Finite Group Databasebeta

← C107×#26786 #41052750

Subgroups — C107×#26786 #41052750

Order 27392.

904 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#483×C107C211yesmaximal, characteristic, complemented
2C2×#476×C107C211yesmaximal, characteristic, complemented
3C107×#2492C211yesmaximal, characteristic, complemented
4C107×#2361C211yesmaximal, characteristic
5C107×#2066C211yesmaximal, characteristic, complemented
6C107×#2058C211yesmaximal, characteristic, complemented
7C107×#2034C211yesmaximal, characteristic
8C107×#2000C211yesmaximal, characteristic
9C107×#1968C211yesmaximal, characteristic, complemented
10C107×#1927C211yesmaximal, characteristic, complemented
11C107×#1926C211yesmaximal, characteristic, complemented
12C107×#1923C211yesmaximal, characteristic, complemented
13C107×#1877C211yesmaximal, characteristic, complemented
14C107×#1853C211yesmaximal, characteristic, complemented
15C4×#106×C107C211yesmaximal, characteristic, complemented
16C22×SD16×C107C2211yescharacteristic
17C2×C4⋊Q8×C107C2211yescharacteristic
18C2×C22⋊Q8×C107C2211yescharacteristic
19C2×#121×C107C2211yescharacteristic
20C2×C4×D4×C107—21no—
21C2×C4×D4×C107C2211yescharacteristic
22C22×C4⋊C4×C107C2211yescharacteristic
23#483×C107—24no—
24#476×C107—24no—
25C2×#106×C107C2211yescharacteristic
26C2×#106×C107C2211yescharacteristic
27C2×#106×C107C2211yescharacteristic
28C2×#106×C107C2211yescharacteristic
29C2×#106×C107C2211yescharacteristic
30C2×C4⋊C8×C107C2211yescharacteristic
31C2×#103×C107C2211yescharacteristic
32C2×#103×C107C2211yescharacteristic
33C2×#103×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×C22⋊C8×C107C2211yescharacteristic
38C2×C22⋊C8×C107C2211yescharacteristic
39C2×C4×C8×C107C2211yescharacteristic
40#400×C107—21no—
41#393×C107—21no—
42#391×C107—21no—
43#391×C107C2211yescharacteristic
44#391×C107C2211yescharacteristic
45#390×C107C2211yescharacteristic
46#389×C107C2211yescharacteristic
47#388×C107—21no—
48#388×C107—21no—
49#386×C107—21no—
50#385×C107—21no—
51#380×C107C2211yescharacteristic
52C4×C4⋊C4×C107C2211yescharacteristic
53C4×C4⋊C4×C107C2211yescharacteristic
54C4×C22⋊C4×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61C22×Q8×C107—21no—
62C22×Q8×C107C2311yescharacteristic
63C22×D4×C107—21no—
64C22×D4×C107C2311yescharacteristic
65C23×C4×C107—21no—
66C23×C4×C107—21no—
67C23×C4×C107C2311yescharacteristic
68C2×SD16×C107—22no—
69C2×SD16×C107—22no—
70C2×SD16×C107—41no—
71C22×C8×C107C2311yescharacteristic
72C22×C8×C107C2311yescharacteristic
73C22×C8×C107C2311yescharacteristic
74C22×C8×C107C2311yescharacteristic
75C4⋊Q8×C107—22no—
76C4⋊Q8×C107—41no—
77C22⋊Q8×C107—22no—
78C22⋊Q8×C107—41no—
79#121×C107—22no—
80#121×C107—22no—
81C4×D4×C107—22no—
82C4×D4×C107—41no—
83C4×D4×C107—44no—
84C2×C4⋊C4×C107—22no—
85C2×C4⋊C4×C107—21no—
86C2×C4⋊C4×C107—21no—
87C2×C4⋊C4×C107—21no—
88C2×C4⋊C4×C107—21no—
89C2×C4⋊C4×C107—41no—
90C2×C4⋊C4×C107C2311yescharacteristic
91C2×C4⋊C4×C107C2311yescharacteristic
92C2×C4⋊C4×C107C2311yescharacteristic
93C2×C4⋊C4×C107C2311yescharacteristic
94C2×C4⋊C4×C107C2311yescharacteristic
95C2×C4⋊C4×C107C2311yescharacteristic
96C2×C22⋊C4×C107—21no—
97C2×C22⋊C4×C107—21no—
98C2×C22⋊C4×C107—21no—
99C2×C22⋊C4×C107—21no—
100C2×C22⋊C4×C107—21no—
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107D411yescharacteristic
103C2×C22⋊C4×C107D411yescharacteristic
104C2×C42×C107—21no—
105C2×C42×C107—21no—
106C2×C42×C107C2311yescharacteristic
107C2×C42×C107C2311yescharacteristic
108#106×C107—22no—
109#106×C107—22no—
110#106×C107—22no—
111#106×C107—41no—
112#106×C107D414yescomplemented
113C4⋊C8×C107—22no—
114#103×C107—22no—
115#103×C107—22no—
116#103×C107—22no—
117#102×C107—22no—
118#102×C107—22no—
119#102×C107—22no—
120C22⋊C8×C107—22no—
121C22⋊C8×C107—22no—
122C4×C8×C107—22no—
123#95×C107—21no—
124#95×C107—21no—
125#95×C107—21no—
126#95×C107—21no—
127#95×C107—21no—
128#95×C107—21no—
129#95×C107—21no—
130#95×C107—21no—
131#95×C107D411yescharacteristic
132#95×C107D411yescharacteristic
133C24×C107—21no—
134C24×C107C2×D411yescharacteristic
135C2×Q8×C107—21no—
136C2×Q8×C107—21no—
137C2×Q8×C107—21no—
138C2×Q8×C107—21no—
139C2×Q8×C107—21no—
140C2×Q8×C107—21no—
141C2×Q8×C107—42no—
142C2×Q8×C107—42no—
143C2×Q8×C107—81no—
144C2×D4×C107—24no—
145C2×D4×C107—21no—
146C2×D4×C107—21no—
147C2×D4×C107—21no—
148C2×D4×C107—21no—
149C2×D4×C107—21no—
150C2×D4×C107—42no—
151C2×D4×C107—42no—
152C2×D4×C107#4112yes—
153C22×C4×C107—21no—
154C22×C4×C107—21no—
155C22×C4×C107—21no—
156C22×C4×C107—21no—
157C22×C4×C107—21no—
158C22×C4×C107—21no—
159C22×C4×C107—21no—
160C22×C4×C107—21no—
161C22×C4×C107—21no—
162C22×C4×C107—21no—
163C22×C4×C107—21no—
164C22×C4×C107—21no—
165C22×C4×C107—21no—
166C22×C4×C107—42no—
167C22×C4×C107—42no—
168C22×C4×C107—42no—
169C22×C4×C107—42no—
170C22×C4×C107—81no—
171C22×C4×C107—81no—
172C22×C4×C107C2×D411yescharacteristic
173C22×C4×C107C2×D411yescharacteristic
174C22×C4×C107C2×D411yescharacteristic
175C22×C4×C107C2×D411yescharacteristic
176C22×C4×C107C2×D411yescharacteristic
177C22×C4×C107C2411yescharacteristic
178SD16×C107—44no—
179C2×C8×C107—21no—
180C2×C8×C107—21no—
181C2×C8×C107—21no—
182C2×C8×C107—21no—
183C2×C8×C107—21no—
184C2×C8×C107—21no—
185C2×C8×C107—21no—
186C2×C8×C107—21no—
187C2×C8×C107—21no—
188C2×C8×C107—21no—
189C2×C8×C107C2×D412yes—
190C2×C8×C107#4112yes—
191C4⋊C4×C107—21no—
192C4⋊C4×C107—21no—
193C4⋊C4×C107—21no—
194C4⋊C4×C107—21no—
195C4⋊C4×C107—21no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—21no—
198C4⋊C4×C107—21no—
199C4⋊C4×C107—21no—
200C4⋊C4×C107—42no—
201C4⋊C4×C107—42no—
202C4⋊C4×C107—42no—
203C4⋊C4×C107—42no—
204C4⋊C4×C107C2×D412yes—
205C4⋊C4×C107C2×D412yes—
206C4⋊C4×C107#4112yes—
207C22⋊C4×C107—24no—
208C22⋊C4×C107—41no—
209C22⋊C4×C107—42no—
210C22⋊C4×C107—42no—
211C22⋊C4×C107—42no—
212C22⋊C4×C107—81no—
213C22⋊C4×C107—81no—
214C22⋊C4×C107SD1614yescomplemented
215C42×C107—21no—
216C42×C107—21no—
217C42×C107—21no—
218C42×C107—21no—
219C42×C107—42no—
220C42×C107—81no—
221C23×C107—21no—
222C23×C107—21no—
223C23×C107—21no—
224C23×C107—21no—
225C23×C107—21no—
226C23×C107—21no—
227C23×C107—22no—
228C23×C107—41no—
229C23×C107—41no—
230C23×C107—41no—
231C23×C107—41no—
232C23×C107—41no—
233C23×C107—41no—
234C23×C107C2×SD1612yes—
235C23×C107C22×D411yescharacteristic
236Q8×C107—41no—
237Q8×C107—41no—
238Q8×C107—41no—
239Q8×C107—41no—
240Q8×C107—84no—
241D4×C107—22no—
242D4×C107—22no—
243D4×C107—48no—
244D4×C107—41no—
245D4×C107—41no—
246C2×C4×C107—21no—
247C2×C4×C107—21no—
248C2×C4×C107—21no—
249C2×C4×C107—21no—
250C2×C4×C107—21no—
251C2×C4×C107—22no—
252C2×C4×C107—21no—
253C2×C4×C107—22no—
254C2×C4×C107—22no—
255C2×C4×C107—21no—
256C2×C4×C107—21no—
257C2×C4×C107—21no—
258C2×C4×C107—21no—
259C2×C4×C107—21no—
260C2×C4×C107—21no—
261C2×C4×C107—21no—
262C2×C4×C107—41no—
263C2×C4×C107—41no—
264C2×C4×C107—41no—
265C2×C4×C107—41no—
266C2×C4×C107—41no—
267C2×C4×C107—41no—
268C2×C4×C107—41no—
269C2×C4×C107—41no—
270C2×C4×C107—41no—
271C2×C4×C107—41no—
272C2×C4×C107—41no—
273C2×C4×C107—41no—
274C2×C4×C107—41no—
275C2×C4×C107—41no—
276C2×C4×C107—41no—
277C2×C4×C107—41no—
278C2×C4×C107—41no—
279C2×C4×C107—41no—
280C2×C4×C107—41no—
281C2×C4×C107—41no—
282C2×C4×C107—41no—
283C2×C4×C107—41no—
284C2×C4×C107—84no—
285C2×C4×C107—84no—
286C2×C4×C107C2×SD1612yes—
287C2×C4×C107C2×SD1612yes—
288C2×C4×C107C22×D411yescharacteristic
289C2×C4×C107C2×#4111yescharacteristic
290C2×C4×C107C2×#4111yescharacteristic
291C2×C4×C107C2×#4111yescharacteristic
292C2×C4×C107H(5,𝔽2)11yescharacteristic
293C2×C4×C1072−1+411yescharacteristic
294C8×C107—22no—
295C8×C107—22no—
296C8×C107—41no—
297C8×C107—41no—
298C22×C107—22no—
299C22×C107—22no—
300C22×C107—22no—
301C22×C107—41no—
302C22×C107—41no—
303C22×C107—41no—
304C22×C107—41no—
305C22×C107—42no—
306C22×C107—42no—
307C22×C107—42no—
308C22×C107—81no—
309C22×C107—81no—
310C22×C107—81no—
311C22×C107—81no—
312C22×C107#52511yescharacteristic
313C22×C107D4211yescharacteristic
314C22×C107#54711yescharacteristic
315C22×C107C22×SD1611yescharacteristic
316C22×C107#57511yescharacteristic
317C22×C107#57711yescharacteristic
318C22×C107#57711yescharacteristic
319C4×C107—22no—
320C4×C107—22no—
321C4×C107—41no—
322C4×C107—42no—
323C4×C107—41no—
324C4×C107—41no—
325C4×C107—42no—
326C4×C107—42no—
327C4×C107—81no—
328C4×C107—81no—
329C4×C107—81no—
330C4×C107—81no—
331C4×C107#53211yescharacteristic
332C4×C107#54211yescharacteristic
333C4×C107#54811yescharacteristic
334C4×C107#55111yescharacteristic
335#26786C10711yesmaximal, characteristic, direct product factor, Sylow
336C2×C107—42no—
337C2×C107—82no—
338C2×C107#246111yescharacteristic
339C2×C107#310111yescharacteristic
340C2×C107#312511yescharacteristic
341C2×C107#327511yescharacteristic
342C2×C107D4×SD1611yescharacteristic
343C2×C107#333511yescharacteristic
344C2×C107#335011yescharacteristic
345C2×#483C2×C10711yescharacteristic, complemented
346C2×#476C2×C10711yescharacteristic, complemented
347#2492C2×C10711yescharacteristic, complemented
348#2361C2×C10711yescharacteristic
349#2066C2×C10711yescharacteristic, complemented
350#2058C2×C10711yescharacteristic, complemented
351#2034C2×C10711yescharacteristic
352#2000C2×C10711yescharacteristic
353#1968C2×C10711yescharacteristic, complemented
354#1927C2×C10711yescharacteristic, complemented
355#1926C2×C10711yescharacteristic, complemented
356#1923C2×C10711yescharacteristic, complemented
357#1877C2×C10711yescharacteristic, complemented
358#1853C2×C10711yescharacteristic, complemented
359C4×#106C2×C10711yescharacteristic, complemented
360C107#2678611yescharacteristic, direct product factor, Sylow
361C22×SD16C22×C10711yescharacteristic
362C2×C4⋊Q8C22×C10711yescharacteristic
363C2×C22⋊Q8C22×C10711yescharacteristic
364C2×#121C22×C10711yescharacteristic
365C2×C4×D4—21no—
366C2×C4×D4C22×C10711yescharacteristic
367C22×C4⋊C4C22×C10711yescharacteristic
368#483—24no—
369#476—24no—
370C2×#106C22×C10711yescharacteristic
371C2×#106C22×C10711yescharacteristic
372C2×#106C22×C10711yescharacteristic
373C2×#106C22×C10711yescharacteristic
374C2×#106C22×C10711yescharacteristic
375C2×C4⋊C8C22×C10711yescharacteristic
376C2×#103C22×C10711yescharacteristic
377C2×#103C22×C10711yescharacteristic
378C2×#103C22×C10711yescharacteristic
379C2×#102C22×C10711yescharacteristic
380C2×#102C22×C10711yescharacteristic
381C2×#102C22×C10711yescharacteristic
382C2×C22⋊C8C22×C10711yescharacteristic
383C2×C22⋊C8C22×C10711yescharacteristic
384C2×C4×C8C22×C10711yescharacteristic
385#400—21no—
386#393—21no—
387#391—21no—
388#391C22×C10711yescharacteristic
389#391C22×C10711yescharacteristic
390#390C22×C10711yescharacteristic
391#389C22×C10711yescharacteristic
392#388—21no—
393#388—21no—
394#386—21no—
395#385—21no—
396#380C22×C10711yescharacteristic
397C4×C4⋊C4C22×C10711yescharacteristic
398C4×C4⋊C4C22×C10711yescharacteristic
399C4×C22⋊C4C22×C10711yescharacteristic
400#340C22×C10711yescharacteristic
401#340C22×C10711yescharacteristic
402#340C22×C10711yescharacteristic
403#340C22×C10711yescharacteristic
404#336C22×C10711yescharacteristic
405#336C22×C10711yescharacteristic
406C22×Q8—21no—
407C22×Q8C23×C10711yescharacteristic
408C22×D4—21no—
409C22×D4C23×C10711yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4C23×C10711yescharacteristic
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16—41no—
416C22×C8C23×C10711yescharacteristic
417C22×C8C23×C10711yescharacteristic
418C22×C8C23×C10711yescharacteristic
419C22×C8C23×C10711yescharacteristic
420C4⋊Q8—22no—
421C4⋊Q8—41no—
422C22⋊Q8—22no—
423C22⋊Q8—41no—
424#121—22no—
425#121—22no—
426C4×D4—22no—
427C4×D4—41no—
428C4×D4—44no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4C23×C10711yescharacteristic
436C2×C4⋊C4C23×C10711yescharacteristic
437C2×C4⋊C4C23×C10711yescharacteristic
438C2×C4⋊C4C23×C10711yescharacteristic
439C2×C4⋊C4C23×C10711yescharacteristic
440C2×C4⋊C4C23×C10711yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C10711yescharacteristic
448C2×C22⋊C4D4×C10711yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C10711yescharacteristic
452C2×C42C23×C10711yescharacteristic
453#106—22no—
454#106—22no—
455#106—22no—
456#106—41no—
457#106D4×C10714yescomplemented
458C4⋊C8—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C4×C8—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95D4×C10711yescharacteristic
477#95D4×C10711yescharacteristic
478C24—21no—
479C24C2×D4×C10711yescharacteristic
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—81no—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4#41×C10712yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4C2×D4×C10711yescharacteristic
518C22×C4C2×D4×C10711yescharacteristic
519C22×C4C2×D4×C10711yescharacteristic
520C22×C4C2×D4×C10711yescharacteristic
521C22×C4C2×D4×C10711yescharacteristic
522C22×C4C24×C10711yescharacteristic
523SD16—44no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8C2×D4×C10712yes—
535C2×C8#41×C10712yes—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4C2×D4×C10712yes—
550C4⋊C4C2×D4×C10712yes—
551C4⋊C4#41×C10712yes—
552C22⋊C4—24no—
553C22⋊C4—41no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4SD16×C10714yescomplemented
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—42no—
565C42—81no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C2×SD16×C10712yes—
580C23C22×D4×C10711yescharacteristic
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—41no—
585Q8—84no—
586D4—22no—
587D4—22no—
588D4—48no—
589D4—41no—
590D4—41no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—84no—
630C2×C4—84no—
631C2×C4C2×SD16×C10712yes—
632C2×C4C2×SD16×C10712yes—
633C2×C4C22×D4×C10711yescharacteristic
634C2×C4C2×#41×C10711yescharacteristic
635C2×C4C2×#41×C10711yescharacteristic
636C2×C4C2×#41×C10711yescharacteristic
637C2×C4H(5,𝔽2)×C10711yescharacteristic
638C2×C42−1+4×C10711yescharacteristic
639C8—22no—
640C8—22no—
641C8—41no—
642C8—41no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22#525×C10711yescharacteristic
658C22D42×C10711yescharacteristic
659C22#547×C10711yescharacteristic
660C22C22×SD16×C10711yescharacteristic
661C22#575×C10711yescharacteristic
662C22#577×C10711yescharacteristic
663C22#577×C10711yescharacteristic
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—42no—
669C4—42no—
670C4—41no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4#532×C10711yescharacteristic
677C4#542×C10711yescharacteristic
678C4#548×C10711yescharacteristic
679C4#551×C10711yescharacteristic
680C2—42no—
681C2—82no—
682C2C107×#246111yescharacteristic
683C2C107×#310111yescharacteristic
684C2C107×#312511yescharacteristic
685C2C107×#327511yescharacteristic
686C2D4×SD16×C10711yescharacteristic
687C2C107×#333511yescharacteristic
688C2C107×#335011yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#121×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
1. C2×#483×C107C2semidirect
2. C2×#476×C107C2semidirect
3. C107×#2492C2semidirect
5. C107×#2066C2semidirect
6. C107×#2058C2semidirect
9. C107×#1968C2semidirect
10. C107×#1927C2semidirect
11. C107×#1926C2semidirect
12. C107×#1923C2semidirect
13. C107×#1877C2semidirect
14. C107×#1853C2semidirect
15. C4×#106×C107C2semidirect
112. #106×C107D4semidirect
214. C22⋊C4×C107SD16semidirect
335. #26786C107direct (N × H)
345. C2×#483C2×C107semidirect
346. C2×#476C2×C107semidirect
347. #2492C2×C107semidirect
349. #2066C2×C107semidirect
350. #2058C2×C107semidirect
353. #1968C2×C107semidirect
354. #1927C2×C107semidirect
355. #1926C2×C107semidirect
356. #1923C2×C107semidirect
357. #1877C2×C107semidirect
358. #1853C2×C107semidirect
359. C4×#106C2×C107semidirect
360. C107#26786direct (N × H)
457. #106D4×C107semidirect
559. C22⋊C4SD16×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#483×C1072
C2×#476×C1072
C107×#24922
C107×#23612
C107×#20662
C107×#20582
C107×#20342
C107×#20002
C107×#19682
C107×#19272
C107×#19262
C107×#19232
C107×#18772
C107×#18532
C4×#106×C1072
#26786107