Finite Group Databasebeta

← C107×#22062 #41048026

Subgroups — C107×#22062 #41048026

Order 27392.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3002C211yesmaximal, characteristic
2C107×#2930C211yesmaximal, characteristic, complemented
3C107×#2879C211yesmaximal, characteristic, complemented
4C107×#1975C211yesmaximal, characteristic, complemented
5C107×#1974C211yesmaximal, characteristic, complemented
6C107×#1938C211yesmaximal, characteristic, complemented
7C107×#1937C211yesmaximal, characteristic, complemented
8C107×#1929C211yesmaximal, characteristic, complemented
9C107×#1929C211yesmaximal, characteristic, complemented
10C107×#1876C211yesmaximal, characteristic, complemented
11C107×#1876C211yesmaximal, characteristic, complemented
12C107×#1871C211yesmaximal, characteristic, complemented
13C107×#1855C211yesmaximal, characteristic, complemented
14C107×#1789C211yesmaximal, characteristic, complemented
15C107×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C2×#135×C107C2211yescharacteristic
18C2×#135×C107C2211yescharacteristic
19C2×#131×C107C2211yescharacteristic, complemented
20C22×M16×C107C2211yescharacteristic
21C22×M16×C107C2211yescharacteristic
22#525×C107C2211yescharacteristic
23#452×C107C411yescharacteristic, complemented
24#452×C107C411yescharacteristic, complemented
25#451×C107C411yescharacteristic, complemented
26#450×C107C411yescharacteristic, complemented
27#449×C107C411yescharacteristic, complemented
28#449×C107C411yescharacteristic, complemented
29#448×C107C411yescharacteristic, complemented
30#447×C107C411yescharacteristic, complemented
31#436×C107—21no—
32#436×C107—21no—
33#435×C107—21no—
34#435×C107—21no—
35C2×#108×C107C2211yescharacteristic, complemented
36C2×#108×C107C2211yescharacteristic, complemented
37#424×C107C2211yescharacteristic, complemented
38C2×#104×C107C2211yescharacteristic
39C2×#104×C107C2211yescharacteristic
40C2×#104×C107C2211yescharacteristic
41C2×#104×C107C2211yescharacteristic
42C2×#104×C107C2211yescharacteristic, complemented
43C2×#104×C107C2211yescharacteristic, complemented
44#416×C107C2211yescharacteristic
45#416×C107C2211yescharacteristic
46#408×C107—21no—
47#408×C107—21no—
48#408×C107C2211yescharacteristic
49#408×C107C2211yescharacteristic
50#408×C107C2211yescharacteristic
51#408×C107C2211yescharacteristic
52#408×C107C2211yescharacteristic, complemented
53#407×C107—21no—
54#407×C107—21no—
55#407×C107C2211yescharacteristic
56C2×C22⋊C8×C107C2211yescharacteristic
57#405×C107C2211yescharacteristic, complemented
58C2×#97×C107C2211yescharacteristic, complemented
59C2×C4×C8×C107C2211yescharacteristic, complemented
60C4×C22⋊C4×C107C2211yescharacteristic
61#341×C107C2211yescharacteristic, complemented
62#341×C107C2211yescharacteristic, complemented
63#339×C107C2211yescharacteristic, complemented
64#339×C107C2211yescharacteristic, complemented
65#336×C107C2211yescharacteristic, complemented
66#336×C107C2211yescharacteristic, complemented
67C2×#41×C107—21no—
68C2×#41×C107—21no—
69C2×#41×C107—41no—
70C2×#41×C107—41no—
71C2×#41×C107—41no—
72C2×#41×C107—41no—
73C2×#41×C107C2×C411yescharacteristic
74C2×#41×C107C2×C411yescharacteristic
75C2×#41×C107C2311yescharacteristic
76C2×#41×C107C2311yescharacteristic
77C2×#41×C107C2311yescharacteristic
78C22×Q8×C107C2×C411yescharacteristic
79C22×D4×C107—21no—
80C22×D4×C107C2×C411yescharacteristic
81C23×C4×C107—21no—
82C23×C4×C107C2311yescharacteristic
83#135×C107—41no—
84#135×C107—41no—
85#135×C107—41no—
86#135×C107—41no—
87C2×Q16×C107C2×C411yescharacteristic
88C2×Q16×C107C2×C411yescharacteristic
89C2×SD16×C107C2×C411yescharacteristic
90C2×SD16×C107C2×C411yescharacteristic
91C2×SD16×C107C2×C411yescharacteristic
92C2×SD16×C107C2×C411yescharacteristic
93C2×D8×C107C2×C411yescharacteristic
94C2×D8×C107C2×C411yescharacteristic
95#131×C107—41no—
96#131×C107—41no—
97C2×M16×C107—21no—
98C2×M16×C107—21no—
99C2×M16×C107—41no—
100C2×M16×C107—41no—
101C2×M16×C107—41no—
102C2×M16×C107—41no—
103C2×M16×C107D411yescharacteristic
104C2×M16×C107D411yescharacteristic
105C2×M16×C107D411yescharacteristic
106C2×M16×C107D411yescharacteristic
107C2×M16×C107C2311yescharacteristic
108C2×M16×C107C2311yescharacteristic
109C2×M16×C107C2311yescharacteristic
110C2×M16×C107C2311yescharacteristic
111C22×C8×C107—21no—
112C22×C8×C107—21no—
113C22×C8×C107C2311yescharacteristic
114C22×C8×C107C2311yescharacteristic
115C22×C8×C107C2311yescharacteristic
116C22×C8×C107C2311yescharacteristic
117#123×C107—21no—
118C22⋊Q8×C107C2×C411yescharacteristic
119C22⋊Q8×C107C2×C411yescharacteristic
120#121×C107C2×C411yescharacteristic
121#121×C107C2×C411yescharacteristic
122#120×C107—21no—
123C4×D4×C107—21no—
124C4×D4×C107—21no—
125#117×C107C2311yescharacteristic
126C2×C22⋊C4×C107—21no—
127C2×C42×C107C2311yescharacteristic
128C2×C42×C107C2311yescharacteristic
129#108×C107—41no—
130#108×C107—41no—
131C4⋊C8×C107—21no—
132C4⋊C8×C107—21no—
133#104×C107—41no—
134#104×C107—41no—
135#104×C107—41no—
136#104×C107—41no—
137#104×C107—41no—
138#104×C107—41no—
139#103×C107C2×C411yescharacteristic
140#103×C107C2×C411yescharacteristic
141#103×C107C2×C411yescharacteristic
142#103×C107C2×C411yescharacteristic
143#102×C107C2×C411yescharacteristic
144#102×C107C2×C411yescharacteristic
145#102×C107C2×C411yescharacteristic
146#102×C107C2×C411yescharacteristic
147C22⋊C8×C107—21no—
148C22⋊C8×C107—21no—
149C22⋊C8×C107—21no—
150C22⋊C8×C107—21no—
151C22⋊C8×C107—21no—
152C22⋊C8×C107—21no—
153C22⋊C8×C107—21no—
154C22⋊C8×C107—21no—
155C22⋊C8×C107—21no—
156C22⋊C8×C107—21no—
157C22⋊C8×C107—21no—
158C22⋊C8×C107—21no—
159C22⋊C8×C107C2×C411yescharacteristic
160C22⋊C8×C107C2×C411yescharacteristic
161C22⋊C8×C107C2×C411yescharacteristic
162C22⋊C8×C107C2×C411yescharacteristic
163#97×C107—21no—
164#97×C107—41no—
165C4×C8×C107—21no—
166C4×C8×C107—41no—
167#95×C107—21no—
168C24×C107—21no—
169C24×C107#4111yescharacteristic
170#41×C107—21no—
171#41×C107—21no—
172#41×C107—21no—
173#41×C107—21no—
174#41×C107—21no—
175#41×C107—21no—
176#41×C107—21no—
177#41×C107—21no—
178#41×C107—21no—
179#41×C107—21no—
180#41×C107—21no—
181#41×C107—21no—
182#41×C107—41no—
183#41×C107—41no—
184#41×C107—41no—
185#41×C107—41no—
186#41×C107—42no—
187#41×C107—42no—
188#41×C107—42no—
189#41×C107—42no—
190C2×Q8×C107—21no—
191C2×Q8×C107—41no—
192C2×Q8×C107—41no—
193C2×Q8×C107C22×C411yescharacteristic
194C2×Q8×C107C22×C411yescharacteristic
195C2×Q8×C107C22×C411yescharacteristic
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—21no—
204C2×D4×C107—41no—
205C2×D4×C107—41no—
206C2×D4×C107—42no—
207C2×D4×C107—42no—
208C2×D4×C107C22×C411yescharacteristic
209C2×D4×C107C22×C411yescharacteristic
210C2×D4×C107C22×C411yescharacteristic
211C22×C4×C107—21no—
212C22×C4×C107—21no—
213C22×C4×C107—21no—
214C22×C4×C107—21no—
215C22×C4×C107—21no—
216C22×C4×C107—21no—
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—42no—
224C22×C4×C107—42no—
225C22×C4×C107C22×C411yescharacteristic
226C22×C4×C107C22×C411yescharacteristic
227C22×C4×C107C2×D411yescharacteristic
228C22×C4×C107C2×D411yescharacteristic
229C22×C4×C107#4111yescharacteristic
230C22×C4×C107C2411yescharacteristic
231Q16×C107—41no—
232Q16×C107—41no—
233SD16×C107—41no—
234SD16×C107—41no—
235SD16×C107—41no—
236SD16×C107—41no—
237D8×C107—41no—
238D8×C107—41no—
239M16×C107—21no—
240M16×C107—21no—
241M16×C107—21no—
242M16×C107—21no—
243M16×C107—21no—
244M16×C107—21no—
245M16×C107—21no—
246M16×C107—21no—
247M16×C107—41no—
248M16×C107—41no—
249M16×C107—41no—
250M16×C107—41no—
251M16×C107—42no—
252M16×C107—42no—
253C2×C8×C107—21no—
254C2×C8×C107—21no—
255C2×C8×C107—21no—
256C2×C8×C107—21no—
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—42no—
266C2×C8×C107—42no—
267C2×C8×C107C22×C411yescharacteristic
268C2×C8×C107C22×C411yescharacteristic
269C2×C8×C107C22×C411yescharacteristic
270C2×C8×C107C22×C411yescharacteristic
271C2×C8×C107C2×D411yescharacteristic
272C2×C8×C107C2×D411yescharacteristic
273C2×C8×C107C2×D411yescharacteristic
274C2×C8×C107C2×D411yescharacteristic
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107C22×C411yescharacteristic
278C4⋊C4×C107C22×C411yescharacteristic
279C22⋊C4×C107—21no—
280C22⋊C4×C107—21no—
281C22⋊C4×C107—21no—
282C22⋊C4×C107—21no—
283C22⋊C4×C107—21no—
284C22⋊C4×C107—42no—
285C42×C107—21no—
286C42×C107—21no—
287C42×C107—21no—
288C42×C107—21no—
289C42×C107—21no—
290C23×C107—21no—
291C23×C107—21no—
292C23×C107—21no—
293C23×C107—21no—
294C23×C107—21no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—42no—
298C23×C107—81no—
299C23×C107—81no—
300C23×C107C4×D411yescharacteristic
301C23×C107C4×D411yescharacteristic
302C23×C107C2×#4111yescharacteristic
303Q8×C107—21no—
304Q8×C107—21no—
305Q8×C107—21no—
306Q8×C107—21no—
307Q8×C107—21no—
308Q8×C107—21no—
309Q8×C107—42no—
310D4×C107—21no—
311D4×C107—21no—
312D4×C107—21no—
313D4×C107—21no—
314D4×C107—21no—
315D4×C107—21no—
316D4×C107—42no—
317D4×C107—42no—
318D4×C107—42no—
319D4×C107—41no—
320D4×C107—41no—
321D4×C107—41no—
322D4×C107—41no—
323D4×C107—41no—
324D4×C107—41no—
325D4×C107—81no—
326D4×C107—81no—
327C2×C4×C107—21no—
328C2×C4×C107—21no—
329C2×C4×C107—21no—
330C2×C4×C107—21no—
331C2×C4×C107—21no—
332C2×C4×C107—21no—
333C2×C4×C107—21no—
334C2×C4×C107—21no—
335C2×C4×C107—21no—
336C2×C4×C107—21no—
337C2×C4×C107—22no—
338C2×C4×C107—21no—
339C2×C4×C107—21no—
340C2×C4×C107—21no—
341C2×C4×C107—21no—
342C2×C4×C107—21no—
343C2×C4×C107—42no—
344C2×C4×C107—42no—
345C2×C4×C107—41no—
346C2×C4×C107—42no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—41no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—41no—
354C2×C4×C107—41no—
355C2×C4×C107—41no—
356C2×C4×C107—41no—
357C2×C4×C107C4×D411yescharacteristic
358C2×C4×C107C4×D411yescharacteristic
359C2×C4×C107C23×C411yescharacteristic
360C2×C4×C107C22×D411yescharacteristic
361C2×C4×C107H(5,𝔽2)11yescharacteristic
362C2×C4×C107H(5,𝔽2)11yescharacteristic
363C2×C4×C107H(5,𝔽2)11yescharacteristic
364C2×C4×C107H(5,𝔽2)11yescharacteristic
365C8×C107—21no—
366C8×C107—21no—
367C8×C107—21no—
368C8×C107—21no—
369C8×C107—21no—
370C8×C107—21no—
371C8×C107—21no—
372C8×C107—21no—
373C8×C107—41no—
374C8×C107—41no—
375C8×C107—41no—
376C8×C107—41no—
377C22×C107—21no—
378C22×C107—21no—
379C22×C107—21no—
380C22×C107—21no—
381C22×C107—21no—
382C22×C107—21no—
383C22×C107—21no—
384C22×C107—21no—
385C22×C107—41no—
386C22×C107—41no—
387C22×C107—41no—
388C22×C107—41no—
389C22×C107—41no—
390C22×C107—41no—
391C22×C107—41no—
392C22×C107—41no—
393C22×C107—41no—
394C22×C107—81no—
395C22×C107—81no—
396C22×C107—84no—
397C22×C107C2×C4×D411yescharacteristic
398C22×C107#53811yescharacteristic
399C22×C107#53811yescharacteristic
400C4×C107—21no—
401C4×C107—21no—
402C4×C107—42no—
403C4×C107—41no—
404C4×C107—41no—
405C4×C107—41no—
406C4×C107—41no—
407C4×C107—41no—
408C4×C107—81no—
409C4×C107#51811yescharacteristic
410C4×C107#51811yescharacteristic
411C4×C107#53411yescharacteristic
412C4×C107#53511yescharacteristic
413#22062C10711yesmaximal, characteristic, direct product factor, Sylow
414C2×C107—21no—
415C2×C107—21no—
416C2×C107—41no—
417C2×C107—41no—
418C2×C107—81no—
419C2×C107—81no—
420C2×C107—81no—
421C2×C107#232111yescharacteristic
422C2×C107#295611yescharacteristic
423C2×C107#295711yescharacteristic
424#3002C2×C10711yescharacteristic
425#2930C2×C10711yescharacteristic, complemented
426#2879C2×C10711yescharacteristic, complemented
427#1975C2×C10711yescharacteristic, complemented
428#1974C2×C10711yescharacteristic, complemented
429#1938C2×C10711yescharacteristic, complemented
430#1937C2×C10711yescharacteristic, complemented
431#1929C2×C10711yescharacteristic, complemented
432#1929C2×C10711yescharacteristic, complemented
433#1876C2×C10711yescharacteristic, complemented
434#1876C2×C10711yescharacteristic, complemented
435#1871C2×C10711yescharacteristic, complemented
436#1855C2×C10711yescharacteristic, complemented
437#1789C2×C10711yescharacteristic, complemented
438#1753C2×C10711yescharacteristic, complemented
439C107#2206211yescharacteristic, direct product factor, Sylow
440C22×#41C22×C10711yescharacteristic
441C2×#135C22×C10711yescharacteristic
442C2×#135C22×C10711yescharacteristic
443C2×#131C22×C10711yescharacteristic, complemented
444C22×M16C22×C10711yescharacteristic
445C22×M16C22×C10711yescharacteristic
446#525C22×C10711yescharacteristic
447#452C4×C10711yescharacteristic, complemented
448#452C4×C10711yescharacteristic, complemented
449#451C4×C10711yescharacteristic, complemented
450#450C4×C10711yescharacteristic, complemented
451#449C4×C10711yescharacteristic, complemented
452#449C4×C10711yescharacteristic, complemented
453#448C4×C10711yescharacteristic, complemented
454#447C4×C10711yescharacteristic, complemented
455#436—21no—
456#436—21no—
457#435—21no—
458#435—21no—
459C2×#108C22×C10711yescharacteristic, complemented
460C2×#108C22×C10711yescharacteristic, complemented
461#424C22×C10711yescharacteristic, complemented
462C2×#104C22×C10711yescharacteristic
463C2×#104C22×C10711yescharacteristic
464C2×#104C22×C10711yescharacteristic
465C2×#104C22×C10711yescharacteristic
466C2×#104C22×C10711yescharacteristic, complemented
467C2×#104C22×C10711yescharacteristic, complemented
468#416C22×C10711yescharacteristic
469#416C22×C10711yescharacteristic
470#408—21no—
471#408—21no—
472#408C22×C10711yescharacteristic
473#408C22×C10711yescharacteristic
474#408C22×C10711yescharacteristic
475#408C22×C10711yescharacteristic
476#408C22×C10711yescharacteristic, complemented
477#407—21no—
478#407—21no—
479#407C22×C10711yescharacteristic
480C2×C22⋊C8C22×C10711yescharacteristic
481#405C22×C10711yescharacteristic, complemented
482C2×#97C22×C10711yescharacteristic, complemented
483C2×C4×C8C22×C10711yescharacteristic, complemented
484C4×C22⋊C4C22×C10711yescharacteristic
485#341C22×C10711yescharacteristic, complemented
486#341C22×C10711yescharacteristic, complemented
487#339C22×C10711yescharacteristic, complemented
488#339C22×C10711yescharacteristic, complemented
489#336C22×C10711yescharacteristic, complemented
490#336C22×C10711yescharacteristic, complemented
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C10711yescharacteristic
498C2×#41C2×C4×C10711yescharacteristic
499C2×#41C23×C10711yescharacteristic
500C2×#41C23×C10711yescharacteristic
501C2×#41C23×C10711yescharacteristic
502C22×Q8C2×C4×C10711yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C10711yescharacteristic
505C23×C4—21no—
506C23×C4C23×C10711yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C10711yescharacteristic
512C2×Q16C2×C4×C10711yescharacteristic
513C2×SD16C2×C4×C10711yescharacteristic
514C2×SD16C2×C4×C10711yescharacteristic
515C2×SD16C2×C4×C10711yescharacteristic
516C2×SD16C2×C4×C10711yescharacteristic
517C2×D8C2×C4×C10711yescharacteristic
518C2×D8C2×C4×C10711yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C10711yescharacteristic
528C2×M16D4×C10711yescharacteristic
529C2×M16D4×C10711yescharacteristic
530C2×M16D4×C10711yescharacteristic
531C2×M16C23×C10711yescharacteristic
532C2×M16C23×C10711yescharacteristic
533C2×M16C23×C10711yescharacteristic
534C2×M16C23×C10711yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C10711yescharacteristic
538C22×C8C23×C10711yescharacteristic
539C22×C8C23×C10711yescharacteristic
540C22×C8C23×C10711yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C10711yescharacteristic
543C22⋊Q8C2×C4×C10711yescharacteristic
544#121C2×C4×C10711yescharacteristic
545#121C2×C4×C10711yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C10711yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C10711yescharacteristic
552C2×C42C23×C10711yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C10711yescharacteristic
564#103C2×C4×C10711yescharacteristic
565#103C2×C4×C10711yescharacteristic
566#103C2×C4×C10711yescharacteristic
567#102C2×C4×C10711yescharacteristic
568#102C2×C4×C10711yescharacteristic
569#102C2×C4×C10711yescharacteristic
570#102C2×C4×C10711yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C10711yescharacteristic
584C22⋊C8C2×C4×C10711yescharacteristic
585C22⋊C8C2×C4×C10711yescharacteristic
586C22⋊C8C2×C4×C10711yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C10711yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C10711yescharacteristic
618C2×Q8C22×C4×C10711yescharacteristic
619C2×Q8C22×C4×C10711yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C10711yescharacteristic
633C2×D4C22×C4×C10711yescharacteristic
634C2×D4C22×C4×C10711yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C10711yescharacteristic
650C22×C4C22×C4×C10711yescharacteristic
651C22×C4C2×D4×C10711yescharacteristic
652C22×C4C2×D4×C10711yescharacteristic
653C22×C4#41×C10711yescharacteristic
654C22×C4C24×C10711yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C10711yescharacteristic
692C2×C8C22×C4×C10711yescharacteristic
693C2×C8C22×C4×C10711yescharacteristic
694C2×C8C22×C4×C10711yescharacteristic
695C2×C8C2×D4×C10711yescharacteristic
696C2×C8C2×D4×C10711yescharacteristic
697C2×C8C2×D4×C10711yescharacteristic
698C2×C8C2×D4×C10711yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C10711yescharacteristic
702C4⋊C4C22×C4×C10711yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C10711yescharacteristic
725C23C4×D4×C10711yescharacteristic
726C23C2×#41×C10711yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C10711yescharacteristic
782C2×C4C4×D4×C10711yescharacteristic
783C2×C4C23×C4×C10711yescharacteristic
784C2×C4C22×D4×C10711yescharacteristic
785C2×C4H(5,𝔽2)×C10711yescharacteristic
786C2×C4H(5,𝔽2)×C10711yescharacteristic
787C2×C4H(5,𝔽2)×C10711yescharacteristic
788C2×C4H(5,𝔽2)×C10711yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C10711yescharacteristic
822C22#538×C10711yescharacteristic
823C22#538×C10711yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4#518×C10711yescharacteristic
834C4#518×C10711yescharacteristic
835C4#534×C10711yescharacteristic
836C4#535×C10711yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C107×#232111yescharacteristic
845C2C107×#295611yescharacteristic
846C2C107×#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 ◁ C22×M16×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2930C2semidirect
3. C107×#2879C2semidirect
4. C107×#1975C2semidirect
5. C107×#1974C2semidirect
6. C107×#1938C2semidirect
7. C107×#1937C2semidirect
8. C107×#1929C2semidirect
9. C107×#1929C2semidirect
10. C107×#1876C2semidirect
11. C107×#1876C2semidirect
12. C107×#1871C2semidirect
13. C107×#1855C2semidirect
14. C107×#1789C2semidirect
15. C107×#1753C2semidirect
19. C2×#131×C107C22semidirect
23. #452×C107C4semidirect
24. #452×C107C4semidirect
25. #451×C107C4semidirect
26. #450×C107C4semidirect
27. #449×C107C4semidirect
28. #449×C107C4semidirect
29. #448×C107C4semidirect
30. #447×C107C4semidirect
35. C2×#108×C107C22semidirect
36. C2×#108×C107C22semidirect
37. #424×C107C22semidirect
42. C2×#104×C107C22semidirect
43. C2×#104×C107C22semidirect
52. #408×C107C22semidirect
57. #405×C107C22semidirect
58. C2×#97×C107C22semidirect
59. C2×C4×C8×C107C22semidirect
61. #341×C107C22semidirect
62. #341×C107C22semidirect
63. #339×C107C22semidirect
64. #339×C107C22semidirect
65. #336×C107C22semidirect
66. #336×C107C22semidirect
413. #22062C107direct (N × H)
425. #2930C2×C107semidirect
426. #2879C2×C107semidirect
427. #1975C2×C107semidirect
428. #1974C2×C107semidirect
429. #1938C2×C107semidirect
430. #1937C2×C107semidirect
431. #1929C2×C107semidirect
432. #1929C2×C107semidirect
433. #1876C2×C107semidirect
434. #1876C2×C107semidirect
435. #1871C2×C107semidirect
436. #1855C2×C107semidirect
437. #1789C2×C107semidirect
438. #1753C2×C107semidirect
439. C107#22062direct (N × H)
443. C2×#131C22×C107semidirect
447. #452C4×C107semidirect
448. #452C4×C107semidirect
449. #451C4×C107semidirect
450. #450C4×C107semidirect
451. #449C4×C107semidirect
452. #449C4×C107semidirect
453. #448C4×C107semidirect
454. #447C4×C107semidirect
459. C2×#108C22×C107semidirect
460. C2×#108C22×C107semidirect
461. #424C22×C107semidirect
466. C2×#104C22×C107semidirect
467. C2×#104C22×C107semidirect
476. #408C22×C107semidirect
481. #405C22×C107semidirect
482. C2×#97C22×C107semidirect
483. C2×C4×C8C22×C107semidirect
485. #341C22×C107semidirect
486. #341C22×C107semidirect
487. #339C22×C107semidirect
488. #339C22×C107semidirect
489. #336C22×C107semidirect
490. #336C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30022
C107×#29302
C107×#28792
C107×#19752
C107×#19742
C107×#19382
C107×#19372
C107×#19292
C107×#18762
C107×#18712
C107×#18552
C107×#17892
C107×#17532
#22062107