Finite Group Databasebeta

← C107×#24031 #41049995

Subgroups — C107×#24031 #41049995

Order 27392.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3488C211yesmaximal, characteristic
2C107×#3093C211yesmaximal, characteristic, complemented
3C107×#2896C211yesmaximal, characteristic, complemented
4C107×#2500C211yesmaximal, characteristic, complemented
5C107×#2040C211yesmaximal, characteristic, complemented
6C107×#2039C211yesmaximal, characteristic, complemented
7C107×#2037C211yesmaximal, characteristic, complemented
8C107×#2037C211yesmaximal, characteristic, complemented
9C107×#1900C211yesmaximal, characteristic, complemented
10C107×#1871C211yesmaximal, characteristic, complemented
11C107×#1860C211yesmaximal, characteristic, complemented
12C107×#1859C211yesmaximal, characteristic, complemented
13C107×#1792C211yesmaximal, characteristic, complemented
14C107×#1792C211yesmaximal, characteristic, complemented
15C107×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C22×M16×C107C2211yescharacteristic, complemented
19#550×C107—21no—
20#548×C107—21no—
21#546×C107—21no—
22#546×C107—22no—
23D42×C107—22no—
24D42×C107—21no—
25#537×C107—21no—
26#537×C107C2211yescharacteristic
27#535×C107—21no—
28#535×C107C2211yescharacteristic
29#525×C107—21no—
30#525×C107C2211yescharacteristic
31C2×#121×C107—21no—
32C2×#121×C107C2211yescharacteristic
33#520×C107C2211yescharacteristic
34C2×#117×C107C2211yescharacteristic, complemented
35#485×C107—21no—
36#485×C107—21no—
37#482×C107—21no—
38#482×C107—21no—
39#428×C107C2211yescharacteristic, complemented
40#428×C107C2211yescharacteristic, complemented
41C2×#104×C107C2211yescharacteristic
42C2×#104×C107C2211yescharacteristic
43C2×#104×C107C2211yescharacteristic, complemented
44C2×#104×C107C2211yescharacteristic, complemented
45C2×#104×C107C2211yescharacteristic, complemented
46C2×#104×C107C2211yescharacteristic, complemented
47#419×C107—21no—
48#418×C107—21no—
49#417×C107C2211yescharacteristic
50#417×C107C2211yescharacteristic
51#417×C107C2211yescharacteristic, complemented
52#417×C107C2211yescharacteristic, complemented
53#417×C107C2211yescharacteristic, complemented
54#417×C107C2211yescharacteristic, complemented
55#416×C107—21no—
56#416×C107—21no—
57C2×#100×C107C2211yescharacteristic, complemented
58C2×#100×C107C2211yescharacteristic, complemented
59#407×C107C2211yescharacteristic, complemented
60#394×C107—22no—
61#390×C107C2211yescharacteristic, complemented
62#390×C107C2211yescharacteristic, complemented
63#388×C107—22no—
64#384×C107C2211yescharacteristic, complemented
65#382×C107C2211yescharacteristic, complemented
66C4×C22⋊C4×C107C2211yescharacteristic, complemented
67#343×C107C2211yescharacteristic, complemented
68#343×C107C2211yescharacteristic, complemented
69#339×C107C2211yescharacteristic, complemented
70#339×C107C2211yescharacteristic, complemented
71H(5,𝔽2)×C107—22no—
72H(5,𝔽2)×C107—22no—
73H(5,𝔽2)×C107—41no—
74H(5,𝔽2)×C107—41no—
75C2×#41×C107—21no—
76C2×#41×C107—21no—
77C2×#41×C107—21no—
78C2×#41×C107—21no—
79C2×#41×C107—22no—
80C2×#41×C107—22no—
81C2×#41×C107—41no—
82C2×#41×C107—41no—
83C2×#41×C107D411yescharacteristic
84C2×#41×C107D411yescharacteristic
85C2×#41×C107C2311yescharacteristic
86C2×#41×C107C2311yescharacteristic
87C2×#41×C107C2311yescharacteristic
88C22×Q8×C107D411yescharacteristic
89C22×D4×C107—21no—
90C22×D4×C107—22no—
91C22×D4×C107—22no—
92C22×D4×C107—21no—
93C22×D4×C107—21no—
94C22×D4×C107D411yescharacteristic
95C22×D4×C107D412yes—
96C22×D4×C107C2311yescharacteristic
97C23×C4×C107—21no—
98C23×C4×C107C2311yescharacteristic
99C2×M16×C107—21no—
100C2×M16×C107—41no—
101C2×M16×C107—41no—
102C2×M16×C107C2311yescharacteristic
103C2×M16×C107C2311yescharacteristic
104C2×M16×C107C2311yescharacteristic
105C2×M16×C107C2311yescharacteristic
106C22×C8×C107—21no—
107#127×C107—22no—
108#127×C107—21no—
109#124×C107—22no—
110#124×C107—21no—
111#123×C107—22no—
112#123×C107—21no—
113C22⋊Q8×C107—22no—
114C22⋊Q8×C107—21no—
115C22⋊Q8×C107—21no—
116C22⋊Q8×C107D411yescharacteristic
117C22⋊Q8×C107D411yescharacteristic
118#121×C107—22no—
119#121×C107—22no—
120#121×C107—22no—
121#121×C107—22no—
122#121×C107—22no—
123#121×C107—21no—
124#121×C107—21no—
125#121×C107—21no—
126#121×C107—21no—
127#121×C107—21no—
128#121×C107—21no—
129#121×C107—22no—
130#121×C107—21no—
131#121×C107—21no—
132#121×C107D411yescharacteristic
133#121×C107D411yescharacteristic
134#120×C107—22no—
135#120×C107—22no—
136#120×C107—22no—
137#120×C107—21no—
138#120×C107—22no—
139C4×Q8×C107—21no—
140C4×D4×C107—22no—
141C4×D4×C107—22no—
142C4×D4×C107—21no—
143C4×D4×C107—22no—
144C4×D4×C107—21no—
145C4×D4×C107—21no—
146#117×C107—21no—
147#117×C107—21no—
148#117×C107—21no—
149#117×C107—21no—
150#117×C107—21no—
151#117×C107C2311yescharacteristic
152C2×C4⋊C4×C107—21no—
153C2×C4⋊C4×C107—22no—
154C2×C4⋊C4×C107C2311yescharacteristic
155C2×C4⋊C4×C107C2311yescharacteristic
156C2×C4⋊C4×C107C2311yescharacteristic
157C2×C22⋊C4×C107—22no—
158C2×C22⋊C4×C107—21no—
159C2×C22⋊C4×C107—22no—
160C2×C22⋊C4×C107—21no—
161C2×C22⋊C4×C107—22no—
162C2×C22⋊C4×C107D412yes—
163C2×C42×C107—21no—
164C2×C42×C107C2311yescharacteristic
165C2×C42×C107C2311yescharacteristic
166#107×C107—21no—
167#107×C107—21no—
168#106×C107—21no—
169#106×C107—21no—
170#104×C107—22no—
171#104×C107—22no—
172#104×C107—41no—
173#104×C107—41no—
174#104×C107—41no—
175#104×C107—41no—
176#103×C107—21no—
177#103×C107—21no—
178#103×C107—21no—
179#103×C107—21no—
180#103×C107—21no—
181#103×C107—21no—
182#102×C107—21no—
183#102×C107—21no—
184#102×C107—21no—
185#102×C107—21no—
186#102×C107—21no—
187#102×C107—21no—
188#100×C107—41no—
189#100×C107—41no—
190C22⋊C8×C107—21no—
191C22⋊C8×C107—21no—
192#95×C107—21no—
193#95×C107—22no—
194C24×C107—22no—
195C24×C107—21no—
196C24×C107C2×D412yes—
197C24×C107C2×D411yescharacteristic
198#41×C107—21no—
199#41×C107—21no—
200#41×C107—22no—
201#41×C107—22no—
202#41×C107—21no—
203#41×C107—21no—
204#41×C107—21no—
205#41×C107—21no—
206#41×C107—21no—
207#41×C107—21no—
208#41×C107—21no—
209#41×C107—21no—
210#41×C107—42no—
211#41×C107—42no—
212#41×C107—41no—
213#41×C107—41no—
214#41×C107—42no—
215#41×C107—42no—
216#41×C107—42no—
217#41×C107—42no—
218#41×C107—42no—
219#41×C107—42no—
220#41×C107#4112yes—
221#41×C107#4112yes—
222C2×Q8×C107—21no—
223C2×Q8×C107—22no—
224C2×Q8×C107—41no—
225C2×Q8×C107C2×D411yescharacteristic
226C2×Q8×C107C2×D411yescharacteristic
227C2×Q8×C107C2×D411yescharacteristic
228C2×D4×C107—21no—
229C2×D4×C107—22no—
230C2×D4×C107—22no—
231C2×D4×C107—22no—
232C2×D4×C107—22no—
233C2×D4×C107—21no—
234C2×D4×C107—21no—
235C2×D4×C107—21no—
236C2×D4×C107—21no—
237C2×D4×C107—21no—
238C2×D4×C107—22no—
239C2×D4×C107—22no—
240C2×D4×C107—22no—
241C2×D4×C107—21no—
242C2×D4×C107—22no—
243C2×D4×C107—21no—
244C2×D4×C107—21no—
245C2×D4×C107—21no—
246C2×D4×C107—21no—
247C2×D4×C107—21no—
248C2×D4×C107—21no—
249C2×D4×C107—21no—
250C2×D4×C107—41no—
251C2×D4×C107—42no—
252C2×D4×C107—42no—
253C2×D4×C107—42no—
254C2×D4×C107—42no—
255C2×D4×C107—44no—
256C2×D4×C107—44no—
257C2×D4×C107—42no—
258C2×D4×C107—42no—
259C2×D4×C107—82no—
260C2×D4×C107—84no—
261C2×D4×C107C2×D411yescharacteristic
262C2×D4×C107C2×D411yescharacteristic
263C2×D4×C107C2×D411yescharacteristic
264C22×C4×C107—21no—
265C22×C4×C107—21no—
266C22×C4×C107—21no—
267C22×C4×C107—21no—
268C22×C4×C107—21no—
269C22×C4×C107—22no—
270C22×C4×C107—21no—
271C22×C4×C107—21no—
272C22×C4×C107—22no—
273C22×C4×C107—21no—
274C22×C4×C107—21no—
275C22×C4×C107—21no—
276C22×C4×C107—21no—
277C22×C4×C107—21no—
278C22×C4×C107—21no—
279C22×C4×C107—21no—
280C22×C4×C107—42no—
281C22×C4×C107—42no—
282C22×C4×C107C2×D411yescharacteristic
283C22×C4×C107C2×D411yescharacteristic
284C22×C4×C107C2×D411yescharacteristic
285C22×C4×C107C2×D411yescharacteristic
286C22×C4×C107C2×D411yescharacteristic
287C22×C4×C107C2×D412yes—
288C22×C4×C107C2411yescharacteristic
289M16×C107—21no—
290M16×C107—21no—
291M16×C107—21no—
292M16×C107—21no—
293M16×C107—21no—
294M16×C107—21no—
295M16×C107—21no—
296M16×C107—21no—
297M16×C107—42no—
298C2×C8×C107—21no—
299C2×C8×C107—21no—
300C2×C8×C107—21no—
301C2×C8×C107—21no—
302C2×C8×C107—42no—
303C4⋊C4×C107—22no—
304C4⋊C4×C107—22no—
305C4⋊C4×C107—21no—
306C4⋊C4×C107—21no—
307C4⋊C4×C107—21no—
308C4⋊C4×C107—21no—
309C4⋊C4×C107—21no—
310C4⋊C4×C107—21no—
311C4⋊C4×C107—21no—
312C4⋊C4×C107—21no—
313C4⋊C4×C107—82no—
314C4⋊C4×C107C2×D411yescharacteristic
315C4⋊C4×C107C2×D411yescharacteristic
316C22⋊C4×C107—22no—
317C22⋊C4×C107—22no—
318C22⋊C4×C107—22no—
319C22⋊C4×C107—22no—
320C22⋊C4×C107—22no—
321C22⋊C4×C107—21no—
322C22⋊C4×C107—21no—
323C22⋊C4×C107—21no—
324C22⋊C4×C107—21no—
325C22⋊C4×C107—22no—
326C22⋊C4×C107—22no—
327C22⋊C4×C107—21no—
328C22⋊C4×C107—42no—
329C22⋊C4×C107—44no—
330C22⋊C4×C107—41no—
331C22⋊C4×C107—41no—
332C22⋊C4×C107—82no—
333C42×C107—22no—
334C42×C107—21no—
335C42×C107—21no—
336C42×C107—21no—
337C42×C107—21no—
338C42×C107—21no—
339C42×C107—41no—
340C42×C107—41no—
341C23×C107—21no—
342C23×C107—21no—
343C23×C107—21no—
344C23×C107—22no—
345C23×C107—21no—
346C23×C107—21no—
347C23×C107—22no—
348C23×C107—22no—
349C23×C107—41no—
350C23×C107—41no—
351C23×C107—42no—
352C23×C107—42no—
353C23×C107—44no—
354C23×C107—42no—
355C23×C107—42no—
356C23×C107—81no—
357C23×C107—82no—
358C23×C107—82no—
359C23×C107#12011yescharacteristic
360C23×C107#12011yescharacteristic
361C23×C107C22×D411yescharacteristic
362Q8×C107—21no—
363Q8×C107—21no—
364Q8×C107—21no—
365Q8×C107—21no—
366Q8×C107—21no—
367Q8×C107—42no—
368Q8×C107#12312yes—
369D4×C107—22no—
370D4×C107—22no—
371D4×C107—21no—
372D4×C107—21no—
373D4×C107—21no—
374D4×C107—21no—
375D4×C107—21no—
376D4×C107—42no—
377D4×C107—42no—
378D4×C107—44no—
379D4×C107—42no—
380D4×C107—44no—
381D4×C107—44no—
382D4×C107—42no—
383D4×C107—41no—
384D4×C107—41no—
385D4×C107—41no—
386D4×C107—41no—
387D4×C107—41no—
388D4×C107—41no—
389D4×C107—41no—
390D4×C107—41no—
391D4×C107—81no—
392D4×C107—82no—
393D4×C107—82no—
394D4×C107—82no—
395D4×C107—82no—
396D4×C107#12312yes—
397C2×C4×C107—21no—
398C2×C4×C107—21no—
399C2×C4×C107—21no—
400C2×C4×C107—21no—
401C2×C4×C107—21no—
402C2×C4×C107—21no—
403C2×C4×C107—21no—
404C2×C4×C107—21no—
405C2×C4×C107—21no—
406C2×C4×C107—21no—
407C2×C4×C107—21no—
408C2×C4×C107—22no—
409C2×C4×C107—22no—
410C2×C4×C107—22no—
411C2×C4×C107—21no—
412C2×C4×C107—22no—
413C2×C4×C107—21no—
414C2×C4×C107—21no—
415C2×C4×C107—21no—
416C2×C4×C107—42no—
417C2×C4×C107—42no—
418C2×C4×C107—42no—
419C2×C4×C107—44no—
420C2×C4×C107—41no—
421C2×C4×C107—41no—
422C2×C4×C107—41no—
423C2×C4×C107—41no—
424C2×C4×C107—41no—
425C2×C4×C107—41no—
426C2×C4×C107—42no—
427C2×C4×C107—41no—
428C2×C4×C107—42no—
429C2×C4×C107—41no—
430C2×C4×C107—42no—
431C2×C4×C107—41no—
432C2×C4×C107—41no—
433C2×C4×C107—41no—
434C2×C4×C107—82no—
435C2×C4×C107#12011yescharacteristic
436C2×C4×C107#12011yescharacteristic
437C2×C4×C107C22×D411yescharacteristic
438C2×C4×C107C22×D411yescharacteristic
439C2×C4×C107C2×#4111yescharacteristic
440C2×C4×C107C2×#4111yescharacteristic
441C2×C4×C107H(5,𝔽2)11yescharacteristic
442C2×C4×C107H(5,𝔽2)11yescharacteristic
443C8×C107—41no—
444C8×C107—41no—
445C8×C107—41no—
446C8×C107—41no—
447C22×C107—21no—
448C22×C107—21no—
449C22×C107—21no—
450C22×C107—21no—
451C22×C107—22no—
452C22×C107—21no—
453C22×C107—21no—
454C22×C107—21no—
455C22×C107—21no—
456C22×C107—41no—
457C22×C107—41no—
458C22×C107—41no—
459C22×C107—41no—
460C22×C107—42no—
461C22×C107—41no—
462C22×C107—42no—
463C22×C107—41no—
464C22×C107—42no—
465C22×C107—41no—
466C22×C107—41no—
467C22×C107—81no—
468C22×C107—81no—
469C22×C107—82no—
470C22×C107—82no—
471C22×C107—84no—
472C22×C107—164no—
473C22×C107C2×#12011yescharacteristic
474C22×C107#54611yescharacteristic
475C22×C107#54611yescharacteristic
476C4×C107—21no—
477C4×C107—21no—
478C4×C107—22no—
479C4×C107—42no—
480C4×C107—41no—
481C4×C107—41no—
482C4×C107—41no—
483C4×C107—42no—
484C4×C107—41no—
485C4×C107—81no—
486C4×C107—81no—
487C4×C107—81no—
488C4×C107C2×#12311yescharacteristic
489C4×C107#53411yescharacteristic
490C4×C107#54611yescharacteristic
491C4×C107#54611yescharacteristic
492#24031C10711yesmaximal, characteristic, direct product factor, Sylow
493C2×C107—21no—
494C2×C107—21no—
495C2×C107—41no—
496C2×C107—41no—
497C2×C107—42no—
498C2×C107—81no—
499C2×C107—82no—
500C2×C107—81no—
501C2×C107#240511yescharacteristic
502C2×C107#301811yescharacteristic
503C2×C107#301911yescharacteristic
504#3488C2×C10711yescharacteristic
505#3093C2×C10711yescharacteristic, complemented
506#2896C2×C10711yescharacteristic, complemented
507#2500C2×C10711yescharacteristic, complemented
508#2040C2×C10711yescharacteristic, complemented
509#2039C2×C10711yescharacteristic, complemented
510#2037C2×C10711yescharacteristic, complemented
511#2037C2×C10711yescharacteristic, complemented
512#1900C2×C10711yescharacteristic, complemented
513#1871C2×C10711yescharacteristic, complemented
514#1860C2×C10711yescharacteristic, complemented
515#1859C2×C10711yescharacteristic, complemented
516#1792C2×C10711yescharacteristic, complemented
517#1792C2×C10711yescharacteristic, complemented
518#1789C2×C10711yescharacteristic, complemented
519C107#2403111yescharacteristic, direct product factor, Sylow
520C2×H(5,𝔽2)C22×C10711yescharacteristic
521C22×#41C22×C10711yescharacteristic
522C22×M16C22×C10711yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C10711yescharacteristic
531#535—21no—
532#535C22×C10711yescharacteristic
533#525—21no—
534#525C22×C10711yescharacteristic
535C2×#121—21no—
536C2×#121C22×C10711yescharacteristic
537#520C22×C10711yescharacteristic
538C2×#117C22×C10711yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C10711yescharacteristic, complemented
544#428C22×C10711yescharacteristic, complemented
545C2×#104C22×C10711yescharacteristic
546C2×#104C22×C10711yescharacteristic
547C2×#104C22×C10711yescharacteristic, complemented
548C2×#104C22×C10711yescharacteristic, complemented
549C2×#104C22×C10711yescharacteristic, complemented
550C2×#104C22×C10711yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C10711yescharacteristic
554#417C22×C10711yescharacteristic
555#417C22×C10711yescharacteristic, complemented
556#417C22×C10711yescharacteristic, complemented
557#417C22×C10711yescharacteristic, complemented
558#417C22×C10711yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C10711yescharacteristic, complemented
562C2×#100C22×C10711yescharacteristic, complemented
563#407C22×C10711yescharacteristic, complemented
564#394—22no—
565#390C22×C10711yescharacteristic, complemented
566#390C22×C10711yescharacteristic, complemented
567#388—22no—
568#384C22×C10711yescharacteristic, complemented
569#382C22×C10711yescharacteristic, complemented
570C4×C22⋊C4C22×C10711yescharacteristic, complemented
571#343C22×C10711yescharacteristic, complemented
572#343C22×C10711yescharacteristic, complemented
573#339C22×C10711yescharacteristic, complemented
574#339C22×C10711yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C10711yescharacteristic
588C2×#41D4×C10711yescharacteristic
589C2×#41C23×C10711yescharacteristic
590C2×#41C23×C10711yescharacteristic
591C2×#41C23×C10711yescharacteristic
592C22×Q8D4×C10711yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C10711yescharacteristic
599C22×D4D4×C10712yes—
600C22×D4C23×C10711yescharacteristic
601C23×C4—21no—
602C23×C4C23×C10711yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C10711yescharacteristic
607C2×M16C23×C10711yescharacteristic
608C2×M16C23×C10711yescharacteristic
609C2×M16C23×C10711yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C10711yescharacteristic
621C22⋊Q8D4×C10711yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C10711yescharacteristic
637#121D4×C10711yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C10711yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C10711yescharacteristic
659C2×C4⋊C4C23×C10711yescharacteristic
660C2×C4⋊C4C23×C10711yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C10712yes—
667C2×C42—21no—
668C2×C42C23×C10711yescharacteristic
669C2×C42C23×C10711yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C10712yes—
701C24C2×D4×C10711yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C10712yes—
725#41#41×C10712yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C10711yescharacteristic
730C2×Q8C2×D4×C10711yescharacteristic
731C2×Q8C2×D4×C10711yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C10711yescharacteristic
766C2×D4C2×D4×C10711yescharacteristic
767C2×D4C2×D4×C10711yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C10711yescharacteristic
787C22×C4C2×D4×C10711yescharacteristic
788C22×C4C2×D4×C10711yescharacteristic
789C22×C4C2×D4×C10711yescharacteristic
790C22×C4C2×D4×C10711yescharacteristic
791C22×C4C2×D4×C10712yes—
792C22×C4C24×C10711yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C10711yescharacteristic
819C4⋊C4C2×D4×C10711yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C10711yescharacteristic
864C23#120×C10711yescharacteristic
865C23C22×D4×C10711yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C10712yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C10712yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C10711yescharacteristic
940C2×C4#120×C10711yescharacteristic
941C2×C4C22×D4×C10711yescharacteristic
942C2×C4C22×D4×C10711yescharacteristic
943C2×C4C2×#41×C10711yescharacteristic
944C2×C4C2×#41×C10711yescharacteristic
945C2×C4H(5,𝔽2)×C10711yescharacteristic
946C2×C4H(5,𝔽2)×C10711yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C10711yescharacteristic
978C22#546×C10711yescharacteristic
979C22#546×C10711yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C10711yescharacteristic
993C4#534×C10711yescharacteristic
994C4#546×C10711yescharacteristic
995C4#546×C10711yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C107×#240511yescharacteristic
1005C2C107×#301811yescharacteristic
1006C2C107×#301911yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3093C2semidirect
3. C107×#2896C2semidirect
4. C107×#2500C2semidirect
5. C107×#2040C2semidirect
6. C107×#2039C2semidirect
7. C107×#2037C2semidirect
8. C107×#2037C2semidirect
9. C107×#1900C2semidirect
10. C107×#1871C2semidirect
11. C107×#1860C2semidirect
12. C107×#1859C2semidirect
13. C107×#1792C2semidirect
14. C107×#1792C2semidirect
15. C107×#1789C2semidirect
18. C22×M16×C107C22semidirect
34. C2×#117×C107C22semidirect
39. #428×C107C22semidirect
40. #428×C107C22semidirect
43. C2×#104×C107C22semidirect
44. C2×#104×C107C22semidirect
45. C2×#104×C107C22semidirect
46. C2×#104×C107C22semidirect
51. #417×C107C22semidirect
52. #417×C107C22semidirect
53. #417×C107C22semidirect
54. #417×C107C22semidirect
57. C2×#100×C107C22semidirect
58. C2×#100×C107C22semidirect
59. #407×C107C22semidirect
61. #390×C107C22semidirect
62. #390×C107C22semidirect
64. #384×C107C22semidirect
65. #382×C107C22semidirect
66. C4×C22⋊C4×C107C22semidirect
67. #343×C107C22semidirect
68. #343×C107C22semidirect
69. #339×C107C22semidirect
70. #339×C107C22semidirect
492. #24031C107direct (N × H)
505. #3093C2×C107semidirect
506. #2896C2×C107semidirect
507. #2500C2×C107semidirect
508. #2040C2×C107semidirect
509. #2039C2×C107semidirect
510. #2037C2×C107semidirect
511. #2037C2×C107semidirect
512. #1900C2×C107semidirect
513. #1871C2×C107semidirect
514. #1860C2×C107semidirect
515. #1859C2×C107semidirect
516. #1792C2×C107semidirect
517. #1792C2×C107semidirect
518. #1789C2×C107semidirect
519. C107#24031direct (N × H)
522. C22×M16C22×C107semidirect
538. C2×#117C22×C107semidirect
543. #428C22×C107semidirect
544. #428C22×C107semidirect
547. C2×#104C22×C107semidirect
548. C2×#104C22×C107semidirect
549. C2×#104C22×C107semidirect
550. C2×#104C22×C107semidirect
555. #417C22×C107semidirect
556. #417C22×C107semidirect
557. #417C22×C107semidirect
558. #417C22×C107semidirect
561. C2×#100C22×C107semidirect
562. C2×#100C22×C107semidirect
563. #407C22×C107semidirect
565. #390C22×C107semidirect
566. #390C22×C107semidirect
568. #384C22×C107semidirect
569. #382C22×C107semidirect
570. C4×C22⋊C4C22×C107semidirect
571. #343C22×C107semidirect
572. #343C22×C107semidirect
573. #339C22×C107semidirect
574. #339C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34882
C107×#30932
C107×#28962
C107×#25002
C107×#20402
C107×#20392
C107×#20372
C107×#19002
C107×#18712
C107×#18602
C107×#18592
C107×#17922
C107×#17892
#24031107