Finite Group Databasebeta

← C107×#25156 #41051120

Subgroups — C107×#25156 #41051120

Order 27392.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C107C211yesmaximal, characteristic, complemented
2C2×#450×C107C211yesmaximal, characteristic
3C2×#450×C107C211yesmaximal, characteristic
4C2×C4×SD16×C107C211yesmaximal, characteristic, complemented
5C107×#2429C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C107C211yesmaximal, characteristic
7C107×#2065C211yesmaximal, characteristic, complemented
8C107×#2035C211yesmaximal, characteristic, complemented
9C107×#2035C211yesmaximal, characteristic, complemented
10C107×#2013C211yesmaximal, characteristic, complemented
11C107×#1968C211yesmaximal, characteristic, complemented
12C107×#1923C211yesmaximal, characteristic, complemented
13C107×#1880C211yesmaximal, characteristic, complemented
14C107×#1877C211yesmaximal, characteristic, complemented
15C107×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×SD16×C107C2211yescharacteristic
20C22×SD16×C107C2211yescharacteristic
21C2×C4⋊Q8×C107C2211yescharacteristic, complemented
22C2×C22⋊Q8×C107C2211yescharacteristic
23C2×C22⋊Q8×C107C2211yescharacteristic
24C2×C4×Q8×C107C2211yescharacteristic, complemented
25C2×C4×D4×C107C2211yescharacteristic
26C2×C4×D4×C107C2211yescharacteristic
27C22×C22⋊C4×C107—21no—
28#461×C107—24no—
29#450×C107—24no—
30#450×C107—24no—
31C4×SD16×C107—24no—
32C2×#106×C107C2211yescharacteristic, complemented
33C2×#106×C107C2211yescharacteristic, complemented
34C2×C4⋊C8×C107C2211yescharacteristic, complemented
35C2×#103×C107C2211yescharacteristic, complemented
36C2×#103×C107C2211yescharacteristic, complemented
37C2×#103×C107C2211yescharacteristic, complemented
38C2×#103×C107C2211yescharacteristic, complemented
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×C22⋊C8×C107C2211yescharacteristic
44C2×C22⋊C8×C107C2211yescharacteristic
45C2×C4×C8×C107C2211yescharacteristic, complemented
46#398×C107—21no—
47#396×C107—21no—
48#391×C107C2211yescharacteristic, complemented
49#390×C107C2211yescharacteristic
50#390×C107C2211yescharacteristic
51#389×C107—21no—
52#389×C107C2211yescharacteristic, complemented
53#388×C107—21no—
54#386×C107—21no—
55#386×C107—21no—
56#380×C107C2211yescharacteristic
57#379×C107—21no—
58C4×C22⋊C4×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic, complemented
60#340×C107C2211yescharacteristic, complemented
61#336×C107C2211yescharacteristic, complemented
62#336×C107C2211yescharacteristic, complemented
63C25×C107—21no—
64C22×Q8×C107C2311yescharacteristic
65C22×Q8×C107C2311yescharacteristic
66C22×D4×C107—22no—
67C22×D4×C107—22no—
68C22×D4×C107—22no—
69C22×D4×C107—22no—
70C22×D4×C107—21no—
71C22×D4×C107—41no—
72C22×D4×C107—41no—
73C22×D4×C107C2311yescharacteristic
74C22×D4×C107C2311yescharacteristic
75C23×C4×C107—21no—
76C23×C4×C107—21no—
77C23×C4×C107C2311yescharacteristic
78C2×SD16×C107—22no—
79C2×SD16×C107—22no—
80C2×SD16×C107—22no—
81C2×SD16×C107—22no—
82C2×SD16×C107—22no—
83C2×SD16×C107—22no—
84C2×SD16×C107—22no—
85C2×SD16×C107—22no—
86C2×SD16×C107—22no—
87C2×SD16×C107—41no—
88C2×SD16×C107—41no—
89C2×SD16×C107D414yes—
90C22×C8×C107C2311yescharacteristic
91C22×C8×C107C2311yescharacteristic
92C22×C8×C107C2311yescharacteristic
93C22×C8×C107C2311yescharacteristic
94C4⋊Q8×C107—22no—
95C4⋊Q8×C107—41no—
96C22⋊Q8×C107—22no—
97C22⋊Q8×C107—22no—
98C22⋊Q8×C107—41no—
99C22⋊Q8×C107—41no—
100C4×Q8×C107—22no—
101C4×Q8×C107—41no—
102C4×D4×C107—22no—
103C4×D4×C107—22no—
104C4×D4×C107—41no—
105C4×D4×C107—41no—
106C2×C4⋊C4×C107—21no—
107C2×C4⋊C4×C107—21no—
108C2×C4⋊C4×C107—21no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107—21no—
112C2×C4⋊C4×C107C2311yescharacteristic
113C2×C4⋊C4×C107C2311yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C22⋊C4×C107—21no—
117C2×C22⋊C4×C107—21no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107—21no—
120C2×C22⋊C4×C107—21no—
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—44no—
126C2×C22⋊C4×C107D411yescharacteristic
127C2×C22⋊C4×C107D411yescharacteristic
128C2×C42×C107—21no—
129C2×C42×C107C2311yescharacteristic
130C2×C42×C107C2311yescharacteristic
131#106×C107—22no—
132#106×C107—41no—
133C4⋊C8×C107—22no—
134#103×C107—22no—
135#103×C107—22no—
136#103×C107—22no—
137#103×C107—41no—
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107D414yes—
142C22⋊C8×C107—22no—
143C22⋊C8×C107—22no—
144C4×C8×C107—22no—
145#95×C107—21no—
146#95×C107—21no—
147#95×C107—21no—
148#95×C107—21no—
149#95×C107D411yescharacteristic
150#95×C107D411yescharacteristic
151C24×C107—21no—
152C24×C107—24no—
153C24×C107—21no—
154C24×C107—42no—
155C24×C107—42no—
156C24×C107—42no—
157C24×C107—42no—
158C24×C107—81no—
159C24×C107—81no—
160C24×C107C2×D411yescharacteristic
161C2×Q8×C107—21no—
162C2×Q8×C107—21no—
163C2×Q8×C107—21no—
164C2×Q8×C107—21no—
165C2×Q8×C107—21no—
166C2×Q8×C107—21no—
167C2×Q8×C107—21no—
168C2×Q8×C107—21no—
169C2×Q8×C107—21no—
170C2×Q8×C107—21no—
171C2×Q8×C107—21no—
172C2×Q8×C107C2×D412yes—
173C2×D4×C107—24no—
174C2×D4×C107—21no—
175C2×D4×C107—21no—
176C2×D4×C107—21no—
177C2×D4×C107—21no—
178C2×D4×C107—21no—
179C2×D4×C107—21no—
180C2×D4×C107—21no—
181C2×D4×C107—21no—
182C2×D4×C107—42no—
183C2×D4×C107—42no—
184C2×D4×C107—44no—
185C2×D4×C107—44no—
186C2×D4×C107—44no—
187C2×D4×C107—44no—
188C2×D4×C107C2×D412yes—
189C2×D4×C107C2×D412yes—
190C2×D4×C107#4112yes—
191C2×D4×C107#4112yes—
192C22×C4×C107—21no—
193C22×C4×C107—21no—
194C22×C4×C107—21no—
195C22×C4×C107—21no—
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—42no—
205C22×C4×C107—42no—
206C22×C4×C107—42no—
207C22×C4×C107—42no—
208C22×C4×C107—81no—
209C22×C4×C107—81no—
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D411yescharacteristic
212C22×C4×C107C2×D411yescharacteristic
213C22×C4×C107C2×D411yescharacteristic
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2411yescharacteristic
216SD16×C107—28no—
217SD16×C107—44no—
218SD16×C107—44no—
219SD16×C107—44no—
220C2×C8×C107—21no—
221C2×C8×C107—21no—
222C2×C8×C107—21no—
223C2×C8×C107—21no—
224C2×C8×C107—21no—
225C2×C8×C107—21no—
226C2×C8×C107—21no—
227C2×C8×C107—21no—
228C2×C8×C107—21no—
229C2×C8×C107—21no—
230C2×C8×C107C2×D412yes—
231C2×C8×C107C2×D412yes—
232C4⋊C4×C107—21no—
233C4⋊C4×C107—21no—
234C4⋊C4×C107—21no—
235C4⋊C4×C107—21no—
236C4⋊C4×C107—21no—
237C4⋊C4×C107—21no—
238C4⋊C4×C107—21no—
239C4⋊C4×C107—42no—
240C4⋊C4×C107—42no—
241C4⋊C4×C107—42no—
242C4⋊C4×C107—42no—
243C4⋊C4×C107—42no—
244C4⋊C4×C107—42no—
245C4⋊C4×C107C2×D412yes—
246C22⋊C4×C107—41no—
247C22⋊C4×C107—42no—
248C22⋊C4×C107—42no—
249C22⋊C4×C107—42no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—42no—
252C22⋊C4×C107—42no—
253C22⋊C4×C107—42no—
254C22⋊C4×C107—81no—
255C22⋊C4×C107—81no—
256C22⋊C4×C107SD1614yescomplemented
257C42×C107—21no—
258C42×C107—21no—
259C42×C107—21no—
260C42×C107—21no—
261C42×C107—42no—
262C23×C107—21no—
263C23×C107—22no—
264C23×C107—21no—
265C23×C107—21no—
266C23×C107—22no—
267C23×C107—22no—
268C23×C107—21no—
269C23×C107—21no—
270C23×C107—21no—
271C23×C107—22no—
272C23×C107—48no—
273C23×C107—48no—
274C23×C107—41no—
275C23×C107—41no—
276C23×C107—41no—
277C23×C107—41no—
278C23×C107—41no—
279C23×C107—41no—
280C23×C107—41no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—84no—
285C23×C107—84no—
286C23×C107—84no—
287C23×C107—84no—
288C23×C107—84no—
289C23×C107C2×SD1612yes—
290C23×C107C22×D411yescharacteristic
291Q8×C107—22no—
292Q8×C107—22no—
293Q8×C107—41no—
294Q8×C107—41no—
295Q8×C107—41no—
296Q8×C107—41no—
297Q8×C107—41no—
298Q8×C107—41no—
299D4×C107—22no—
300D4×C107—22no—
301D4×C107—22no—
302D4×C107—22no—
303D4×C107—22no—
304D4×C107—48no—
305D4×C107—41no—
306D4×C107—41no—
307D4×C107#12114yes—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—21no—
313C2×C4×C107—21no—
314C2×C4×C107—21no—
315C2×C4×C107—22no—
316C2×C4×C107—22no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
319C2×C4×C107—21no—
320C2×C4×C107—21no—
321C2×C4×C107—21no—
322C2×C4×C107—21no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—41no—
331C2×C4×C107—41no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—41no—
336C2×C4×C107—41no—
337C2×C4×C107—41no—
338C2×C4×C107—41no—
339C2×C4×C107—41no—
340C2×C4×C107—41no—
341C2×C4×C107—41no—
342C2×C4×C107—41no—
343C2×C4×C107—84no—
344C2×C4×C107—84no—
345C2×C4×C107C2×SD1612yes—
346C2×C4×C107C2×SD1612yes—
347C2×C4×C107C22×D411yescharacteristic
348C2×C4×C107C22×D411yescharacteristic
349C2×C4×C107C2×#4111yescharacteristic
350C2×C4×C107C2×#4111yescharacteristic
351C2×C4×C107H(5,𝔽2)11yescharacteristic
352C2×C4×C107H(5,𝔽2)11yescharacteristic
353C8×C107—22no—
354C8×C107—22no—
355C8×C107—41no—
356C8×C107—41no—
357C22×C107—22no—
358C22×C107—24no—
359C22×C107—22no—
360C22×C107—22no—
361C22×C107—42no—
362C22×C107—41no—
363C22×C107—42no—
364C22×C107—41no—
365C22×C107—41no—
366C22×C107—42no—
367C22×C107—41no—
368C22×C107—42no—
369C22×C107—42no—
370C22×C107—42no—
371C22×C107—42no—
372C22×C107—42no—
373C22×C107—42no—
374C22×C107—816no—
375C22×C107—81no—
376C22×C107—81no—
377C22×C107—81no—
378C22×C107—81no—
379C22×C107#52511yescharacteristic
380C22×C107D4211yescharacteristic
381C22×C107D4211yescharacteristic
382C22×C107C22×SD1611yescharacteristic
383C22×C107#57511yescharacteristic
384C22×C107#57711yescharacteristic
385C22×C107#57711yescharacteristic
386C4×C107—22no—
387C4×C107—22no—
388C4×C107—41no—
389C4×C107—42no—
390C4×C107—41no—
391C4×C107—42no—
392C4×C107—41no—
393C4×C107—81no—
394C4×C107—81no—
395C4×C107—81no—
396C4×C107—81no—
397C4×C107C2×#12111yescharacteristic
398C4×C107#53811yescharacteristic
399C4×C107#54611yescharacteristic
400C4×C107#54611yescharacteristic
401#25156C10711yesmaximal, characteristic, direct product factor, Sylow
402C2×C107—42no—
403C2×C107—44no—
404C2×C107—82no—
405C2×C107#242411yescharacteristic
406C2×C107#310111yescharacteristic
407C2×C107#312311yescharacteristic
408C2×C107#326711yescharacteristic
409C2×C107#327511yescharacteristic
410C2×C107D4×SD1611yescharacteristic
411C2×C107D4×SD1611yescharacteristic
412C2×#461C2×C10711yescharacteristic, complemented
413C2×#450C2×C10711yescharacteristic
414C2×#450C2×C10711yescharacteristic
415C2×C4×SD16C2×C10711yescharacteristic, complemented
416#2429C2×C10711yescharacteristic, complemented
417D4×C22⋊C4C2×C10711yescharacteristic
418#2065C2×C10711yescharacteristic, complemented
419#2035C2×C10711yescharacteristic, complemented
420#2035C2×C10711yescharacteristic, complemented
421#2013C2×C10711yescharacteristic, complemented
422#1968C2×C10711yescharacteristic, complemented
423#1923C2×C10711yescharacteristic, complemented
424#1880C2×C10711yescharacteristic, complemented
425#1877C2×C10711yescharacteristic, complemented
426#1864C2×C10711yescharacteristic, complemented
427C107#2515611yescharacteristic, direct product factor, Sylow
428C23×D4C22×C10711yescharacteristic
429C22×SD16C22×C10711yescharacteristic
430C22×SD16C22×C10711yescharacteristic
431C22×SD16C22×C10711yescharacteristic
432C22×SD16C22×C10711yescharacteristic
433C2×C4⋊Q8C22×C10711yescharacteristic, complemented
434C2×C22⋊Q8C22×C10711yescharacteristic
435C2×C22⋊Q8C22×C10711yescharacteristic
436C2×C4×Q8C22×C10711yescharacteristic, complemented
437C2×C4×D4C22×C10711yescharacteristic
438C2×C4×D4C22×C10711yescharacteristic
439C22×C22⋊C4—21no—
440#461—24no—
441#450—24no—
442#450—24no—
443C4×SD16—24no—
444C2×#106C22×C10711yescharacteristic, complemented
445C2×#106C22×C10711yescharacteristic, complemented
446C2×C4⋊C8C22×C10711yescharacteristic, complemented
447C2×#103C22×C10711yescharacteristic, complemented
448C2×#103C22×C10711yescharacteristic, complemented
449C2×#103C22×C10711yescharacteristic, complemented
450C2×#103C22×C10711yescharacteristic, complemented
451C2×#102C22×C10711yescharacteristic
452C2×#102C22×C10711yescharacteristic
453C2×#102C22×C10711yescharacteristic
454C2×#102C22×C10711yescharacteristic
455C2×C22⋊C8C22×C10711yescharacteristic
456C2×C22⋊C8C22×C10711yescharacteristic
457C2×C4×C8C22×C10711yescharacteristic, complemented
458#398—21no—
459#396—21no—
460#391C22×C10711yescharacteristic, complemented
461#390C22×C10711yescharacteristic
462#390C22×C10711yescharacteristic
463#389—21no—
464#389C22×C10711yescharacteristic, complemented
465#388—21no—
466#386—21no—
467#386—21no—
468#380C22×C10711yescharacteristic
469#379—21no—
470C4×C22⋊C4C22×C10711yescharacteristic
471#340C22×C10711yescharacteristic, complemented
472#340C22×C10711yescharacteristic, complemented
473#336C22×C10711yescharacteristic, complemented
474#336C22×C10711yescharacteristic, complemented
475C25—21no—
476C22×Q8C23×C10711yescharacteristic
477C22×Q8C23×C10711yescharacteristic
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4C23×C10711yescharacteristic
486C22×D4C23×C10711yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C23×C10711yescharacteristic
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16D4×C10714yes—
502C22×C8C23×C10711yescharacteristic
503C22×C8C23×C10711yescharacteristic
504C22×C8C23×C10711yescharacteristic
505C22×C8C23×C10711yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8—41no—
512C4×Q8—22no—
513C4×Q8—41no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4C23×C10711yescharacteristic
525C2×C4⋊C4C23×C10711yescharacteristic
526C2×C4⋊C4C23×C10711yescharacteristic
527C2×C4⋊C4C23×C10711yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—44no—
538C2×C22⋊C4D4×C10711yescharacteristic
539C2×C22⋊C4D4×C10711yescharacteristic
540C2×C42—21no—
541C2×C42C23×C10711yescharacteristic
542C2×C42C23×C10711yescharacteristic
543#106—22no—
544#106—41no—
545C4⋊C8—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#103—41no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102D4×C10714yes—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C4×C8—22no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95D4×C10711yescharacteristic
562#95D4×C10711yescharacteristic
563C24—21no—
564C24—24no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24C2×D4×C10711yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×D4×C10712yes—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4C2×D4×C10712yes—
601C2×D4C2×D4×C10712yes—
602C2×D4#41×C10712yes—
603C2×D4#41×C10712yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C10711yescharacteristic
623C22×C4C2×D4×C10711yescharacteristic
624C22×C4C2×D4×C10711yescharacteristic
625C22×C4C2×D4×C10711yescharacteristic
626C22×C4C2×D4×C10711yescharacteristic
627C22×C4C24×C10711yescharacteristic
628SD16—28no—
629SD16—44no—
630SD16—44no—
631SD16—44no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8C2×D4×C10712yes—
643C2×C8C2×D4×C10712yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C10712yes—
658C22⋊C4—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4SD16×C10714yescomplemented
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—42no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C2×SD16×C10712yes—
702C23C22×D4×C10711yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4#121×C10714yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4C2×SD16×C10712yes—
758C2×C4C2×SD16×C10712yes—
759C2×C4C22×D4×C10711yescharacteristic
760C2×C4C22×D4×C10711yescharacteristic
761C2×C4C2×#41×C10711yescharacteristic
762C2×C4C2×#41×C10711yescharacteristic
763C2×C4H(5,𝔽2)×C10711yescharacteristic
764C2×C4H(5,𝔽2)×C10711yescharacteristic
765C8—22no—
766C8—22no—
767C8—41no—
768C8—41no—
769C22—24no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22#525×C10711yescharacteristic
792C22D42×C10711yescharacteristic
793C22D42×C10711yescharacteristic
794C22C22×SD16×C10711yescharacteristic
795C22#575×C10711yescharacteristic
796C22#577×C10711yescharacteristic
797C22#577×C10711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×#121×C10711yescharacteristic
810C4#538×C10711yescharacteristic
811C4#546×C10711yescharacteristic
812C4#546×C10711yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2C107×#242411yescharacteristic
817C2C107×#310111yescharacteristic
818C2C107×#312311yescharacteristic
819C2C107×#326711yescharacteristic
820C2C107×#327511yescharacteristic
821C2D4×SD16×C10711yescharacteristic
822C2D4×SD16×C10711yescharacteristic
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
1. C2×#461×C107C2semidirect
4. C2×C4×SD16×C107C2semidirect
5. C107×#2429C2semidirect
7. C107×#2065C2semidirect
8. C107×#2035C2semidirect
9. C107×#2035C2semidirect
10. C107×#2013C2semidirect
11. C107×#1968C2semidirect
12. C107×#1923C2semidirect
13. C107×#1880C2semidirect
14. C107×#1877C2semidirect
15. C107×#1864C2semidirect
21. C2×C4⋊Q8×C107C22semidirect
24. C2×C4×Q8×C107C22semidirect
32. C2×#106×C107C22semidirect
33. C2×#106×C107C22semidirect
34. C2×C4⋊C8×C107C22semidirect
35. C2×#103×C107C22semidirect
36. C2×#103×C107C22semidirect
37. C2×#103×C107C22semidirect
38. C2×#103×C107C22semidirect
45. C2×C4×C8×C107C22semidirect
48. #391×C107C22semidirect
52. #389×C107C22semidirect
59. #340×C107C22semidirect
60. #340×C107C22semidirect
61. #336×C107C22semidirect
62. #336×C107C22semidirect
256. C22⋊C4×C107SD16semidirect
401. #25156C107direct (N × H)
412. C2×#461C2×C107semidirect
415. C2×C4×SD16C2×C107semidirect
416. #2429C2×C107semidirect
418. #2065C2×C107semidirect
419. #2035C2×C107semidirect
420. #2035C2×C107semidirect
421. #2013C2×C107semidirect
422. #1968C2×C107semidirect
423. #1923C2×C107semidirect
424. #1880C2×C107semidirect
425. #1877C2×C107semidirect
426. #1864C2×C107semidirect
427. C107#25156direct (N × H)
433. C2×C4⋊Q8C22×C107semidirect
436. C2×C4×Q8C22×C107semidirect
444. C2×#106C22×C107semidirect
445. C2×#106C22×C107semidirect
446. C2×C4⋊C8C22×C107semidirect
447. C2×#103C22×C107semidirect
448. C2×#103C22×C107semidirect
449. C2×#103C22×C107semidirect
450. C2×#103C22×C107semidirect
457. C2×C4×C8C22×C107semidirect
460. #391C22×C107semidirect
464. #389C22×C107semidirect
471. #340C22×C107semidirect
472. #340C22×C107semidirect
473. #336C22×C107semidirect
474. #336C22×C107semidirect
668. C22⋊C4SD16×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1072
C2×#450×C1072
C2×C4×SD16×C1072
C107×#24292
D4×C22⋊C4×C1072
C107×#20652
C107×#20352
C107×#20132
C107×#19682
C107×#19232
C107×#18802
C107×#18772
C107×#18642
#25156107