Finite Group Databasebeta

← C107×#25139 #41051103

Subgroups — C107×#25139 #41051103

Order 27392.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C107C211yesmaximal, characteristic, complemented
2C2×#449×C107C211yesmaximal, characteristic, complemented
3C2×#436×C107C211yesmaximal, characteristic, complemented
4C2×#417×C107C211yesmaximal, characteristic, complemented
5C107×#2416C211yesmaximal, characteristic, complemented
6C107×#2407C211yesmaximal, characteristic, complemented
7C107×#2067C211yesmaximal, characteristic, complemented
8C107×#2055C211yesmaximal, characteristic, complemented
9C107×#2036C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1970C211yesmaximal, characteristic, complemented
12C107×#1933C211yesmaximal, characteristic, complemented
13C107×#1895C211yesmaximal, characteristic, complemented
14C107×#1895C211yesmaximal, characteristic, complemented
15C107×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic
20C22×M16×C107C2211yescharacteristic
21C2×C22⋊Q8×C107C2211yescharacteristic
22C2×#121×C107—21no—
23C2×#121×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C2×#121×C107C2211yescharacteristic
26C2×C4×D4×C107C2211yescharacteristic
27C22×C4⋊C4×C107C2211yescharacteristic
28#468×C107—24no—
29#449×C107—24no—
30#436×C107—24no—
31C2×#107×C107C2211yescharacteristic
32C2×#107×C107C2211yescharacteristic
33C2×C4⋊C8×C107C2211yescharacteristic
34#417×C107—24no—
35C2×#103×C107C2211yescharacteristic
36C2×#103×C107C2211yescharacteristic
37C2×#103×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×C22⋊C8×C107C2211yescharacteristic
44C2×C22⋊C8×C107C2211yescharacteristic
45C2×C4×C8×C107C2211yescharacteristic
46#396×C107—21no—
47#394×C107—21no—
48#394×C107—21no—
49#392×C107—21no—
50#391×C107C2211yescharacteristic
51#390×C107C2211yescharacteristic
52#390×C107C2211yescharacteristic
53#389×C107C2211yescharacteristic
54#386×C107—21no—
55#386×C107—21no—
56#385×C107—21no—
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—41no—
68C2×#41×C107—41no—
69C22×Q8×C107C2311yescharacteristic
70C22×D4×C107—21no—
71C22×D4×C107—21no—
72C22×D4×C107—21no—
73C22×D4×C107—21no—
74C22×D4×C107D411yescharacteristic
75C22×D4×C107C2311yescharacteristic
76C22×D4×C107C2311yescharacteristic
77C23×C4×C107—21no—
78C23×C4×C107—21no—
79C23×C4×C107C2311yescharacteristic
80C23×C4×C107C2311yescharacteristic
81C2×SD16×C107—22no—
82C2×SD16×C107—22no—
83C2×SD16×C107—41no—
84C2×D8×C107—22no—
85C2×D8×C107—22no—
86C2×D8×C107—41no—
87C2×M16×C107—22no—
88C2×M16×C107—22no—
89C2×M16×C107—22no—
90C2×M16×C107—22no—
91C2×M16×C107—41no—
92C2×M16×C107—41no—
93C22×C8×C107C2311yescharacteristic
94C22×C8×C107C2311yescharacteristic
95C22×C8×C107C2311yescharacteristic
96C22×C8×C107C2311yescharacteristic
97C22⋊Q8×C107—22no—
98C22⋊Q8×C107—41no—
99#121×C107—22no—
100#121×C107—22no—
101#121×C107—22no—
102#121×C107—22no—
103#121×C107—41no—
104#121×C107—41no—
105#121×C107—44no—
106C4×D4×C107—22no—
107C4×D4×C107—22no—
108C2×C4⋊C4×C107—22no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107—21no—
112C2×C4⋊C4×C107—41no—
113C2×C4⋊C4×C107D411yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C4⋊C4×C107C2311yescharacteristic
117C2×C4⋊C4×C107C2311yescharacteristic
118C2×C4⋊C4×C107C2311yescharacteristic
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—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107D411yescharacteristic
130C2×C22⋊C4×C107D411yescharacteristic
131C2×C42×C107C2311yescharacteristic
132#107×C107—22no—
133#107×C107—41no—
134C4⋊C8×C107—22no—
135#103×C107—22no—
136#103×C107—22no—
137#103×C107D414yescomplemented
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107—41no—
143C22⋊C8×C107—22no—
144C22⋊C8×C107D414yescomplemented
145C4×C8×C107—22no—
146#95×C107—21no—
147#95×C107—21no—
148#95×C107—21no—
149#95×C107—21no—
150#95×C107—21no—
151C24×C107—21no—
152C24×C107—21no—
153C24×C107C2×D411yescharacteristic
154C24×C107C2×D411yescharacteristic
155#41×C107—28no—
156#41×C107—44no—
157#41×C107—44no—
158#41×C107—44no—
159C2×Q8×C107—21no—
160C2×Q8×C107—21no—
161C2×Q8×C107—21no—
162C2×Q8×C107—21no—
163C2×Q8×C107—21no—
164C2×Q8×C107C2×D412yes—
165C2×D4×C107—22no—
166C2×D4×C107—22no—
167C2×D4×C107—21no—
168C2×D4×C107—21no—
169C2×D4×C107—21no—
170C2×D4×C107—21no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—21no—
174C2×D4×C107—21no—
175C2×D4×C107—21no—
176C2×D4×C107—21no—
177C2×D4×C107—21no—
178C2×D4×C107—41no—
179C2×D4×C107—42no—
180C2×D4×C107—42no—
181C2×D4×C107—42no—
182C2×D4×C107—42no—
183C2×D4×C107—42no—
184C2×D4×C107—42no—
185C2×D4×C107—42no—
186C2×D4×C107—42no—
187C2×D4×C107—42no—
188C2×D4×C107—42no—
189C2×D4×C107—81no—
190C2×D4×C107—81no—
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—21no—
205C22×C4×C107—21no—
206C22×C4×C107—21no—
207C22×C4×C107—21no—
208C22×C4×C107—42no—
209C22×C4×C107—42no—
210C22×C4×C107—42no—
211C22×C4×C107—42no—
212C22×C4×C107—42no—
213C22×C4×C107—81no—
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2×D411yescharacteristic
217C22×C4×C107C2×D412yes—
218C22×C4×C107C2×D411yescharacteristic
219C22×C4×C107#4112yes—
220C22×C4×C107C2411yescharacteristic
221SD16×C107—44no—
222D8×C107—44no—
223M16×C107—44no—
224M16×C107—44no—
225C2×C8×C107—21no—
226C2×C8×C107—21no—
227C2×C8×C107—21no—
228C2×C8×C107—21no—
229C2×C8×C107—21no—
230C2×C8×C107—21no—
231C2×C8×C107—21no—
232C2×C8×C107—21no—
233C2×C8×C107—21no—
234C2×C8×C107C2×D412yes—
235C2×C8×C107C2×D412yes—
236C2×C8×C107C2×D412yes—
237C4⋊C4×C107—22no—
238C4⋊C4×C107—21no—
239C4⋊C4×C107—21no—
240C4⋊C4×C107—21no—
241C4⋊C4×C107—21no—
242C4⋊C4×C107—21no—
243C4⋊C4×C107—21no—
244C4⋊C4×C107—21no—
245C4⋊C4×C107—21no—
246C4⋊C4×C107—21no—
247C4⋊C4×C107—42no—
248C4⋊C4×C107—42no—
249C4⋊C4×C107—42no—
250C4⋊C4×C107C2×D412yes—
251C22⋊C4×C107—22no—
252C22⋊C4×C107—22no—
253C22⋊C4×C107—42no—
254C22⋊C4×C107—42no—
255C22⋊C4×C107—42no—
256C22⋊C4×C107—42no—
257C22⋊C4×C107—42no—
258C22⋊C4×C107—42no—
259C22⋊C4×C107—42no—
260C22⋊C4×C107—81no—
261C22⋊C4×C107—81no—
262C22⋊C4×C107—81no—
263C42×C107—21no—
264C42×C107—21no—
265C23×C107—21no—
266C23×C107—21no—
267C23×C107—21no—
268C23×C107—21no—
269C23×C107—21no—
270C23×C107—21no—
271C23×C107—21no—
272C23×C107—21no—
273C23×C107—22no—
274C23×C107—21no—
275C23×C107—21no—
276C23×C107—21no—
277C23×C107—21no—
278C23×C107—21no—
279C23×C107—41no—
280C23×C107—41no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107—41no—
286C23×C107—41no—
287C23×C107—41no—
288C23×C107—41no—
289C23×C107—41no—
290C23×C107—41no—
291C23×C107—41no—
292C23×C107#12112yes—
293C23×C107C22×D411yescharacteristic
294Q8×C107—22no—
295Q8×C107—22no—
296Q8×C107—41no—
297Q8×C107—41no—
298D4×C107—22no—
299D4×C107—22no—
300D4×C107—44no—
301D4×C107—48no—
302D4×C107—41no—
303D4×C107—41no—
304D4×C107—41no—
305D4×C107—41no—
306D4×C107—41no—
307D4×C107—41no—
308D4×C107—84no—
309D4×C107—84no—
310D4×C107—84no—
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—22no—
318C2×C4×C107—22no—
319C2×C4×C107—21no—
320C2×C4×C107—21no—
321C2×C4×C107—21no—
322C2×C4×C107—22no—
323C2×C4×C107—22no—
324C2×C4×C107—21no—
325C2×C4×C107—21no—
326C2×C4×C107—21no—
327C2×C4×C107—48no—
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—41no—
344C2×C4×C107—41no—
345C2×C4×C107—41no—
346C2×C4×C107—41no—
347C2×C4×C107—41no—
348C2×C4×C107—84no—
349C2×C4×C107#12112yes—
350C2×C4×C107AGL(1,ℤ/8)12yes—
351C2×C4×C107C22×D411yescharacteristic
352C2×C4×C107C22×D411yescharacteristic
353C2×C4×C107C2×#4111yescharacteristic
354C2×C4×C107C2×#4111yescharacteristic
355C2×C4×C107H(5,𝔽2)11yescharacteristic
356C2×C4×C107H(5,𝔽2)11yescharacteristic
357C8×C107—22no—
358C8×C107—22no—
359C8×C107—22no—
360C8×C107—41no—
361C22×C107—22no—
362C22×C107—22no—
363C22×C107—22no—
364C22×C107—41no—
365C22×C107—41no—
366C22×C107—41no—
367C22×C107—41no—
368C22×C107—41no—
369C22×C107—42no—
370C22×C107—42no—
371C22×C107—41no—
372C22×C107—41no—
373C22×C107—41no—
374C22×C107—41no—
375C22×C107—41no—
376C22×C107—41no—
377C22×C107—42no—
378C22×C107—81no—
379C22×C107—81no—
380C22×C107—81no—
381C22×C107—81no—
382C22×C107—81no—
383C22×C107—81no—
384C22×C107—81no—
385C22×C107—81no—
386C22×C107—81no—
387C22×C107—81no—
388C22×C107—81no—
389C22×C107C2×#12111yescharacteristic
390C22×C107D4211yescharacteristic
391C22×C107#54611yescharacteristic
392C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C107#57511yescharacteristic
394C22×C107#57611yescharacteristic
395C22×C107#57811yescharacteristic
396C4×C107—22no—
397C4×C107—22no—
398C4×C107—41no—
399C4×C107—42no—
400C4×C107—42no—
401C4×C107—41no—
402C4×C107—81no—
403C4×C107—81no—
404C4×C107—81no—
405C4×C107—81no—
406C4×C107#52511yescharacteristic
407C4×C107#53811yescharacteristic
408C4×C107D4211yescharacteristic
409C4×C107#54611yescharacteristic
410#25139C10711yesmaximal, characteristic, direct product factor, Sylow
411C2×C107—42no—
412C2×C107—81no—
413C2×C107—82no—
414C2×C107—161no—
415C2×C107#242411yescharacteristic
416C2×C107#305511yescharacteristic
417C2×C107#306111yescharacteristic
418C2×C107#327411yescharacteristic
419C2×C107#327711yescharacteristic
420C2×C107#332211yescharacteristic
421C2×C107#333011yescharacteristic
422C2×#468C2×C10711yescharacteristic, complemented
423C2×#449C2×C10711yescharacteristic, complemented
424C2×#436C2×C10711yescharacteristic, complemented
425C2×#417C2×C10711yescharacteristic, complemented
426#2416C2×C10711yescharacteristic, complemented
427#2407C2×C10711yescharacteristic, complemented
428#2067C2×C10711yescharacteristic, complemented
429#2055C2×C10711yescharacteristic, complemented
430#2036C2×C10711yescharacteristic, complemented
431#1999C2×C10711yescharacteristic, complemented
432#1970C2×C10711yescharacteristic, complemented
433#1933C2×C10711yescharacteristic, complemented
434#1895C2×C10711yescharacteristic, complemented
435#1895C2×C10711yescharacteristic, complemented
436#1852C2×C10711yescharacteristic, complemented
437C107#2513911yescharacteristic, direct product factor, Sylow
438C22×#41C22×C10711yescharacteristic
439C22×SD16C22×C10711yescharacteristic
440C22×D8C22×C10711yescharacteristic
441C22×M16C22×C10711yescharacteristic
442C22×M16C22×C10711yescharacteristic
443C2×C22⋊Q8C22×C10711yescharacteristic
444C2×#121—21no—
445C2×#121C22×C10711yescharacteristic
446C2×#121C22×C10711yescharacteristic
447C2×#121C22×C10711yescharacteristic
448C2×C4×D4C22×C10711yescharacteristic
449C22×C4⋊C4C22×C10711yescharacteristic
450#468—24no—
451#449—24no—
452#436—24no—
453C2×#107C22×C10711yescharacteristic
454C2×#107C22×C10711yescharacteristic
455C2×C4⋊C8C22×C10711yescharacteristic
456#417—24no—
457C2×#103C22×C10711yescharacteristic
458C2×#103C22×C10711yescharacteristic
459C2×#103C22×C10711yescharacteristic
460C2×#102C22×C10711yescharacteristic
461C2×#102C22×C10711yescharacteristic
462C2×#102C22×C10711yescharacteristic
463C2×#102C22×C10711yescharacteristic
464C2×#102C22×C10711yescharacteristic
465C2×C22⋊C8C22×C10711yescharacteristic
466C2×C22⋊C8C22×C10711yescharacteristic
467C2×C4×C8C22×C10711yescharacteristic
468#396—21no—
469#394—21no—
470#394—21no—
471#392—21no—
472#391C22×C10711yescharacteristic
473#390C22×C10711yescharacteristic
474#390C22×C10711yescharacteristic
475#389C22×C10711yescharacteristic
476#386—21no—
477#386—21no—
478#385—21no—
479#380C22×C10711yescharacteristic
480#380C22×C10711yescharacteristic
481#340C22×C10711yescharacteristic
482#340C22×C10711yescharacteristic
483#340C22×C10711yescharacteristic
484#340C22×C10711yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8C23×C10711yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4D4×C10711yescharacteristic
497C22×D4C23×C10711yescharacteristic
498C22×D4C23×C10711yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C23×C10711yescharacteristic
502C23×C4C23×C10711yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C23×C10711yescharacteristic
516C22×C8C23×C10711yescharacteristic
517C22×C8C23×C10711yescharacteristic
518C22×C8C23×C10711yescharacteristic
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—44no—
528C4×D4—22no—
529C4×D4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4D4×C10711yescharacteristic
536C2×C4⋊C4C23×C10711yescharacteristic
537C2×C4⋊C4C23×C10711yescharacteristic
538C2×C4⋊C4C23×C10711yescharacteristic
539C2×C4⋊C4C23×C10711yescharacteristic
540C2×C4⋊C4C23×C10711yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4D4×C10711yescharacteristic
552C2×C22⋊C4D4×C10711yescharacteristic
553C2×C42C23×C10711yescharacteristic
554#107—22no—
555#107—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#103D4×C10714yescomplemented
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—41no—
565C22⋊C8—22no—
566C22⋊C8D4×C10714yescomplemented
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573C24—21no—
574C24—21no—
575C24C2×D4×C10711yescharacteristic
576C24C2×D4×C10711yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C10712yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C10712yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C10711yescharacteristic
637C22×C4C2×D4×C10711yescharacteristic
638C22×C4C2×D4×C10711yescharacteristic
639C22×C4C2×D4×C10712yes—
640C22×C4C2×D4×C10711yescharacteristic
641C22×C4#41×C10712yes—
642C22×C4C24×C10711yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8C2×D4×C10712yes—
657C2×C8C2×D4×C10712yes—
658C2×C8C2×D4×C10712yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C10712yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23#121×C10712yes—
715C23C22×D4×C10711yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—84no—
771C2×C4#121×C10712yes—
772C2×C4AGL(1,ℤ/8)×C10712yes—
773C2×C4C22×D4×C10711yescharacteristic
774C2×C4C22×D4×C10711yescharacteristic
775C2×C4C2×#41×C10711yescharacteristic
776C2×C4C2×#41×C10711yescharacteristic
777C2×C4H(5,𝔽2)×C10711yescharacteristic
778C2×C4H(5,𝔽2)×C10711yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×#121×C10711yescharacteristic
812C22D42×C10711yescharacteristic
813C22#546×C10711yescharacteristic
814C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
815C22#575×C10711yescharacteristic
816C22#576×C10711yescharacteristic
817C22#578×C10711yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4#525×C10711yescharacteristic
829C4#538×C10711yescharacteristic
830C4D42×C10711yescharacteristic
831C4#546×C10711yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2C107×#242411yescharacteristic
837C2C107×#305511yescharacteristic
838C2C107×#306111yescharacteristic
839C2C107×#327411yescharacteristic
840C2C107×#327711yescharacteristic
841C2C107×#332211yescharacteristic
842C2C107×#333011yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
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
1. C2×#468×C107C2semidirect
2. C2×#449×C107C2semidirect
3. C2×#436×C107C2semidirect
4. C2×#417×C107C2semidirect
5. C107×#2416C2semidirect
6. C107×#2407C2semidirect
7. C107×#2067C2semidirect
8. C107×#2055C2semidirect
9. C107×#2036C2semidirect
10. C107×#1999C2semidirect
11. C107×#1970C2semidirect
12. C107×#1933C2semidirect
13. C107×#1895C2semidirect
14. C107×#1895C2semidirect
15. C107×#1852C2semidirect
137. #103×C107D4semidirect
144. C22⋊C8×C107D4semidirect
410. #25139C107direct (N × H)
422. C2×#468C2×C107semidirect
423. C2×#449C2×C107semidirect
424. C2×#436C2×C107semidirect
425. C2×#417C2×C107semidirect
426. #2416C2×C107semidirect
427. #2407C2×C107semidirect
428. #2067C2×C107semidirect
429. #2055C2×C107semidirect
430. #2036C2×C107semidirect
431. #1999C2×C107semidirect
432. #1970C2×C107semidirect
433. #1933C2×C107semidirect
434. #1895C2×C107semidirect
435. #1895C2×C107semidirect
436. #1852C2×C107semidirect
437. C107#25139direct (N × H)
559. #103D4×C107semidirect
566. C22⋊C8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1072
C2×#449×C1072
C2×#436×C1072
C2×#417×C1072
C107×#24162
C107×#24072
C107×#20672
C107×#20552
C107×#20362
C107×#19992
C107×#19702
C107×#19332
C107×#18952
C107×#18522
#25139107