×C107—22no—
358C2×C4×C107—21no—
359C2×C4×C107—22no—
360C2×C4×C107—21no—
361C2×C4×C107—22no—
362C2×C4×C107—21no—
363C2×C4×C107—21no—
364C2×C4×C107—21no—
365C2×C4×C107—21no—
366C2×C4×C107—48no—
367C2×C4×C107—48no—
368C2×C4×C107—41no—
369C2×C4×C107—41no—
370C2×C4×C107—41no—
371C2×C4×C107—41no—
372C2×C4×C107—41no—
373C2×C4×C107—41no—
374C2×C4×C107—41no—
375C2×C4×C107—41no—
376C2×C4×C107—41no—
377C2×C4×C107—41no—
378C2×C4×C107—41no—
379C2×C4×C107—41no—
380C2×C4×C107—41no—
381C2×C4×C107—41no—
382C2×C4×C107—41no—
383C2×C4×C107—41no—
384C2×C4×C107—41no—
385C2×C4×C107—84no—
386C2×C4×C107#12012yes—
387C2×C4×C107#13712yes—
388C2×C4×C107C22×D411yescharacteristic
389C2×C4×C107C22×D411yescharacteristic
390C2×C4×C107C22×D411yescharacteristic
391C2×C4×C107C2×#4111yescharacteristic
392C2×C4×C107H(5,𝔽2)11yescharacteristic
393C2×C4×C107H(5,𝔽2)11yescharacteristic
394C8×C107—22no—
395C8×C107—41no—
396C8×C107—41no—
397C8×C107—41no—
398C22×C107—22no—
399C22×C107—22no—
400C22×C107—22no—
401C22×C107—41no—
402C22×C107—41no—
403C22×C107—41no—
404C22×C107—41no—
405C22×C107—41no—
406C22×C107—42no—
407C22×C107—42no—
408C22×C107—41no—
409C22×C107—41no—
410C22×C107—42no—
411C22×C107—42no—
412C22×C107—41no—
413C22×C107—42no—
414C22×C107—42no—
415C22×C107—41no—
416C22×C107—41no—
417C22×C107—41no—
418C22×C107—81no—
419C22×C107—81no—
420C22×C107—81no—
421C22×C107—81no—
422C22×C107—81no—
423C22×C107—81no—
424C22×C107—81no—
425C22×C107—81no—
426C22×C107C2×#12011yescharacteristic
427C22×C107D4211yescharacteristic
428C22×C107#54611yescharacteristic
429C22×C107C2×#13711yescharacteristic
430C22×C107#57511yescharacteristic
431C22×C107#57611yescharacteristic
432C22×C107#57711yescharacteristic
433C4×C107—22no—
434C4×C107—24no—
435C4×C107—22no—
436C4×C107—41no—
437C4×C107—41no—
438C4×C107—42no—
439C4×C107—42no—
440C4×C107—81no—
441C4×C107—81no—
442C4×C107—81no—
443C4×C107C2×#12111yescharacteristic
444C4×C107#53411yescharacteristic
445C4×C107D4211yescharacteristic
446C4×C107#54611yescharacteristic
447#24443C10711yesmaximal, characteristic, direct product factor, Sylow
448C2×C107—42no—
449C2×C107—81no—
450C2×C107—82no—
451C2×C107—82no—
452C2×C107#241011yescharacteristic
453C2×C107#300711yescharacteristic
454C2×C107#301211yescharacteristic
455C2×C107#326811yescharacteristic
456C2×C107#327811yescharacteristic
457C2×C107#331711yescharacteristic
458C2×C107#333311yescharacteristic
459C2×#550C2×C10711yescharacteristic
460C2×#468C2×C10711yescharacteristic, complemented
461C2×#452C2×C10711yescharacteristic, complemented
462C2×#452C2×C10711yescharacteristic, complemented
463C2×#417C2×C10711yescharacteristic, complemented
464#2417C2×C10711yescharacteristic, complemented
465#2041C2×C10711yescharacteristic, complemented
466#2033C2×C10711yescharacteristic, complemented
467#2014C2×C10711yescharacteristic, complemented
468#2000C2×C10711yescharacteristic, complemented
469#1878C2×C10711yescharacteristic, complemented
470#1874C2×C10711yescharacteristic, complemented
471#1870C2×C10711yescharacteristic, complemented
472#1863C2×C10711yescharacteristic, complemented
473#1788C2×C10711yescharacteristic, complemented
474C107#2444311yescharacteristic, direct product factor, Sylow
475C22×#41C22×C10711yescharacteristic
476C22×#41C22×C10711yescharacteristic
477C22×Q16C22×C10711yescharacteristic
478C22×SD16C22×C10711yescharacteristic
479C22×SD16C22×C10711yescharacteristic
480C22×M16C22×C10711yescharacteristic
481#550—24no—
482#550—24no—
483C2×#127—21no—
484C2×#127C22×C10711yescharacteristic
485C2×C22⋊Q8C22×C10711yescharacteristic
486C2×C22⋊Q8C22×C10711yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C10711yescharacteristic
490C2×#121C22×C10711yescharacteristic
491C2×C4×Q8C22×C10711yescharacteristic
492C2×C4×D4—21no—
493C2×C4×D4C22×C10711yescharacteristic
494C22×C4⋊C4C22×C10711yescharacteristic
495#468—24no—
496#452—24no—
497#452—24no—
498C2×#107C22×C10711yescharacteristic
499#417—24no—
500C2×#103C22×C10711yescharacteristic
501C2×#103C22×C10711yescharacteristic
502C2×#103C22×C10711yescharacteristic
503C2×#103C22×C10711yescharacteristic
504C2×#102C22×C10711yescharacteristic
505C2×#102C22×C10711yescharacteristic
506C2×#102C22×C10711yescharacteristic
507C2×#102C22×C10711yescharacteristic
508C2×#102C22×C10711yescharacteristic
509C2×#102C22×C10711yescharacteristic
510C2×C22⋊C8C22×C10711yescharacteristic
511C2×C22⋊C8C22×C10711yescharacteristic
512C2×C22⋊C8C22×C10711yescharacteristic
513#398—21no—
514#396—21no—
515#391C22×C10711yescharacteristic
516#389C22×C10711yescharacteristic
517#386—21no—
518#380—21no—
519#380C22×C10711yescharacteristic
520#340C22×C10711yescharacteristic
521#340C22×C10711yescharacteristic
522#336C22×C10711yescharacteristic
523#336C22×C10711yescharacteristic
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C10714yes—
536C22×Q8C23×C10711yescharacteristic
537C22×Q8C23×C10711yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4D4×C10711yescharacteristic
545C22×D4C23×C10711yescharacteristic
546C22×D4C23×C10711yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C23×C10711yescharacteristic
551C23×C4C23×C10711yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C22×C8C23×C10711yescharacteristic
565C22×C8C23×C10711yescharacteristic
566C22×C8C23×C10711yescharacteristic
567C22×C8C23×C10711yescharacteristic
568#127—28no—
569#127—22no—
570#127—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575#121—28no—
576#121—28no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121D4×C10714yes—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—28no—
584C4×D4—22no—
585C4×D4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4D4×C10711yescharacteristic
594C2×C4⋊C4C23×C10711yescharacteristic
595C2×C4⋊C4C23×C10711yescharacteristic
596C2×C4⋊C4C23×C10711yescharacteristic
597C2×C4⋊C4C23×C10711yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4D4×C10711yescharacteristic
604C2×C22⋊C4D4×C10711yescharacteristic
605C2×C42—21no—
606C2×C42C23×C10711yescharacteristic
607#107—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103D4×C10714yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C10711yescharacteristic
628C24C2×D4×C10711yescharacteristic
629#41—28no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8C2×D4×C10712yes—
647C2×Q8C2×D4×C10712yes—
648C2×Q8#41×C10712yes—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4C2×D4×C10712yes—
681C2×D4C2×D4×C10712yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—81no—
707C22×C4C2×D4×C10711yescharacteristic
708C22×C4C2×D4×C10711yescharacteristic
709C22×C4C2×D4×C10711yescharacteristic
710C22×C4C2×D4×C10712yes—
711C22×C4C2×D4×C10712yes—
712C22×C4C2×D4×C10711yescharacteristic
713C22×C4C24×C10711yescharacteristic
714Q16—44no—
715SD16—44no—
716SD16—44no—
717M16—44no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8C2×D4×C10712yes—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C10712yes—
743C4⋊C4C2×D4×C10712yes—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—81no—
751C42—24no—
752C42—21no—
753C42—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—22no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#120×C10712yes—
782C23C22×D4×C10711yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8#121×C10714yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—48no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—84no—
804D4—84no—
805D4—84no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—48no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4#120×C10712yes—
846C2×C4#137×C10712yes—
847C2×C4C22×D4×C10711yescharacteristic
848C2×C4C22×D4×C10711yescharacteristic
849C2×C4C22×D4×C10711yescharacteristic
850C2×C4C2×#41×C10711yescharacteristic
851C2×C4H(5,𝔽2)×C10711yescharacteristic
852C2×C4H(5,𝔽2)×C10711yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C10711yescharacteristic
886C22D42×C10711yescharacteristic
887C22#546×C10711yescharacteristic
888C22C2×#137×C10711yescharacteristic
889C22#575×C10711yescharacteristic
890C22#576×C10711yescharacteristic
891C22#577×C10711yescharacteristic
892C4—22no—
893C4—24no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4C2×#121×C10711yescharacteristic
903C4#534×C10711yescharacteristic
904C4D42×C10711yescharacteristic
905C4#546×C10711yescharacteristic
906C2—42no—
907C2—81no—
908C2—82no—
909C2—82no—
910C2C107×#241011yescharacteristic
911C2C107×#300711yescharacteristic
912C2C107×#301211yescharacteristic
913C2C107×#326811yescharacteristic
914C2C107×#327811yescharacteristic
915C2C107×#331711yescharacteristic
916C2C107×#333311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#550×C107C2
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
2. C2×#468×C107C2semidirect
3. C2×#452×C107C2semidirect
4. C2×#452×C107C2semidirect
5. C2×#417×C107C2semidirect
6. C107×#2417C2semidirect
7. C107×#2041C2semidirect
8. C107×#2033C2semidirect
9. C107×#2014C2semidirect
10. C107×#2000C2semidirect
11. C107×#1878C2semidirect
12. C107×#1874C2semidirect
13. C107×#1870C2semidirect
14. C107×#1863C2semidirect
15. C107×#1788C2semidirect
152. #103×C107D4semidirect
447. #24443C107direct (N × H)
460. C2×#468C2×C107semidirect
461. C2×#452C2×C107semidirect
462. C2×#452C2×C107semidirect
463. C2×#417C2×C107semidirect
464. #2417C2×C107semidirect
465. #2041C2×C107semidirect
466. #2033C2×C107semidirect
467. #2014C2×C107semidirect
468. #2000C2×C107semidirect
469. #1878C2×C107semidirect
470. #1874C2×C107semidirect
471. #1870C2×C107semidirect
472. #1863C2×C107semidirect
473. #1788C2×C107semidirect
474. C107#24443direct (N × H)
611. #103D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1072
C2×#468×C1072
C2×#452×C1072
C2×#417×C1072
C107×#24172
C107×#20412
C107×#20332
C107×#20142
C107×#20002
C107×#18782
C107×#18742
C107×#18702
C107×#18632
C107×#17882
#24443107