Finite Group Databasebeta

← C107×#22055 #41048019

Subgroups — C107×#22055 #41048019

Order 27392.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C107C211yesmaximal, characteristic
2C107×#2324C211yesmaximal, characteristic, complemented
3C107×#2311C211yesmaximal, characteristic, complemented
4C107×#1973C211yesmaximal, characteristic, complemented
5C107×#1970C211yesmaximal, characteristic, complemented
6C107×#1936C211yesmaximal, characteristic, complemented
7C107×#1933C211yesmaximal, characteristic, complemented
8C107×#1928C211yesmaximal, characteristic, complemented
9C107×#1925C211yesmaximal, characteristic, complemented
10C107×#1879C211yesmaximal, characteristic, complemented
11C107×#1877C211yesmaximal, characteristic, complemented
12C107×#1874C211yesmaximal, characteristic, complemented
13C107×#1852C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C2×#121×C107C2211yescharacteristic
20C2×C4×D4×C107C2211yescharacteristic
21C2×#117×C107C2211yescharacteristic
22C22×C4⋊C4×C107C2211yescharacteristic
23#449×C107C418yescomplemented
24C2×#107×C107C2211yescharacteristic
25C2×#107×C107C2211yescharacteristic
26C2×#103×C107C2211yescharacteristic
27C2×#103×C107C2211yescharacteristic
28C2×#103×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×C22⋊C8×C107C2211yescharacteristic
35C2×C22⋊C8×C107C2211yescharacteristic
36C2×#97×C107C2211yescharacteristic
37C2×C4×C8×C107C2211yescharacteristic
38#391×C107C2211yescharacteristic
39#391×C107C2211yescharacteristic
40#390×C107—21no—
41#390×C107C2211yescharacteristic
42#390×C107C2211yescharacteristic
43#390×C107C2211yescharacteristic
44#389×C107C2211yescharacteristic
45#388×C107—21no—
46#386×C107—21no—
47#386×C107—21no—
48#386×C107—21no—
49#385×C107—21no—
50#380×C107—21no—
51#380×C107—21no—
52#380×C107C2211yescharacteristic
53C4×C4⋊C4×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60C2×#41×C107—22no—
61C2×#41×C107—41no—
62C2×#41×C107—41no—
63C2×#41×C107—41no—
64C2×#41×C107—41no—
65C2×#41×C107C2×C414yescomplemented
66C22×Q8×C107C2311yescharacteristic
67C22×D4×C107—21no—
68C22×D4×C107—21no—
69C22×D4×C107C2311yescharacteristic
70C22×D4×C107C2311yescharacteristic
71C23×C4×C107—21no—
72C23×C4×C107—21no—
73C23×C4×C107—21no—
74C23×C4×C107C2311yescharacteristic
75C2×SD16×C107—41no—
76C2×SD16×C107—41no—
77C2×SD16×C107C2×C414yescomplemented
78C2×D8×C107—41no—
79C2×D8×C107—41no—
80C2×D8×C107C2×C414yescomplemented
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83C22×C8×C107C2311yescharacteristic
84C22×C8×C107C2311yescharacteristic
85#121×C107—22no—
86#121×C107C2×C414yes—
87C4×D4×C107—41no—
88C4×D4×C107—41no—
89#117×C107—41no—
90#117×C107—41no—
91C2×C4⋊C4×C107—21no—
92C2×C4⋊C4×C107—21no—
93C2×C4⋊C4×C107—41no—
94C2×C4⋊C4×C107—41no—
95C2×C4⋊C4×C107D411yescharacteristic
96C2×C4⋊C4×C107D411yescharacteristic
97C2×C4⋊C4×C107C2311yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C4⋊C4×C107C2311yescharacteristic
101C2×C4⋊C4×C107C2311yescharacteristic
102C2×C22⋊C4×C107—21no—
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×C107D411yescharacteristic
112C2×C22⋊C4×C107D411yescharacteristic
113C2×C42×C107—21no—
114C2×C42×C107C2311yescharacteristic
115C2×C42×C107C2311yescharacteristic
116#107×C107—41no—
117#107×C107—41no—
118#103×C107—41no—
119#103×C107—41no—
120#103×C107C2×C414yescomplemented
121#102×C107—41no—
122#102×C107—41no—
123#102×C107—41no—
124#102×C107—41no—
125#102×C107C2×C414yescomplemented
126C22⋊C8×C107—22no—
127C22⋊C8×C107C2×C414yescomplemented
128#97×C107—41no—
129C4×C8×C107—41no—
130#95×C107—21no—
131#95×C107—21no—
132#95×C107—21no—
133#95×C107—21no—
134#95×C107—21no—
135#95×C107—21no—
136#95×C107—21no—
137C24×C107—21no—
138C24×C107—21no—
139C24×C107C2×D411yescharacteristic
140#41×C107—44no—
141#41×C107—44no—
142#41×C107—44no—
143#41×C107—44no—
144C2×Q8×C107—21no—
145C2×Q8×C107—21no—
146C2×Q8×C107—21no—
147C2×Q8×C107—21no—
148C2×Q8×C107—21no—
149C2×Q8×C107C22×C412yes—
150C2×D4×C107—24no—
151C2×D4×C107—24no—
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—21no—
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—42no—
163C2×D4×C107—42no—
164C2×D4×C107—81no—
165C2×D4×C107—81no—
166C2×D4×C107C22×C412yes—
167C2×D4×C107C22×C412yes—
168C22×C4×C107—21no—
169C22×C4×C107—21no—
170C22×C4×C107—21no—
171C22×C4×C107—21no—
172C22×C4×C107—21no—
173C22×C4×C107—21no—
174C22×C4×C107—24no—
175C22×C4×C107—21no—
176C22×C4×C107—21no—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—42no—
180C22×C4×C107—42no—
181C22×C4×C107—42no—
182C22×C4×C107—42no—
183C22×C4×C107—81no—
184C22×C4×C107—81no—
185C22×C4×C107—81no—
186C22×C4×C107—81no—
187C22×C4×C107C22×C412yes—
188C22×C4×C107C2×D411yescharacteristic
189C22×C4×C107C2×D411yescharacteristic
190C22×C4×C107C2×D411yescharacteristic
191C22×C4×C107C2×D411yescharacteristic
192C22×C4×C107C2×D411yescharacteristic
193C22×C4×C107#4112yes—
194C22×C4×C107C2411yescharacteristic
195SD16×C107—44no—
196D8×C107—44no—
197C2×C8×C107—21no—
198C2×C8×C107—21no—
199C2×C8×C107—21no—
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×C107C22×C412yes—
208C2×C8×C107C22×C412yes—
209C4⋊C4×C107—21no—
210C4⋊C4×C107—21no—
211C4⋊C4×C107—21no—
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—41no—
219C4⋊C4×C107—41no—
220C4⋊C4×C107—42no—
221C4⋊C4×C107—81no—
222C4⋊C4×C107C22×C412yes—
223C22⋊C4×C107—24no—
224C22⋊C4×C107—41no—
225C22⋊C4×C107—41no—
226C22⋊C4×C107—42no—
227C22⋊C4×C107—81no—
228C22⋊C4×C107—81no—
229C22⋊C4×C107—81no—
230C22⋊C4×C107—81no—
231C22⋊C4×C107—81no—
232C22⋊C4×C107—81no—
233C22⋊C4×C107—81no—
234C42×C107—21no—
235C42×C107—21no—
236C42×C107—21no—
237C42×C107—21no—
238C42×C107—81no—
239C23×C107—21no—
240C23×C107—21no—
241C23×C107—21no—
242C23×C107—21no—
243C23×C107—21no—
244C23×C107—21no—
245C23×C107—22no—
246C23×C107—22no—
247C23×C107—41no—
248C23×C107—41no—
249C23×C107—41no—
250C23×C107—41no—
251C23×C107—41no—
252C23×C107—41no—
253C23×C107—41no—
254C23×C107—41no—
255C23×C107—41no—
256C23×C107—41no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107C4×D412yes—
260C23×C107C22×D411yescharacteristic
261Q8×C107—22no—
262Q8×C107—22no—
263Q8×C107—41no—
264Q8×C107—41no—
265D4×C107—22no—
266D4×C107—22no—
267D4×C107—22no—
268D4×C107—22no—
269D4×C107—48no—
270D4×C107—41no—
271D4×C107—41no—
272D4×C107—41no—
273D4×C107—41no—
274D4×C107—84no—
275C2×C4×C107—21no—
276C2×C4×C107—21no—
277C2×C4×C107—22no—
278C2×C4×C107—22no—
279C2×C4×C107—22no—
280C2×C4×C107—22no—
281C2×C4×C107—22no—
282C2×C4×C107—22no—
283C2×C4×C107—21no—
284C2×C4×C107—21no—
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—21no—
292C2×C4×C107—21no—
293C2×C4×C107—21no—
294C2×C4×C107—21no—
295C2×C4×C107—48no—
296C2×C4×C107—41no—
297C2×C4×C107—41no—
298C2×C4×C107—41no—
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—84no—
313C2×C4×C107—84no—
314C2×C4×C107C4×D412yes—
315C2×C4×C107C23×C411yescharacteristic
316C2×C4×C107C2×#4111yescharacteristic
317C2×C4×C107H(5,𝔽2)11yescharacteristic
318C2×C4×C107H(5,𝔽2)11yescharacteristic
319C2×C4×C107H(5,𝔽2)11yescharacteristic
320C2×C4×C107H(5,𝔽2)11yescharacteristic
321C8×C107—22no—
322C8×C107—22no—
323C8×C107—41no—
324C8×C107—41no—
325C22×C107—22no—
326C22×C107—22no—
327C22×C107—22no—
328C22×C107—41no—
329C22×C107—41no—
330C22×C107—41no—
331C22×C107—41no—
332C22×C107—42no—
333C22×C107—42no—
334C22×C107—42no—
335C22×C107—42no—
336C22×C107—42no—
337C22×C107—42no—
338C22×C107—81no—
339C22×C107—81no—
340C22×C107—81no—
341C22×C107—81no—
342C22×C107—81no—
343C22×C107—81no—
344C22×C107—81no—
345C22×C107—81no—
346C22×C107C2×C4×D411yescharacteristic
347C22×C107#53411yescharacteristic
348C22×C107#53511yescharacteristic
349C22×C107#57611yescharacteristic
350C22×C107#57611yescharacteristic
351C22×C107#57711yescharacteristic
352C22×C107#57811yescharacteristic
353C4×C107—22no—
354C4×C107—42no—
355C4×C107—41no—
356C4×C107—41no—
357C4×C107—42no—
358C4×C107—41no—
359C4×C107—41no—
360C4×C107—81no—
361C4×C107—81no—
362C4×C107—81no—
363C4×C107—81no—
364C4×C107#51811yescharacteristic
365C4×C107#51811yescharacteristic
366C4×C107#53811yescharacteristic
367C4×C107#53811yescharacteristic
368#22055C10711yesmaximal, characteristic, direct product factor, Sylow
369C2×C107—42no—
370C2×C107—82no—
371C2×C107—82no—
372C2×C107#232111yescharacteristic
373C2×C107#294611yescharacteristic
374C2×C107#295111yescharacteristic
375C2×C107#319811yescharacteristic
376C2×C107#320311yescharacteristic
377C2×C107#322011yescharacteristic
378C2×C107#322511yescharacteristic
379C2×#449C2×C10711yescharacteristic
380#2324C2×C10711yescharacteristic, complemented
381#2311C2×C10711yescharacteristic, complemented
382#1973C2×C10711yescharacteristic, complemented
383#1970C2×C10711yescharacteristic, complemented
384#1936C2×C10711yescharacteristic, complemented
385#1933C2×C10711yescharacteristic, complemented
386#1928C2×C10711yescharacteristic, complemented
387#1925C2×C10711yescharacteristic, complemented
388#1879C2×C10711yescharacteristic, complemented
389#1877C2×C10711yescharacteristic, complemented
390#1874C2×C10711yescharacteristic, complemented
391#1852C2×C10711yescharacteristic, complemented
392#1788C2×C10711yescharacteristic, complemented
393#1750C2×C10711yescharacteristic, complemented
394C107#2205511yescharacteristic, direct product factor, Sylow
395C22×#41C22×C10711yescharacteristic
396C22×SD16C22×C10711yescharacteristic
397C22×D8C22×C10711yescharacteristic
398C2×#121C22×C10711yescharacteristic
399C2×C4×D4C22×C10711yescharacteristic
400C2×#117C22×C10711yescharacteristic
401C22×C4⋊C4C22×C10711yescharacteristic
402#449C4×C10718yescomplemented
403C2×#107C22×C10711yescharacteristic
404C2×#107C22×C10711yescharacteristic
405C2×#103C22×C10711yescharacteristic
406C2×#103C22×C10711yescharacteristic
407C2×#103C22×C10711yescharacteristic
408C2×#102C22×C10711yescharacteristic
409C2×#102C22×C10711yescharacteristic
410C2×#102C22×C10711yescharacteristic
411C2×#102C22×C10711yescharacteristic
412C2×#102C22×C10711yescharacteristic
413C2×C22⋊C8C22×C10711yescharacteristic
414C2×C22⋊C8C22×C10711yescharacteristic
415C2×#97C22×C10711yescharacteristic
416C2×C4×C8C22×C10711yescharacteristic
417#391C22×C10711yescharacteristic
418#391C22×C10711yescharacteristic
419#390—21no—
420#390C22×C10711yescharacteristic
421#390C22×C10711yescharacteristic
422#390C22×C10711yescharacteristic
423#389C22×C10711yescharacteristic
424#388—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#385—21no—
429#380—21no—
430#380—21no—
431#380C22×C10711yescharacteristic
432C4×C4⋊C4C22×C10711yescharacteristic
433#340C22×C10711yescharacteristic
434#340C22×C10711yescharacteristic
435#340C22×C10711yescharacteristic
436#340C22×C10711yescharacteristic
437#336C22×C10711yescharacteristic
438#336C22×C10711yescharacteristic
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41C2×C4×C10714yescomplemented
445C22×Q8C23×C10711yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C23×C10711yescharacteristic
449C22×D4C23×C10711yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—21no—
453C23×C4C23×C10711yescharacteristic
454C2×SD16—41no—
455C2×SD16—41no—
456C2×SD16C2×C4×C10714yescomplemented
457C2×D8—41no—
458C2×D8—41no—
459C2×D8C2×C4×C10714yescomplemented
460C22×C8C23×C10711yescharacteristic
461C22×C8C23×C10711yescharacteristic
462C22×C8C23×C10711yescharacteristic
463C22×C8C23×C10711yescharacteristic
464#121—22no—
465#121C2×C4×C10714yes—
466C4×D4—41no—
467C4×D4—41no—
468#117—41no—
469#117—41no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—41no—
474C2×C4⋊C4D4×C10711yescharacteristic
475C2×C4⋊C4D4×C10711yescharacteristic
476C2×C4⋊C4C23×C10711yescharacteristic
477C2×C4⋊C4C23×C10711yescharacteristic
478C2×C4⋊C4C23×C10711yescharacteristic
479C2×C4⋊C4C23×C10711yescharacteristic
480C2×C4⋊C4C23×C10711yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4D4×C10711yescharacteristic
491C2×C22⋊C4D4×C10711yescharacteristic
492C2×C42—21no—
493C2×C42C23×C10711yescharacteristic
494C2×C42C23×C10711yescharacteristic
495#107—41no—
496#107—41no—
497#103—41no—
498#103—41no—
499#103C2×C4×C10714yescomplemented
500#102—41no—
501#102—41no—
502#102—41no—
503#102—41no—
504#102C2×C4×C10714yescomplemented
505C22⋊C8—22no—
506C22⋊C8C2×C4×C10714yescomplemented
507#97—41no—
508C4×C8—41no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C24—21no—
517C24—21no—
518C24C2×D4×C10711yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C22×C4×C10712yes—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4C22×C4×C10712yes—
546C2×D4C22×C4×C10712yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4C22×C4×C10712yes—
567C22×C4C2×D4×C10711yescharacteristic
568C22×C4C2×D4×C10711yescharacteristic
569C22×C4C2×D4×C10711yescharacteristic
570C22×C4C2×D4×C10711yescharacteristic
571C22×C4C2×D4×C10711yescharacteristic
572C22×C4#41×C10712yes—
573C22×C4C24×C10711yescharacteristic
574SD16—44no—
575D8—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8C22×C4×C10712yes—
587C2×C8C22×C4×C10712yes—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—42no—
600C4⋊C4—81no—
601C4⋊C4C22×C4×C10712yes—
602C22⋊C4—24no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—81no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23C4×D4×C10712yes—
639C23C22×D4×C10711yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—48no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—48no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4C4×D4×C10712yes—
694C2×C4C23×C4×C10711yescharacteristic
695C2×C4C2×#41×C10711yescharacteristic
696C2×C4H(5,𝔽2)×C10711yescharacteristic
697C2×C4H(5,𝔽2)×C10711yescharacteristic
698C2×C4H(5,𝔽2)×C10711yescharacteristic
699C2×C4H(5,𝔽2)×C10711yescharacteristic
700C8—22no—
701C8—22no—
702C8—41no—
703C8—41no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22C2×C4×D4×C10711yescharacteristic
726C22#534×C10711yescharacteristic
727C22#535×C10711yescharacteristic
728C22#576×C10711yescharacteristic
729C22#576×C10711yescharacteristic
730C22#577×C10711yescharacteristic
731C22#578×C10711yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4#518×C10711yescharacteristic
744C4#518×C10711yescharacteristic
745C4#538×C10711yescharacteristic
746C4#538×C10711yescharacteristic
747C2—42no—
748C2—82no—
749C2—82no—
750C2C107×#232111yescharacteristic
751C2C107×#294611yescharacteristic
752C2C107×#295111yescharacteristic
753C2C107×#319811yescharacteristic
754C2C107×#320311yescharacteristic
755C2C107×#322011yescharacteristic
756C2C107×#322511yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC2×#449×C107C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×#117×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2324C2semidirect
3. C107×#2311C2semidirect
4. C107×#1973C2semidirect
5. C107×#1970C2semidirect
6. C107×#1936C2semidirect
7. C107×#1933C2semidirect
8. C107×#1928C2semidirect
9. C107×#1925C2semidirect
10. C107×#1879C2semidirect
11. C107×#1877C2semidirect
12. C107×#1874C2semidirect
13. C107×#1852C2semidirect
14. C107×#1788C2semidirect
15. C107×#1750C2semidirect
23. #449×C107C4semidirect
65. C2×#41×C107C2×C4semidirect
77. C2×SD16×C107C2×C4semidirect
80. C2×D8×C107C2×C4semidirect
120. #103×C107C2×C4semidirect
125. #102×C107C2×C4semidirect
127. C22⋊C8×C107C2×C4semidirect
368. #22055C107direct (N × H)
380. #2324C2×C107semidirect
381. #2311C2×C107semidirect
382. #1973C2×C107semidirect
383. #1970C2×C107semidirect
384. #1936C2×C107semidirect
385. #1933C2×C107semidirect
386. #1928C2×C107semidirect
387. #1925C2×C107semidirect
388. #1879C2×C107semidirect
389. #1877C2×C107semidirect
390. #1874C2×C107semidirect
391. #1852C2×C107semidirect
392. #1788C2×C107semidirect
393. #1750C2×C107semidirect
394. C107#22055direct (N × H)
402. #449C4×C107semidirect
444. C2×#41C2×C4×C107semidirect
456. C2×SD16C2×C4×C107semidirect
459. C2×D8C2×C4×C107semidirect
499. #103C2×C4×C107semidirect
504. #102C2×C4×C107semidirect
506. C22⋊C8C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1072
C107×#23242
C107×#23112
C107×#19732
C107×#19702
C107×#19362
C107×#19332
C107×#19282
C107×#19252
C107×#18792
C107×#18772
C107×#18742
C107×#18522
C107×#17882
C107×#17502
#22055107