Finite Group Databasebeta

← C107×#22889 #41048853

Subgroups — C107×#22889 #41048853

Order 27392.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3002C211yesmaximal, characteristic
2C2×#443×C107C211yesmaximal, characteristic, complemented
3C107×#2933C211yesmaximal, characteristic, complemented
4C2×#421×C107C211yesmaximal, characteristic, complemented
5C107×#2880C211yesmaximal, characteristic, complemented
6C107×#1975C211yesmaximal, characteristic, complemented
7C107×#1937C211yesmaximal, characteristic, complemented
8C107×#1929C211yesmaximal, characteristic, complemented
9C107×#1897C211yesmaximal, characteristic, complemented
10C107×#1876C211yesmaximal, characteristic, complemented
11C107×#1876C211yesmaximal, characteristic, complemented
12C107×#1866C211yesmaximal, characteristic, complemented
13C107×#1855C211yesmaximal, characteristic, complemented
14C107×#1765C211yesmaximal, characteristic, complemented
15C107×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C2×#135×C107C2211yescharacteristic
18C2×#135×C107C2211yescharacteristic
19C2×#131×C107C2211yescharacteristic
20C2×#131×C107C2211yescharacteristic
21C2×#131×C107C2211yescharacteristic, complemented
22C22×M16×C107C2211yescharacteristic
23#525×C107C2211yescharacteristic
24C2×#117×C107C2211yescharacteristic
25#452×C107C411yescharacteristic, complemented
26#452×C107C411yescharacteristic, complemented
27#451×C107C411yescharacteristic, complemented
28#450×C107C411yescharacteristic, complemented
29#449×C107C411yescharacteristic, complemented
30#449×C107C411yescharacteristic, complemented
31#448×C107C411yescharacteristic, complemented
32#447×C107C411yescharacteristic, complemented
33#443×C107—24no—
34#436×C107—21no—
35#435×C107—21no—
36#435×C107—21no—
37C8×D4×C107—21no—
38C2×#108×C107C2211yescharacteristic, complemented
39C2×#108×C107C2211yescharacteristic, complemented
40#424×C107C2211yescharacteristic, complemented
41#421×C107—24no—
42C2×#104×C107C2211yescharacteristic
43C2×#104×C107C2211yescharacteristic
44C2×#104×C107C2211yescharacteristic
45C2×#104×C107C2211yescharacteristic
46C2×#104×C107C2211yescharacteristic, complemented
47C2×#104×C107C2211yescharacteristic, complemented
48#416×C107C2211yescharacteristic
49#416×C107C2211yescharacteristic
50#408×C107—21no—
51#408×C107—21no—
52#408×C107C2211yescharacteristic
53#408×C107C2211yescharacteristic
54#408×C107C2211yescharacteristic, complemented
55#407×C107—21no—
56#407×C107C2211yescharacteristic
57C2×C22⋊C8×C107—21no—
58C2×C22⋊C8×C107C2211yescharacteristic
59C2×C22⋊C8×C107C2211yescharacteristic
60#405×C107C2211yescharacteristic, complemented
61C2×#97×C107C2211yescharacteristic, complemented
62C2×C4×C8×C107C2211yescharacteristic, complemented
63#341×C107C2211yescharacteristic, complemented
64#341×C107C2211yescharacteristic, complemented
65#339×C107C2211yescharacteristic, complemented
66#339×C107C2211yescharacteristic, complemented
67#336×C107C2211yescharacteristic, complemented
68#336×C107C2211yescharacteristic, complemented
69C2×#41×C107—21no—
70C2×#41×C107—21no—
71C2×#41×C107—22no—
72C2×#41×C107—22no—
73C2×#41×C107—41no—
74C2×#41×C107—41no—
75C2×#41×C107C2×C411yescharacteristic
76C2×#41×C107C2×C411yescharacteristic
77C2×#41×C107C2311yescharacteristic
78C2×#41×C107C2311yescharacteristic
79C2×#41×C107C2311yescharacteristic
80C22×Q8×C107C2×C411yescharacteristic
81C22×D4×C107—21no—
82C22×D4×C107C2×C411yescharacteristic
83C23×C4×C107—21no—
84C23×C4×C107C2311yescharacteristic
85#135×C107—22no—
86#135×C107—22no—
87#135×C107—41no—
88#135×C107—41no—
89C2×Q16×C107C2×C411yescharacteristic
90C2×Q16×C107C2×C411yescharacteristic
91C2×SD16×C107C2×C411yescharacteristic
92C2×SD16×C107C2×C411yescharacteristic
93C2×SD16×C107C2×C411yescharacteristic
94C2×SD16×C107C2×C411yescharacteristic
95C2×D8×C107C2×C411yescharacteristic
96C2×D8×C107C2×C411yescharacteristic
97#131×C107—22no—
98#131×C107—22no—
99#131×C107—22no—
100#131×C107—41no—
101#131×C107—41no—
102#131×C107—41no—
103C2×M16×C107—21no—
104C2×M16×C107—21no—
105C2×M16×C107—21no—
106C2×M16×C107—21no—
107C2×M16×C107—22no—
108C2×M16×C107—41no—
109C2×M16×C107C2311yescharacteristic
110C2×M16×C107C2311yescharacteristic
111C2×M16×C107C2311yescharacteristic
112C2×M16×C107C2311yescharacteristic
113C22×C8×C107—21no—
114C22×C8×C107—21no—
115C22×C8×C107—21no—
116C22×C8×C107—21no—
117C22×C8×C107C2311yescharacteristic
118C22×C8×C107C2311yescharacteristic
119C22×C8×C107C2311yescharacteristic
120C22×C8×C107C2311yescharacteristic
121#123×C107—21no—
122C22⋊Q8×C107C2×C411yescharacteristic
123C22⋊Q8×C107C2×C411yescharacteristic
124#121×C107C2×C411yescharacteristic
125#121×C107C2×C411yescharacteristic
126#120×C107—21no—
127C4×D4×C107—21no—
128C4×D4×C107—21no—
129#117×C107—22no—
130#117×C107—41no—
131#117×C107C2311yescharacteristic
132C2×C4⋊C4×C107—21no—
133C2×C22⋊C4×C107—21no—
134C2×C42×C107C2311yescharacteristic
135C2×C42×C107C2311yescharacteristic
136#108×C107—22no—
137#108×C107—41no—
138C4⋊C8×C107—21no—
139C4⋊C8×C107—21no—
140#104×C107—22no—
141#104×C107—22no—
142#104×C107—22no—
143#104×C107—22no—
144#104×C107—41no—
145#104×C107D414yescomplemented
146#103×C107C2×C411yescharacteristic
147#103×C107C2×C411yescharacteristic
148#103×C107C2×C411yescharacteristic
149#103×C107C2×C411yescharacteristic
150#102×C107C2×C411yescharacteristic
151#102×C107C2×C411yescharacteristic
152#102×C107C2×C411yescharacteristic
153#102×C107C2×C411yescharacteristic
154C22⋊C8×C107—21no—
155C22⋊C8×C107—21no—
156C22⋊C8×C107—21no—
157C22⋊C8×C107—21no—
158C22⋊C8×C107—21no—
159C22⋊C8×C107—21no—
160C22⋊C8×C107—21no—
161C22⋊C8×C107—21no—
162C22⋊C8×C107C2×C411yescharacteristic
163C22⋊C8×C107C2×C411yescharacteristic
164C22⋊C8×C107C2×C411yescharacteristic
165C22⋊C8×C107C2×C411yescharacteristic
166C22⋊C8×C107D411yescharacteristic
167C22⋊C8×C107D411yescharacteristic
168C22⋊C8×C107D411yescharacteristic
169C22⋊C8×C107D411yescharacteristic
170#97×C107—21no—
171#97×C107—41no—
172C4×C8×C107—21no—
173C4×C8×C107—22no—
174C24×C107—21no—
175C24×C107#4111yescharacteristic
176#41×C107—21no—
177#41×C107—21no—
178#41×C107—22no—
179#41×C107—22no—
180#41×C107—21no—
181#41×C107—21no—
182#41×C107—21no—
183#41×C107—21no—
184#41×C107—21no—
185#41×C107—21no—
186#41×C107—21no—
187#41×C107—21no—
188#41×C107—42no—
189#41×C107—42no—
190#41×C107—41no—
191#41×C107—41no—
192#41×C107—42no—
193#41×C107—42no—
194#41×C107C2×D412yes—
195#41×C107#4112yes—
196C2×Q8×C107—21no—
197C2×Q8×C107—22no—
198C2×Q8×C107—41no—
199C2×Q8×C107C22×C411yescharacteristic
200C2×Q8×C107C22×C411yescharacteristic
201C2×Q8×C107C22×C411yescharacteristic
202C2×D4×C107—21no—
203C2×D4×C107—22no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—21no—
208C2×D4×C107—21no—
209C2×D4×C107—21no—
210C2×D4×C107—21no—
211C2×D4×C107—41no—
212C2×D4×C107—42no—
213C2×D4×C107—42no—
214C2×D4×C107C22×C411yescharacteristic
215C2×D4×C107C22×C411yescharacteristic
216C2×D4×C107C22×C411yescharacteristic
217C22×C4×C107—21no—
218C22×C4×C107—21no—
219C22×C4×C107—21no—
220C22×C4×C107—21no—
221C22×C4×C107—21no—
222C22×C4×C107—21no—
223C22×C4×C107—21no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—21no—
229C22×C4×C107—42no—
230C22×C4×C107—42no—
231C22×C4×C107C22×C411yescharacteristic
232C22×C4×C107C22×C411yescharacteristic
233C22×C4×C107C2×D411yescharacteristic
234C22×C4×C107C2×D411yescharacteristic
235C22×C4×C107#4111yescharacteristic
236C22×C4×C107C2411yescharacteristic
237Q16×C107—22no—
238Q16×C107—41no—
239SD16×C107—22no—
240SD16×C107—22no—
241SD16×C107—41no—
242SD16×C107—41no—
243D8×C107—22no—
244D8×C107—41no—
245M16×C107—21no—
246M16×C107—21no—
247M16×C107—21no—
248M16×C107—21no—
249M16×C107—21no—
250M16×C107—21no—
251M16×C107—21no—
252M16×C107—42no—
253M16×C107—42no—
254M16×C107—42no—
255M16×C107—42no—
256M16×C107C2×D412yes—
257C2×C8×C107—21no—
258C2×C8×C107—21no—
259C2×C8×C107—21no—
260C2×C8×C107—21no—
261C2×C8×C107—21no—
262C2×C8×C107—21no—
263C2×C8×C107—21no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107—21no—
267C2×C8×C107—21no—
268C2×C8×C107—21no—
269C2×C8×C107—42no—
270C2×C8×C107—42no—
271C2×C8×C107—42no—
272C2×C8×C107—42no—
273C2×C8×C107C22×C411yescharacteristic
274C2×C8×C107C22×C411yescharacteristic
275C2×C8×C107C22×C411yescharacteristic
276C2×C8×C107C22×C411yescharacteristic
277C2×C8×C107C2×D411yescharacteristic
278C2×C8×C107C2×D411yescharacteristic
279C2×C8×C107C2×D411yescharacteristic
280C2×C8×C107C2×D411yescharacteristic
281C4⋊C4×C107—21no—
282C4⋊C4×C107—21no—
283C4⋊C4×C107—42no—
284C4⋊C4×C107C22×C411yescharacteristic
285C4⋊C4×C107C22×C411yescharacteristic
286C22⋊C4×C107—21no—
287C22⋊C4×C107—21no—
288C22⋊C4×C107—21no—
289C22⋊C4×C107—21no—
290C22⋊C4×C107—21no—
291C22⋊C4×C107—42no—
292C42×C107—21no—
293C42×C107—21no—
294C42×C107—21no—
295C42×C107—21no—
296C42×C107C2×D412yes—
297C23×C107—21no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—41no—
303C23×C107—41no—
304C23×C107—42no—
305C23×C107—42no—
306C23×C107—81no—
307C23×C107C4×D411yescharacteristic
308C23×C107C4×D411yescharacteristic
309C23×C107C2×#4111yescharacteristic
310Q8×C107—21no—
311Q8×C107—21no—
312Q8×C107—21no—
313Q8×C107—21no—
314Q8×C107—21no—
315Q8×C107—42no—
316Q8×C107C4×D412yes—
317D4×C107—22no—
318D4×C107—22no—
319D4×C107—21no—
320D4×C107—21no—
321D4×C107—21no—
322D4×C107—21no—
323D4×C107—21no—
324D4×C107—42no—
325D4×C107—42no—
326D4×C107—42no—
327D4×C107—42no—
328D4×C107—41no—
329D4×C107—41no—
330D4×C107—41no—
331D4×C107—41no—
332D4×C107—81no—
333D4×C107C4×D412yes—
334C2×C4×C107—21no—
335C2×C4×C107—21no—
336C2×C4×C107—21no—
337C2×C4×C107—21no—
338C2×C4×C107—21no—
339C2×C4×C107—21no—
340C2×C4×C107—21no—
341C2×C4×C107—21no—
342C2×C4×C107—22no—
343C2×C4×C107—21no—
344C2×C4×C107—22no—
345C2×C4×C107—21no—
346C2×C4×C107—21no—
347C2×C4×C107—21no—
348C2×C4×C107—21no—
349C2×C4×C107—21no—
350C2×C4×C107—21no—
351C2×C4×C107—22no—
352C2×C4×C107—42no—
353C2×C4×C107—42no—
354C2×C4×C107—42no—
355C2×C4×C107—41no—
356C2×C4×C107—41no—
357C2×C4×C107—41no—
358C2×C4×C107—41no—
359C2×C4×C107—41no—
360C2×C4×C107—41no—
361C2×C4×C107—41no—
362C2×C4×C107—41no—
363C2×C4×C107—41no—
364C2×C4×C107C4×D411yescharacteristic
365C2×C4×C107C4×D411yescharacteristic
366C2×C4×C107C23×C411yescharacteristic
367C2×C4×C107C22×D411yescharacteristic
368C2×C4×C107C22×D411yescharacteristic
369C2×C4×C107C2×#4111yescharacteristic
370C2×C4×C107H(5,𝔽2)11yescharacteristic
371C2×C4×C107H(5,𝔽2)11yescharacteristic
372C8×C107—21no—
373C8×C107—21no—
374C8×C107—21no—
375C8×C107—21no—
376C8×C107—21no—
377C8×C107—21no—
378C8×C107—22no—
379C8×C107—21no—
380C8×C107—21no—
381C8×C107—41no—
382C8×C107—41no—
383C8×C107—41no—
384C22×C107—21no—
385C22×C107—21no—
386C22×C107—21no—
387C22×C107—21no—
388C22×C107—22no—
389C22×C107—21no—
390C22×C107—21no—
391C22×C107—21no—
392C22×C107—21no—
393C22×C107—41no—
394C22×C107—41no—
395C22×C107—41no—
396C22×C107—41no—
397C22×C107—41no—
398C22×C107—41no—
399C22×C107—41no—
400C22×C107—41no—
401C22×C107—81no—
402C22×C107—81no—
403C22×C107—84no—
404C22×C107C2×C4×D411yescharacteristic
405C22×C107#54611yescharacteristic
406C22×C107#55111yescharacteristic
407C4×C107—21no—
408C4×C107—21no—
409C4×C107—22no—
410C4×C107—42no—
411C4×C107—41no—
412C4×C107—41no—
413C4×C107—41no—
414C4×C107—41no—
415C4×C107—81no—
416C4×C107C2×C4×D411yescharacteristic
417C4×C107#51811yescharacteristic
418C4×C107D4211yescharacteristic
419C4×C107#54611yescharacteristic
420#22889C10711yesmaximal, characteristic, direct product factor, Sylow
421C2×C107—21no—
422C2×C107—21no—
423C2×C107—41no—
424C2×C107—41no—
425C2×C107—42no—
426C2×C107—81no—
427C2×C107—81no—
428C2×C107#235811yescharacteristic
429C2×C107#295511yescharacteristic
430C2×C107#295711yescharacteristic
431#3002C2×C10711yescharacteristic
432C2×#443C2×C10711yescharacteristic, complemented
433#2933C2×C10711yescharacteristic, complemented
434C2×#421C2×C10711yescharacteristic, complemented
435#2880C2×C10711yescharacteristic, complemented
436#1975C2×C10711yescharacteristic, complemented
437#1937C2×C10711yescharacteristic, complemented
438#1929C2×C10711yescharacteristic, complemented
439#1897C2×C10711yescharacteristic, complemented
440#1876C2×C10711yescharacteristic, complemented
441#1876C2×C10711yescharacteristic, complemented
442#1866C2×C10711yescharacteristic, complemented
443#1855C2×C10711yescharacteristic, complemented
444#1765C2×C10711yescharacteristic, complemented
445#1750C2×C10711yescharacteristic, complemented
446C107#2288911yescharacteristic, direct product factor, Sylow
447C22×#41C22×C10711yescharacteristic
448C2×#135C22×C10711yescharacteristic
449C2×#135C22×C10711yescharacteristic
450C2×#131C22×C10711yescharacteristic
451C2×#131C22×C10711yescharacteristic
452C2×#131C22×C10711yescharacteristic, complemented
453C22×M16C22×C10711yescharacteristic
454#525C22×C10711yescharacteristic
455C2×#117C22×C10711yescharacteristic
456#452C4×C10711yescharacteristic, complemented
457#452C4×C10711yescharacteristic, complemented
458#451C4×C10711yescharacteristic, complemented
459#450C4×C10711yescharacteristic, complemented
460#449C4×C10711yescharacteristic, complemented
461#449C4×C10711yescharacteristic, complemented
462#448C4×C10711yescharacteristic, complemented
463#447C4×C10711yescharacteristic, complemented
464#443—24no—
465#436—21no—
466#435—21no—
467#435—21no—
468C8×D4—21no—
469C2×#108C22×C10711yescharacteristic, complemented
470C2×#108C22×C10711yescharacteristic, complemented
471#424C22×C10711yescharacteristic, complemented
472#421—24no—
473C2×#104C22×C10711yescharacteristic
474C2×#104C22×C10711yescharacteristic
475C2×#104C22×C10711yescharacteristic
476C2×#104C22×C10711yescharacteristic
477C2×#104C22×C10711yescharacteristic, complemented
478C2×#104C22×C10711yescharacteristic, complemented
479#416C22×C10711yescharacteristic
480#416C22×C10711yescharacteristic
481#408—21no—
482#408—21no—
483#408C22×C10711yescharacteristic
484#408C22×C10711yescharacteristic
485#408C22×C10711yescharacteristic, complemented
486#407—21no—
487#407C22×C10711yescharacteristic
488C2×C22⋊C8—21no—
489C2×C22⋊C8C22×C10711yescharacteristic
490C2×C22⋊C8C22×C10711yescharacteristic
491#405C22×C10711yescharacteristic, complemented
492C2×#97C22×C10711yescharacteristic, complemented
493C2×C4×C8C22×C10711yescharacteristic, complemented
494#341C22×C10711yescharacteristic, complemented
495#341C22×C10711yescharacteristic, complemented
496#339C22×C10711yescharacteristic, complemented
497#339C22×C10711yescharacteristic, complemented
498#336C22×C10711yescharacteristic, complemented
499#336C22×C10711yescharacteristic, complemented
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C10711yescharacteristic
507C2×#41C2×C4×C10711yescharacteristic
508C2×#41C23×C10711yescharacteristic
509C2×#41C23×C10711yescharacteristic
510C2×#41C23×C10711yescharacteristic
511C22×Q8C2×C4×C10711yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C10711yescharacteristic
514C23×C4—21no—
515C23×C4C23×C10711yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C10711yescharacteristic
521C2×Q16C2×C4×C10711yescharacteristic
522C2×SD16C2×C4×C10711yescharacteristic
523C2×SD16C2×C4×C10711yescharacteristic
524C2×SD16C2×C4×C10711yescharacteristic
525C2×SD16C2×C4×C10711yescharacteristic
526C2×D8C2×C4×C10711yescharacteristic
527C2×D8C2×C4×C10711yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C10711yescharacteristic
541C2×M16C23×C10711yescharacteristic
542C2×M16C23×C10711yescharacteristic
543C2×M16C23×C10711yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C10711yescharacteristic
549C22×C8C23×C10711yescharacteristic
550C22×C8C23×C10711yescharacteristic
551C22×C8C23×C10711yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C10711yescharacteristic
554C22⋊Q8C2×C4×C10711yescharacteristic
555#121C2×C4×C10711yescharacteristic
556#121C2×C4×C10711yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C10711yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C10711yescharacteristic
566C2×C42C23×C10711yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C10714yescomplemented
577#103C2×C4×C10711yescharacteristic
578#103C2×C4×C10711yescharacteristic
579#103C2×C4×C10711yescharacteristic
580#103C2×C4×C10711yescharacteristic
581#102C2×C4×C10711yescharacteristic
582#102C2×C4×C10711yescharacteristic
583#102C2×C4×C10711yescharacteristic
584#102C2×C4×C10711yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C10711yescharacteristic
594C22⋊C8C2×C4×C10711yescharacteristic
595C22⋊C8C2×C4×C10711yescharacteristic
596C22⋊C8C2×C4×C10711yescharacteristic
597C22⋊C8D4×C10711yescharacteristic
598C22⋊C8D4×C10711yescharacteristic
599C22⋊C8D4×C10711yescharacteristic
600C22⋊C8D4×C10711yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C10711yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C10712yes—
626#41#41×C10712yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C10711yescharacteristic
631C2×Q8C22×C4×C10711yescharacteristic
632C2×Q8C22×C4×C10711yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C10711yescharacteristic
646C2×D4C22×C4×C10711yescharacteristic
647C2×D4C22×C4×C10711yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C10711yescharacteristic
663C22×C4C22×C4×C10711yescharacteristic
664C22×C4C2×D4×C10711yescharacteristic
665C22×C4C2×D4×C10711yescharacteristic
666C22×C4#41×C10711yescharacteristic
667C22×C4C24×C10711yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C10712yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C10711yescharacteristic
705C2×C8C22×C4×C10711yescharacteristic
706C2×C8C22×C4×C10711yescharacteristic
707C2×C8C22×C4×C10711yescharacteristic
708C2×C8C2×D4×C10711yescharacteristic
709C2×C8C2×D4×C10711yescharacteristic
710C2×C8C2×D4×C10711yescharacteristic
711C2×C8C2×D4×C10711yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C10711yescharacteristic
716C4⋊C4C22×C4×C10711yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C10712yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C10711yescharacteristic
739C23C4×D4×C10711yescharacteristic
740C23C2×#41×C10711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C10712yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C10712yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C10711yescharacteristic
796C2×C4C4×D4×C10711yescharacteristic
797C2×C4C23×C4×C10711yescharacteristic
798C2×C4C22×D4×C10711yescharacteristic
799C2×C4C22×D4×C10711yescharacteristic
800C2×C4C2×#41×C10711yescharacteristic
801C2×C4H(5,𝔽2)×C10711yescharacteristic
802C2×C4H(5,𝔽2)×C10711yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C10711yescharacteristic
836C22#546×C10711yescharacteristic
837C22#551×C10711yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C10711yescharacteristic
848C4#518×C10711yescharacteristic
849C4D42×C10711yescharacteristic
850C4#546×C10711yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C107×#235811yescharacteristic
859C2C107×#295511yescharacteristic
860C2C107×#295711yescharacteristic
subgroupG/H
centerC2×C4×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
socleC22×C107C2×C4×D4
prime radicalC107×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C22⋊C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#443×C107C2semidirect
3. C107×#2933C2semidirect
4. C2×#421×C107C2semidirect
5. C107×#2880C2semidirect
6. C107×#1975C2semidirect
7. C107×#1937C2semidirect
8. C107×#1929C2semidirect
9. C107×#1897C2semidirect
10. C107×#1876C2semidirect
11. C107×#1876C2semidirect
12. C107×#1866C2semidirect
13. C107×#1855C2semidirect
14. C107×#1765C2semidirect
15. C107×#1750C2semidirect
21. C2×#131×C107C22semidirect
25. #452×C107C4semidirect
26. #452×C107C4semidirect
27. #451×C107C4semidirect
28. #450×C107C4semidirect
29. #449×C107C4semidirect
30. #449×C107C4semidirect
31. #448×C107C4semidirect
32. #447×C107C4semidirect
38. C2×#108×C107C22semidirect
39. C2×#108×C107C22semidirect
40. #424×C107C22semidirect
46. C2×#104×C107C22semidirect
47. C2×#104×C107C22semidirect
54. #408×C107C22semidirect
60. #405×C107C22semidirect
61. C2×#97×C107C22semidirect
62. C2×C4×C8×C107C22semidirect
63. #341×C107C22semidirect
64. #341×C107C22semidirect
65. #339×C107C22semidirect
66. #339×C107C22semidirect
67. #336×C107C22semidirect
68. #336×C107C22semidirect
145. #104×C107D4semidirect
420. #22889C107direct (N × H)
432. C2×#443C2×C107semidirect
433. #2933C2×C107semidirect
434. C2×#421C2×C107semidirect
435. #2880C2×C107semidirect
436. #1975C2×C107semidirect
437. #1937C2×C107semidirect
438. #1929C2×C107semidirect
439. #1897C2×C107semidirect
440. #1876C2×C107semidirect
441. #1876C2×C107semidirect
442. #1866C2×C107semidirect
443. #1855C2×C107semidirect
444. #1765C2×C107semidirect
445. #1750C2×C107semidirect
446. C107#22889direct (N × H)
452. C2×#131C22×C107semidirect
456. #452C4×C107semidirect
457. #452C4×C107semidirect
458. #451C4×C107semidirect
459. #450C4×C107semidirect
460. #449C4×C107semidirect
461. #449C4×C107semidirect
462. #448C4×C107semidirect
463. #447C4×C107semidirect
469. C2×#108C22×C107semidirect
470. C2×#108C22×C107semidirect
471. #424C22×C107semidirect
477. C2×#104C22×C107semidirect
478. C2×#104C22×C107semidirect
485. #408C22×C107semidirect
491. #405C22×C107semidirect
492. C2×#97C22×C107semidirect
493. C2×C4×C8C22×C107semidirect
494. #341C22×C107semidirect
495. #341C22×C107semidirect
496. #339C22×C107semidirect
497. #339C22×C107semidirect
498. #336C22×C107semidirect
499. #336C22×C107semidirect
576. #104D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30022
C2×#443×C1072
C107×#29332
C2×#421×C1072
C107×#28802
C107×#19752
C107×#19372
C107×#19292
C107×#18972
C107×#18762
C107×#18662
C107×#18552
C107×#17652
C107×#17502
#22889107