Finite Group Databasebeta

← C107×#24901 #41050865

Subgroups — C107×#24901 #41050865

Order 27392.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C107C211yesmaximal, characteristic
2C2×C4×SD16×C107C211yesmaximal, characteristic, complemented
3C107×#2423C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C107C211yesmaximal, characteristic
5C107×#2094C211yesmaximal, characteristic, complemented
6C107×#2077C211yesmaximal, characteristic, complemented
7C107×#2055C211yesmaximal, characteristic, complemented
8C107×#2035C211yesmaximal, characteristic, complemented
9C107×#1934C211yesmaximal, characteristic, complemented
10C107×#1923C211yesmaximal, characteristic, complemented
11C107×#1880C211yesmaximal, characteristic, complemented
12C107×#1877C211yesmaximal, characteristic, complemented
13C107×#1864C211yesmaximal, characteristic, complemented
14C107×#1802C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic
16C23×D4×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C2×C22⋊Q8×C107C2211yescharacteristic
20C2×C4×Q8×C107C2211yescharacteristic, complemented
21C2×C4×D4×C107C2211yescharacteristic
22C2×C4×D4×C107C2211yescharacteristic
23C22×C22⋊C4×C107—21no—
24#450×C107—24no—
25C4×SD16×C107—24no—
26C2×#106×C107C2211yescharacteristic, complemented
27C2×#106×C107C2211yescharacteristic, complemented
28C2×C4⋊C8×C107C2211yescharacteristic, complemented
29C2×#103×C107C2211yescharacteristic, complemented
30C2×#103×C107C2211yescharacteristic, complemented
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×C22⋊C8×C107C2211yescharacteristic
38C2×C22⋊C8×C107C2211yescharacteristic
39C2×C4×C8×C107C2211yescharacteristic, complemented
40#399×C107—21no—
41#398×C107—21no—
42#391×C107C2211yescharacteristic, complemented
43#390×C107C2211yescharacteristic
44#390×C107C2211yescharacteristic
45#389×C107C2211yescharacteristic, complemented
46#388×C107—21no—
47#387×C107—21no—
48#386×C107—21no—
49#386×C107—21no—
50#384×C107C2211yescharacteristic, complemented
51#380×C107C2211yescharacteristic
52#380×C107C2211yescharacteristic
53#379×C107—21no—
54C4×C22⋊C4×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic, complemented
56#340×C107C2211yescharacteristic, complemented
57#340×C107C2211yescharacteristic, complemented
58#340×C107C2211yescharacteristic, complemented
59#336×C107C2211yescharacteristic, complemented
60#336×C107C2211yescharacteristic, complemented
61C25×C107—21no—
62C22×Q8×C107C2311yescharacteristic
63C22×D4×C107—22no—
64C22×D4×C107—22no—
65C22×D4×C107—22no—
66C22×D4×C107—22no—
67C22×D4×C107—21no—
68C22×D4×C107—41no—
69C22×D4×C107—41no—
70C22×D4×C107C2311yescharacteristic
71C22×D4×C107C2311yescharacteristic
72C23×C4×C107—21no—
73C23×C4×C107—21no—
74C23×C4×C107C2311yescharacteristic
75C2×SD16×C107—22no—
76C2×SD16×C107—22no—
77C2×SD16×C107—22no—
78C2×SD16×C107—22no—
79C2×SD16×C107—41no—
80C2×SD16×C107D414yes—
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83C22×C8×C107C2311yescharacteristic
84C22×C8×C107C2311yescharacteristic
85C22⋊Q8×C107—22no—
86C22⋊Q8×C107—41no—
87C4×Q8×C107—22no—
88C4×Q8×C107—41no—
89C4×D4×C107—22no—
90C4×D4×C107—22no—
91C4×D4×C107—41no—
92C4×D4×C107—41no—
93C2×C4⋊C4×C107—21no—
94C2×C4⋊C4×C107—21no—
95C2×C4⋊C4×C107—21no—
96C2×C4⋊C4×C107—21no—
97C2×C4⋊C4×C107—21no—
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C4⋊C4×C107C2311yescharacteristic
101C2×C4⋊C4×C107C2311yescharacteristic
102C2×C4⋊C4×C107C2311yescharacteristic
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—21no—
105C2×C22⋊C4×C107—21no—
106C2×C22⋊C4×C107—21no—
107C2×C22⋊C4×C107—21no—
108C2×C22⋊C4×C107—21no—
109C2×C22⋊C4×C107—21no—
110C2×C22⋊C4×C107—21no—
111C2×C22⋊C4×C107—21no—
112C2×C22⋊C4×C107—44no—
113C2×C22⋊C4×C107D411yescharacteristic
114C2×C22⋊C4×C107D411yescharacteristic
115C2×C42×C107—21no—
116C2×C42×C107C2311yescharacteristic
117C2×C42×C107C2311yescharacteristic
118#106×C107—22no—
119#106×C107—41no—
120C4⋊C8×C107—41no—
121#103×C107—22no—
122#103×C107—41no—
123#102×C107—22no—
124#102×C107—22no—
125#102×C107—22no—
126#102×C107—22no—
127#102×C107—22no—
128#102×C107—41no—
129C22⋊C8×C107—22no—
130C22⋊C8×C107—41no—
131C4×C8×C107—22no—
132#95×C107—21no—
133#95×C107—21no—
134#95×C107—21no—
135#95×C107—21no—
136#95×C107—21no—
137#95×C107D411yescharacteristic
138#95×C107D411yescharacteristic
139C24×C107—21no—
140C24×C107—24no—
141C24×C107—21no—
142C24×C107—42no—
143C24×C107—42no—
144C24×C107—42no—
145C24×C107—42no—
146C24×C107—81no—
147C24×C107—81no—
148C24×C107C2×D411yescharacteristic
149C2×Q8×C107—21no—
150C2×Q8×C107—21no—
151C2×Q8×C107—21no—
152C2×Q8×C107—21no—
153C2×Q8×C107—21no—
154C2×Q8×C107C2×D412yes—
155C2×D4×C107—24no—
156C2×D4×C107—21no—
157C2×D4×C107—21no—
158C2×D4×C107—21no—
159C2×D4×C107—21no—
160C2×D4×C107—21no—
161C2×D4×C107—21no—
162C2×D4×C107—21no—
163C2×D4×C107—21no—
164C2×D4×C107—42no—
165C2×D4×C107—42no—
166C2×D4×C107—44no—
167C2×D4×C107—44no—
168C2×D4×C107—44no—
169C2×D4×C107—44no—
170C2×D4×C107C2×D412yes—
171C2×D4×C107#4112yes—
172C2×D4×C107#4112yes—
173C2×D4×C107#4112yes—
174C22×C4×C107—21no—
175C22×C4×C107—21no—
176C22×C4×C107—21no—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—42no—
187C22×C4×C107—42no—
188C22×C4×C107—42no—
189C22×C4×C107—42no—
190C22×C4×C107—81no—
191C22×C4×C107—81no—
192C22×C4×C107C2×D411yescharacteristic
193C22×C4×C107C2×D411yescharacteristic
194C22×C4×C107C2×D411yescharacteristic
195C22×C4×C107C2×D411yescharacteristic
196C22×C4×C107C2×D411yescharacteristic
197C22×C4×C107C2411yescharacteristic
198SD16×C107—28no—
199SD16×C107—44no—
200C2×C8×C107—21no—
201C2×C8×C107—21no—
202C2×C8×C107—21no—
203C2×C8×C107—21no—
204C2×C8×C107—21no—
205C2×C8×C107—21no—
206C2×C8×C107—21no—
207C2×C8×C107—21no—
208C2×C8×C107—21no—
209C2×C8×C107—21no—
210C2×C8×C107—21no—
211C2×C8×C107C2×D412yes—
212C4⋊C4×C107—21no—
213C4⋊C4×C107—21no—
214C4⋊C4×C107—21no—
215C4⋊C4×C107—21no—
216C4⋊C4×C107—21no—
217C4⋊C4×C107—21no—
218C4⋊C4×C107—21no—
219C4⋊C4×C107—21no—
220C4⋊C4×C107—21no—
221C4⋊C4×C107—21no—
222C4⋊C4×C107—42no—
223C4⋊C4×C107—42no—
224C4⋊C4×C107—42no—
225C4⋊C4×C107—81no—
226C4⋊C4×C107—81no—
227C22⋊C4×C107—41no—
228C22⋊C4×C107—42no—
229C22⋊C4×C107—42no—
230C22⋊C4×C107—42no—
231C22⋊C4×C107—42no—
232C22⋊C4×C107—42no—
233C22⋊C4×C107—42no—
234C22⋊C4×C107—81no—
235C22⋊C4×C107—81no—
236C22⋊C4×C107—81no—
237C22⋊C4×C107SD1614yescomplemented
238C42×C107—21no—
239C42×C107—21no—
240C42×C107—21no—
241C42×C107—21no—
242C42×C107—42no—
243C23×C107—21no—
244C23×C107—22no—
245C23×C107—21no—
246C23×C107—22no—
247C23×C107—22no—
248C23×C107—21no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107—21no—
252C23×C107—22no—
253C23×C107—48no—
254C23×C107—48no—
255C23×C107—41no—
256C23×C107—41no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107—41no—
260C23×C107—41no—
261C23×C107—41no—
262C23×C107—41no—
263C23×C107—41no—
264C23×C107—41no—
265C23×C107—84no—
266C23×C107—84no—
267C23×C107—84no—
268C23×C107—84no—
269C23×C107—84no—
270C23×C107C2×SD1612yes—
271C23×C107C22×D411yescharacteristic
272Q8×C107—22no—
273Q8×C107—22no—
274Q8×C107—41no—
275Q8×C107—41no—
276D4×C107—22no—
277D4×C107—22no—
278D4×C107—22no—
279D4×C107—22no—
280D4×C107—22no—
281D4×C107—48no—
282D4×C107—41no—
283D4×C107—41no—
284D4×C107#12314yes—
285C2×C4×C107—21no—
286C2×C4×C107—21no—
287C2×C4×C107—21no—
288C2×C4×C107—21no—
289C2×C4×C107—21no—
290C2×C4×C107—21no—
291C2×C4×C107—22no—
292C2×C4×C107—21no—
293C2×C4×C107—21no—
294C2×C4×C107—21no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—21no—
298C2×C4×C107—21no—
299C2×C4×C107—41no—
300C2×C4×C107—41no—
301C2×C4×C107—41no—
302C2×C4×C107—41no—
303C2×C4×C107—41no—
304C2×C4×C107—41no—
305C2×C4×C107—41no—
306C2×C4×C107—41no—
307C2×C4×C107—41no—
308C2×C4×C107—41no—
309C2×C4×C107—41no—
310C2×C4×C107—41no—
311C2×C4×C107—41no—
312C2×C4×C107—41no—
313C2×C4×C107—41no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—84no—
321C2×C4×C107—84no—
322C2×C4×C107C2×SD1612yes—
323C2×C4×C107C2×SD1612yes—
324C2×C4×C107C22×D411yescharacteristic
325C2×C4×C107C2×#4111yescharacteristic
326C2×C4×C107C2×#4111yescharacteristic
327C2×C4×C107C2×#4111yescharacteristic
328C2×C4×C107H(5,𝔽2)11yescharacteristic
329C2×C4×C107H(5,𝔽2)11yescharacteristic
330C8×C107—22no—
331C8×C107—41no—
332C8×C107—41no—
333C8×C107—41no—
334C22×C107—22no—
335C22×C107—24no—
336C22×C107—22no—
337C22×C107—22no—
338C22×C107—42no—
339C22×C107—41no—
340C22×C107—42no—
341C22×C107—41no—
342C22×C107—41no—
343C22×C107—42no—
344C22×C107—42no—
345C22×C107—42no—
346C22×C107—41no—
347C22×C107—42no—
348C22×C107—42no—
349C22×C107—42no—
350C22×C107—42no—
351C22×C107—816no—
352C22×C107—81no—
353C22×C107—81no—
354C22×C107—81no—
355C22×C107—81no—
356C22×C107#52511yescharacteristic
357C22×C107D4211yescharacteristic
358C22×C107#54611yescharacteristic
359C22×C107C22×SD1611yescharacteristic
360C22×C107#57511yescharacteristic
361C22×C107#57611yescharacteristic
362C22×C107#57711yescharacteristic
363C4×C107—22no—
364C4×C107—22no—
365C4×C107—41no—
366C4×C107—42no—
367C4×C107—41no—
368C4×C107—41no—
369C4×C107—81no—
370C4×C107—81no—
371C4×C107—81no—
372C4×C107—81no—
373C4×C107—81no—
374C4×C107C2×#12311yescharacteristic
375C4×C107#53811yescharacteristic
376C4×C107#54611yescharacteristic
377C4×C107#55111yescharacteristic
378#24901C10711yesmaximal, characteristic, direct product factor, Sylow
379C2×C107—42no—
380C2×C107—44no—
381C2×C107—82no—
382C2×C107#241811yescharacteristic
383C2×C107#310111yescharacteristic
384C2×C107#311811yescharacteristic
385C2×C107#326811yescharacteristic
386C2×C107D4×SD1611yescharacteristic
387C2×C107#329511yescharacteristic
388C2×C107#332311yescharacteristic
389C2×#450C2×C10711yescharacteristic
390C2×C4×SD16C2×C10711yescharacteristic, complemented
391#2423C2×C10711yescharacteristic, complemented
392D4×C22⋊C4C2×C10711yescharacteristic
393#2094C2×C10711yescharacteristic, complemented
394#2077C2×C10711yescharacteristic, complemented
395#2055C2×C10711yescharacteristic, complemented
396#2035C2×C10711yescharacteristic, complemented
397#1934C2×C10711yescharacteristic, complemented
398#1923C2×C10711yescharacteristic, complemented
399#1880C2×C10711yescharacteristic, complemented
400#1877C2×C10711yescharacteristic, complemented
401#1864C2×C10711yescharacteristic, complemented
402#1802C2×C10711yescharacteristic, complemented
403#1786C2×C10711yescharacteristic
404C107#2490111yescharacteristic, direct product factor, Sylow
405C23×D4C22×C10711yescharacteristic
406C22×SD16C22×C10711yescharacteristic
407C22×SD16C22×C10711yescharacteristic
408C2×C22⋊Q8C22×C10711yescharacteristic
409C2×C4×Q8C22×C10711yescharacteristic, complemented
410C2×C4×D4C22×C10711yescharacteristic
411C2×C4×D4C22×C10711yescharacteristic
412C22×C22⋊C4—21no—
413#450—24no—
414C4×SD16—24no—
415C2×#106C22×C10711yescharacteristic, complemented
416C2×#106C22×C10711yescharacteristic, complemented
417C2×C4⋊C8C22×C10711yescharacteristic, complemented
418C2×#103C22×C10711yescharacteristic, complemented
419C2×#103C22×C10711yescharacteristic, complemented
420C2×#102C22×C10711yescharacteristic
421C2×#102C22×C10711yescharacteristic
422C2×#102C22×C10711yescharacteristic
423C2×#102C22×C10711yescharacteristic
424C2×#102C22×C10711yescharacteristic
425C2×#102C22×C10711yescharacteristic
426C2×C22⋊C8C22×C10711yescharacteristic
427C2×C22⋊C8C22×C10711yescharacteristic
428C2×C4×C8C22×C10711yescharacteristic, complemented
429#399—21no—
430#398—21no—
431#391C22×C10711yescharacteristic, complemented
432#390C22×C10711yescharacteristic
433#390C22×C10711yescharacteristic
434#389C22×C10711yescharacteristic, complemented
435#388—21no—
436#387—21no—
437#386—21no—
438#386—21no—
439#384C22×C10711yescharacteristic, complemented
440#380C22×C10711yescharacteristic
441#380C22×C10711yescharacteristic
442#379—21no—
443C4×C22⋊C4C22×C10711yescharacteristic
444#340C22×C10711yescharacteristic, complemented
445#340C22×C10711yescharacteristic, complemented
446#340C22×C10711yescharacteristic, complemented
447#340C22×C10711yescharacteristic, complemented
448#336C22×C10711yescharacteristic, complemented
449#336C22×C10711yescharacteristic, complemented
450C25—21no—
451C22×Q8C23×C10711yescharacteristic
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C23×C10711yescharacteristic
460C22×D4C23×C10711yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C10711yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16D4×C10714yes—
470C22×C8C23×C10711yescharacteristic
471C22×C8C23×C10711yescharacteristic
472C22×C8C23×C10711yescharacteristic
473C22×C8C23×C10711yescharacteristic
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C10711yescharacteristic
488C2×C4⋊C4C23×C10711yescharacteristic
489C2×C4⋊C4C23×C10711yescharacteristic
490C2×C4⋊C4C23×C10711yescharacteristic
491C2×C4⋊C4C23×C10711yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4D4×C10711yescharacteristic
503C2×C22⋊C4D4×C10711yescharacteristic
504C2×C42—21no—
505C2×C42C23×C10711yescharacteristic
506C2×C42C23×C10711yescharacteristic
507#106—22no—
508#106—41no—
509C4⋊C8—41no—
510#103—22no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—41no—
520C4×C8—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C10711yescharacteristic
527#95D4×C10711yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×D4×C10711yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C10712yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×D4×C10712yes—
560C2×D4#41×C10712yes—
561C2×D4#41×C10712yes—
562C2×D4#41×C10712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C10711yescharacteristic
582C22×C4C2×D4×C10711yescharacteristic
583C22×C4C2×D4×C10711yescharacteristic
584C22×C4C2×D4×C10711yescharacteristic
585C22×C4C2×D4×C10711yescharacteristic
586C22×C4C24×C10711yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×D4×C10712yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4—81no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4SD16×C10714yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×SD16×C10712yes—
660C23C22×D4×C10711yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#123×C10714yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C2×SD16×C10712yes—
712C2×C4C2×SD16×C10712yes—
713C2×C4C22×D4×C10711yescharacteristic
714C2×C4C2×#41×C10711yescharacteristic
715C2×C4C2×#41×C10711yescharacteristic
716C2×C4C2×#41×C10711yescharacteristic
717C2×C4H(5,𝔽2)×C10711yescharacteristic
718C2×C4H(5,𝔽2)×C10711yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—24no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#525×C10711yescharacteristic
746C22D42×C10711yescharacteristic
747C22#546×C10711yescharacteristic
748C22C22×SD16×C10711yescharacteristic
749C22#575×C10711yescharacteristic
750C22#576×C10711yescharacteristic
751C22#577×C10711yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×#123×C10711yescharacteristic
764C4#538×C10711yescharacteristic
765C4#546×C10711yescharacteristic
766C4#551×C10711yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2C107×#241811yescharacteristic
771C2C107×#310111yescharacteristic
772C2C107×#311811yescharacteristic
773C2C107×#326811yescharacteristic
774C2D4×SD16×C10711yescharacteristic
775C2C107×#329511yescharacteristic
776C2C107×#332311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC23×D4×C107C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C22⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C107C2semidirect
3. C107×#2423C2semidirect
5. C107×#2094C2semidirect
6. C107×#2077C2semidirect
7. C107×#2055C2semidirect
8. C107×#2035C2semidirect
9. C107×#1934C2semidirect
10. C107×#1923C2semidirect
11. C107×#1880C2semidirect
12. C107×#1877C2semidirect
13. C107×#1864C2semidirect
14. C107×#1802C2semidirect
20. C2×C4×Q8×C107C22semidirect
26. C2×#106×C107C22semidirect
27. C2×#106×C107C22semidirect
28. C2×C4⋊C8×C107C22semidirect
29. C2×#103×C107C22semidirect
30. C2×#103×C107C22semidirect
39. C2×C4×C8×C107C22semidirect
42. #391×C107C22semidirect
45. #389×C107C22semidirect
50. #384×C107C22semidirect
55. #340×C107C22semidirect
56. #340×C107C22semidirect
57. #340×C107C22semidirect
58. #340×C107C22semidirect
59. #336×C107C22semidirect
60. #336×C107C22semidirect
237. C22⋊C4×C107SD16semidirect
378. #24901C107direct (N × H)
390. C2×C4×SD16C2×C107semidirect
391. #2423C2×C107semidirect
393. #2094C2×C107semidirect
394. #2077C2×C107semidirect
395. #2055C2×C107semidirect
396. #2035C2×C107semidirect
397. #1934C2×C107semidirect
398. #1923C2×C107semidirect
399. #1880C2×C107semidirect
400. #1877C2×C107semidirect
401. #1864C2×C107semidirect
402. #1802C2×C107semidirect
404. C107#24901direct (N × H)
409. C2×C4×Q8C22×C107semidirect
415. C2×#106C22×C107semidirect
416. C2×#106C22×C107semidirect
417. C2×C4⋊C8C22×C107semidirect
418. C2×#103C22×C107semidirect
419. C2×#103C22×C107semidirect
428. C2×C4×C8C22×C107semidirect
431. #391C22×C107semidirect
434. #389C22×C107semidirect
439. #384C22×C107semidirect
444. #340C22×C107semidirect
445. #340C22×C107semidirect
446. #340C22×C107semidirect
447. #340C22×C107semidirect
448. #336C22×C107semidirect
449. #336C22×C107semidirect
626. C22⋊C4SD16×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1072
C2×C4×SD16×C1072
C107×#24232
D4×C22⋊C4×C1072
C107×#20942
C107×#20772
C107×#20552
C107×#20352
C107×#19342
C107×#19232
C107×#18802
C107×#18772
C107×#18642
C107×#18022
C107×#17862
#24901107