Finite Group Databasebeta

← C107×#22588 #41048552

Subgroups — C107×#22588 #41048552

Order 27392.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2924C211yesmaximal, characteristic, complemented
2C107×#2896C211yesmaximal, characteristic
3C107×#2880C211yesmaximal, characteristic
4C107×#1938C211yesmaximal, characteristic, complemented
5C107×#1937C211yesmaximal, characteristic, complemented
6C107×#1929C211yesmaximal, characteristic, complemented
7C107×#1929C211yesmaximal, characteristic, complemented
8C107×#1866C211yesmaximal, characteristic, complemented
9C107×#1866C211yesmaximal, characteristic, complemented
10C107×#1826C211yesmaximal, characteristic, complemented
11C107×#1811C211yesmaximal, characteristic, complemented
12C107×#1789C211yesmaximal, characteristic
13C107×#1765C211yesmaximal, characteristic, complemented
14C107×#1764C211yesmaximal, characteristic, complemented
15C107×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C2×#131×C107C2211yescharacteristic
18C2×#131×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic
20C2×#117×C107C2211yescharacteristic
21#433×C107—21no—
22#433×C107—21no—
23#432×C107—21no—
24#431×C107—21no—
25C2×#108×C107C2211yescharacteristic, complemented
26C2×#108×C107C2211yescharacteristic, complemented
27#424×C107C2211yescharacteristic, complemented
28#424×C107C2211yescharacteristic, complemented
29C2×#104×C107C2211yescharacteristic
30C2×#104×C107C2211yescharacteristic
31C2×#104×C107C2211yescharacteristic
32C2×#104×C107C2211yescharacteristic
33#419×C107C411yescharacteristic, complemented
34#419×C107C411yescharacteristic, complemented
35#418×C107C411yescharacteristic, complemented
36#418×C107C411yescharacteristic, complemented
37#417×C107C411yescharacteristic, complemented
38#417×C107C411yescharacteristic, complemented
39#417×C107C411yescharacteristic, complemented
40#417×C107C411yescharacteristic, complemented
41#416×C107C2211yescharacteristic
42#416×C107C2211yescharacteristic
43#416×C107C2211yescharacteristic
44#416×C107C2211yescharacteristic
45#408×C107—21no—
46#408×C107—21no—
47#408×C107C2211yescharacteristic
48#408×C107C2211yescharacteristic
49#407×C107—21no—
50#407×C107C2211yescharacteristic
51#407×C107C2211yescharacteristic
52C2×C22⋊C8×C107—21no—
53C2×C22⋊C8×C107C2211yescharacteristic
54#405×C107C2211yescharacteristic, complemented
55#405×C107C2211yescharacteristic, complemented
56C2×#97×C107C2211yescharacteristic, complemented
57C2×C4×C8×C107C2211yescharacteristic, complemented
58C4×C22⋊C4×C107C2211yescharacteristic
59#341×C107C2211yescharacteristic, complemented
60#341×C107C2211yescharacteristic, complemented
61#339×C107C2211yescharacteristic, complemented
62#339×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—22no—
70C2×#41×C107—22no—
71C2×#41×C107—41no—
72C2×#41×C107—41no—
73C2×#41×C107C2×C411yescharacteristic
74C2×#41×C107C2×C411yescharacteristic
75C2×#41×C107C2311yescharacteristic
76C2×#41×C107C2311yescharacteristic
77C22×Q8×C107C2×C411yescharacteristic
78C22×D4×C107—21no—
79C22×D4×C107C2×C411yescharacteristic
80C23×C4×C107—21no—
81C23×C4×C107C2311yescharacteristic
82#131×C107—22no—
83#131×C107—22no—
84#131×C107—41no—
85#131×C107—41no—
86C2×M16×C107—21no—
87C2×M16×C107—21no—
88C2×M16×C107—41no—
89C2×M16×C107—41no—
90C2×M16×C107C2×C411yescharacteristic
91C2×M16×C107C2×C411yescharacteristic
92C2×M16×C107C2×C411yescharacteristic
93C2×M16×C107C2×C411yescharacteristic
94C2×M16×C107C2311yescharacteristic
95C2×M16×C107C2311yescharacteristic
96C2×M16×C107C2311yescharacteristic
97C2×M16×C107C2311yescharacteristic
98C22×C8×C107—21no—
99C22×C8×C107—21no—
100C22×C8×C107C2311yescharacteristic
101C22×C8×C107C2311yescharacteristic
102C22×C8×C107C2311yescharacteristic
103C22×C8×C107C2311yescharacteristic
104#117×C107—21no—
105#117×C107—21no—
106#117×C107C2×C411yescharacteristic
107#117×C107C2×C411yescharacteristic
108#117×C107C2311yescharacteristic
109#117×C107C2311yescharacteristic
110C2×C4⋊C4×C107C2×C411yescharacteristic
111C2×C4⋊C4×C107C2×C411yescharacteristic
112C2×C22⋊C4×C107—21no—
113C2×C22⋊C4×C107—21no—
114C2×C42×C107—21no—
115C2×C42×C107C2311yescharacteristic
116C2×C42×C107C2311yescharacteristic
117#108×C107—41no—
118#108×C107—41no—
119C4⋊C8×C107—21no—
120C4⋊C8×C107—21no—
121C4⋊C8×C107—21no—
122C4⋊C8×C107—21no—
123#104×C107—22no—
124#104×C107—22no—
125#104×C107—41no—
126#104×C107—41no—
127#103×C107C2×C411yescharacteristic
128#103×C107C2×C411yescharacteristic
129#103×C107C2×C411yescharacteristic
130#103×C107C2×C411yescharacteristic
131#103×C107C2×C411yescharacteristic
132#103×C107C2×C411yescharacteristic
133#103×C107C2×C411yescharacteristic
134#103×C107C2×C411yescharacteristic
135#102×C107C2×C411yescharacteristic
136#102×C107C2×C411yescharacteristic
137#102×C107C2×C411yescharacteristic
138#102×C107C2×C411yescharacteristic
139#102×C107C2×C411yescharacteristic
140#102×C107C2×C411yescharacteristic
141#102×C107C2×C411yescharacteristic
142#102×C107C2×C411yescharacteristic
143C22⋊C8×C107—21no—
144C22⋊C8×C107—21no—
145C22⋊C8×C107—21no—
146C22⋊C8×C107—21no—
147C22⋊C8×C107—21no—
148C22⋊C8×C107—21no—
149C22⋊C8×C107—21no—
150C22⋊C8×C107—21no—
151C22⋊C8×C107D411yescharacteristic
152C22⋊C8×C107D411yescharacteristic
153C22⋊C8×C107D411yescharacteristic
154C22⋊C8×C107D411yescharacteristic
155#97×C107—21no—
156#97×C107—21no—
157#97×C107—41no—
158C4×C8×C107—21no—
159C4×C8×C107—21no—
160C4×C8×C107—41no—
161#95×C107—21no—
162C24×C107—21no—
163C24×C107#4111yescharacteristic
164#41×C107—21no—
165#41×C107—21no—
166#41×C107—22no—
167#41×C107—22no—
168#41×C107—21no—
169#41×C107—21no—
170#41×C107—21no—
171#41×C107—21no—
172#41×C107—42no—
173#41×C107—42no—
174#41×C107—41no—
175#41×C107—41no—
176#41×C107—42no—
177#41×C107—42no—
178#41×C107#4112yes—
179#41×C107#4112yes—
180C2×Q8×C107—21no—
181C2×Q8×C107—22no—
182C2×Q8×C107—41no—
183C2×Q8×C107C22×C411yescharacteristic
184C2×Q8×C107C22×C411yescharacteristic
185C2×D4×C107—21no—
186C2×D4×C107—22no—
187C2×D4×C107—21no—
188C2×D4×C107—21no—
189C2×D4×C107—21no—
190C2×D4×C107—21no—
191C2×D4×C107—41no—
192C2×D4×C107—42no—
193C2×D4×C107—42no—
194C2×D4×C107C22×C411yescharacteristic
195C2×D4×C107C22×C411yescharacteristic
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—21no—
206C22×C4×C107—21no—
207C22×C4×C107—21no—
208C22×C4×C107—21no—
209C22×C4×C107—42no—
210C22×C4×C107—42no—
211C22×C4×C107C22×C411yescharacteristic
212C22×C4×C107C22×C411yescharacteristic
213C22×C4×C107C2×D411yescharacteristic
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107#4111yescharacteristic
216C22×C4×C107C2411yescharacteristic
217M16×C107—21no—
218M16×C107—21no—
219M16×C107—21no—
220M16×C107—21no—
221M16×C107—21no—
222M16×C107—21no—
223M16×C107—21no—
224M16×C107—21no—
225M16×C107—41no—
226M16×C107—41no—
227M16×C107—41no—
228M16×C107—41no—
229M16×C107—42no—
230M16×C107—42no—
231C2×C8×C107—21no—
232C2×C8×C107—21no—
233C2×C8×C107—21no—
234C2×C8×C107—21no—
235C2×C8×C107—21no—
236C2×C8×C107—21no—
237C2×C8×C107—21no—
238C2×C8×C107—21no—
239C2×C8×C107—21no—
240C2×C8×C107—21no—
241C2×C8×C107—21no—
242C2×C8×C107—21no—
243C2×C8×C107—42no—
244C2×C8×C107—42no—
245C2×C8×C107C22×C411yescharacteristic
246C2×C8×C107C22×C411yescharacteristic
247C2×C8×C107C22×C411yescharacteristic
248C2×C8×C107C22×C411yescharacteristic
249C2×C8×C107C2×D411yescharacteristic
250C2×C8×C107C2×D411yescharacteristic
251C2×C8×C107C2×D411yescharacteristic
252C2×C8×C107C2×D411yescharacteristic
253C4⋊C4×C107—21no—
254C4⋊C4×C107—21no—
255C4⋊C4×C107C22×C411yescharacteristic
256C4⋊C4×C107C22×C411yescharacteristic
257C4⋊C4×C107C22×C411yescharacteristic
258C4⋊C4×C107C22×C411yescharacteristic
259C22⋊C4×C107—21no—
260C22⋊C4×C107—21no—
261C22⋊C4×C107—21no—
262C22⋊C4×C107—21no—
263C22⋊C4×C107—42no—
264C42×C107—21no—
265C42×C107—21no—
266C42×C107—21no—
267C42×C107—21no—
268C42×C107—21no—
269C42×C107—21no—
270C42×C107—21no—
271C42×C107—21no—
272C23×C107—21no—
273C23×C107—21no—
274C23×C107—21no—
275C23×C107—21no—
276C23×C107—41no—
277C23×C107—41no—
278C23×C107—42no—
279C23×C107—42no—
280C23×C107—81no—
281C23×C107C4×D411yescharacteristic
282C23×C107C4×D411yescharacteristic
283C23×C107C2×#4111yescharacteristic
284Q8×C107—21no—
285Q8×C107—21no—
286Q8×C107—21no—
287Q8×C107—42no—
288Q8×C107#11712yes—
289D4×C107—22no—
290D4×C107—22no—
291D4×C107—21no—
292D4×C107—21no—
293D4×C107—21no—
294D4×C107—42no—
295D4×C107—42no—
296D4×C107—42no—
297D4×C107—41no—
298D4×C107—41no—
299D4×C107#11712yes—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—22no—
308C2×C4×C107—22no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—21no—
313C2×C4×C107—22no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—21no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
319C2×C4×C107—42no—
320C2×C4×C107—42no—
321C2×C4×C107—42no—
322C2×C4×C107—41no—
323C2×C4×C107—42no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—81no—
331C2×C4×C107C4×D411yescharacteristic
332C2×C4×C107C4×D411yescharacteristic
333C2×C4×C107C23×C411yescharacteristic
334C2×C4×C107C22×D411yescharacteristic
335C2×C4×C107C2×#4111yescharacteristic
336C2×C4×C107C2×#4111yescharacteristic
337C2×C4×C107H(5,𝔽2)11yescharacteristic
338C2×C4×C107H(5,𝔽2)11yescharacteristic
339C8×C107—21no—
340C8×C107—21no—
341C8×C107—21no—
342C8×C107—21no—
343C8×C107—21no—
344C8×C107—21no—
345C8×C107—21no—
346C8×C107—21no—
347C8×C107—41no—
348C8×C107—41no—
349C8×C107—41no—
350C8×C107—41no—
351C22×C107—21no—
352C22×C107—21no—
353C22×C107—21no—
354C22×C107—21no—
355C22×C107—22no—
356C22×C107—21no—
357C22×C107—21no—
358C22×C107—21no—
359C22×C107—21no—
360C22×C107—41no—
361C22×C107—41no—
362C22×C107—41no—
363C22×C107—41no—
364C22×C107—41no—
365C22×C107—81no—
366C22×C107—81no—
367C22×C107—84no—
368C22×C107C2×C4×D411yescharacteristic
369C22×C107#55111yescharacteristic
370C22×C107#55111yescharacteristic
371C4×C107—21no—
372C4×C107—21no—
373C4×C107—22no—
374C4×C107—42no—
375C4×C107—41no—
376C4×C107—41no—
377C4×C107—41no—
378C4×C107—41no—
379C4×C107—41no—
380C4×C107—81no—
381C4×C107C2×#11711yescharacteristic
382C4×C107#51811yescharacteristic
383C4×C107#54611yescharacteristic
384C4×C107#54611yescharacteristic
385#22588C10711yesmaximal, characteristic, direct product factor, Sylow
386C2×C107—21no—
387C2×C107—21no—
388C2×C107—41no—
389C2×C107—41no—
390C2×C107—42no—
391C2×C107—81no—
392C2×C107#234211yescharacteristic
393C2×C107#295511yescharacteristic
394C2×C107#295611yescharacteristic
395#2924C2×C10711yescharacteristic, complemented
396#2896C2×C10711yescharacteristic
397#2880C2×C10711yescharacteristic
398#1938C2×C10711yescharacteristic, complemented
399#1937C2×C10711yescharacteristic, complemented
400#1929C2×C10711yescharacteristic, complemented
401#1929C2×C10711yescharacteristic, complemented
402#1866C2×C10711yescharacteristic, complemented
403#1866C2×C10711yescharacteristic, complemented
404#1826C2×C10711yescharacteristic, complemented
405#1811C2×C10711yescharacteristic, complemented
406#1789C2×C10711yescharacteristic
407#1765C2×C10711yescharacteristic, complemented
408#1764C2×C10711yescharacteristic, complemented
409#1753C2×C10711yescharacteristic, complemented
410C107#2258811yescharacteristic, direct product factor, Sylow
411C22×#41C22×C10711yescharacteristic
412C2×#131C22×C10711yescharacteristic
413C2×#131C22×C10711yescharacteristic
414C22×M16C22×C10711yescharacteristic
415C2×#117C22×C10711yescharacteristic
416#433—21no—
417#433—21no—
418#432—21no—
419#431—21no—
420C2×#108C22×C10711yescharacteristic, complemented
421C2×#108C22×C10711yescharacteristic, complemented
422#424C22×C10711yescharacteristic, complemented
423#424C22×C10711yescharacteristic, complemented
424C2×#104C22×C10711yescharacteristic
425C2×#104C22×C10711yescharacteristic
426C2×#104C22×C10711yescharacteristic
427C2×#104C22×C10711yescharacteristic
428#419C4×C10711yescharacteristic, complemented
429#419C4×C10711yescharacteristic, complemented
430#418C4×C10711yescharacteristic, complemented
431#418C4×C10711yescharacteristic, complemented
432#417C4×C10711yescharacteristic, complemented
433#417C4×C10711yescharacteristic, complemented
434#417C4×C10711yescharacteristic, complemented
435#417C4×C10711yescharacteristic, complemented
436#416C22×C10711yescharacteristic
437#416C22×C10711yescharacteristic
438#416C22×C10711yescharacteristic
439#416C22×C10711yescharacteristic
440#408—21no—
441#408—21no—
442#408C22×C10711yescharacteristic
443#408C22×C10711yescharacteristic
444#407—21no—
445#407C22×C10711yescharacteristic
446#407C22×C10711yescharacteristic
447C2×C22⋊C8—21no—
448C2×C22⋊C8C22×C10711yescharacteristic
449#405C22×C10711yescharacteristic, complemented
450#405C22×C10711yescharacteristic, complemented
451C2×#97C22×C10711yescharacteristic, complemented
452C2×C4×C8C22×C10711yescharacteristic, complemented
453C4×C22⋊C4C22×C10711yescharacteristic
454#341C22×C10711yescharacteristic, complemented
455#341C22×C10711yescharacteristic, complemented
456#339C22×C10711yescharacteristic, complemented
457#339C22×C10711yescharacteristic, complemented
458#339C22×C10711yescharacteristic, complemented
459#339C22×C10711yescharacteristic, complemented
460#336C22×C10711yescharacteristic, complemented
461#336C22×C10711yescharacteristic, complemented
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×C4×C10711yescharacteristic
469C2×#41C2×C4×C10711yescharacteristic
470C2×#41C23×C10711yescharacteristic
471C2×#41C23×C10711yescharacteristic
472C22×Q8C2×C4×C10711yescharacteristic
473C22×D4—21no—
474C22×D4C2×C4×C10711yescharacteristic
475C23×C4—21no—
476C23×C4C23×C10711yescharacteristic
477#131—22no—
478#131—22no—
479#131—41no—
480#131—41no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—41no—
484C2×M16—41no—
485C2×M16C2×C4×C10711yescharacteristic
486C2×M16C2×C4×C10711yescharacteristic
487C2×M16C2×C4×C10711yescharacteristic
488C2×M16C2×C4×C10711yescharacteristic
489C2×M16C23×C10711yescharacteristic
490C2×M16C23×C10711yescharacteristic
491C2×M16C23×C10711yescharacteristic
492C2×M16C23×C10711yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8C23×C10711yescharacteristic
496C22×C8C23×C10711yescharacteristic
497C22×C8C23×C10711yescharacteristic
498C22×C8C23×C10711yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×C4×C10711yescharacteristic
502#117C2×C4×C10711yescharacteristic
503#117C23×C10711yescharacteristic
504#117C23×C10711yescharacteristic
505C2×C4⋊C4C2×C4×C10711yescharacteristic
506C2×C4⋊C4C2×C4×C10711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C23×C10711yescharacteristic
511C2×C42C23×C10711yescharacteristic
512#108—41no—
513#108—41no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—22no—
519#104—22no—
520#104—41no—
521#104—41no—
522#103C2×C4×C10711yescharacteristic
523#103C2×C4×C10711yescharacteristic
524#103C2×C4×C10711yescharacteristic
525#103C2×C4×C10711yescharacteristic
526#103C2×C4×C10711yescharacteristic
527#103C2×C4×C10711yescharacteristic
528#103C2×C4×C10711yescharacteristic
529#103C2×C4×C10711yescharacteristic
530#102C2×C4×C10711yescharacteristic
531#102C2×C4×C10711yescharacteristic
532#102C2×C4×C10711yescharacteristic
533#102C2×C4×C10711yescharacteristic
534#102C2×C4×C10711yescharacteristic
535#102C2×C4×C10711yescharacteristic
536#102C2×C4×C10711yescharacteristic
537#102C2×C4×C10711yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C22⋊C8D4×C10711yescharacteristic
547C22⋊C8D4×C10711yescharacteristic
548C22⋊C8D4×C10711yescharacteristic
549C22⋊C8D4×C10711yescharacteristic
550#97—21no—
551#97—21no—
552#97—41no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—41no—
556#95—21no—
557C24—21no—
558C24#41×C10711yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#41×C10712yes—
574#41#41×C10712yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×C4×C10711yescharacteristic
579C2×Q8C22×C4×C10711yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×C4×C10711yescharacteristic
590C2×D4C22×C4×C10711yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C22×C4×C10711yescharacteristic
607C22×C4C22×C4×C10711yescharacteristic
608C22×C4C2×D4×C10711yescharacteristic
609C22×C4C2×D4×C10711yescharacteristic
610C22×C4#41×C10711yescharacteristic
611C22×C4C24×C10711yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—42no—
625M16—42no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8C22×C4×C10711yescharacteristic
641C2×C8C22×C4×C10711yescharacteristic
642C2×C8C22×C4×C10711yescharacteristic
643C2×C8C22×C4×C10711yescharacteristic
644C2×C8C2×D4×C10711yescharacteristic
645C2×C8C2×D4×C10711yescharacteristic
646C2×C8C2×D4×C10711yescharacteristic
647C2×C8C2×D4×C10711yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×C4×C10711yescharacteristic
651C4⋊C4C22×C4×C10711yescharacteristic
652C4⋊C4C22×C4×C10711yescharacteristic
653C4⋊C4C22×C4×C10711yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×D4×C10711yescharacteristic
677C23C4×D4×C10711yescharacteristic
678C23C2×#41×C10711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#117×C10712yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#117×C10712yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4C4×D4×C10711yescharacteristic
727C2×C4C4×D4×C10711yescharacteristic
728C2×C4C23×C4×C10711yescharacteristic
729C2×C4C22×D4×C10711yescharacteristic
730C2×C4C2×#41×C10711yescharacteristic
731C2×C4C2×#41×C10711yescharacteristic
732C2×C4H(5,𝔽2)×C10711yescharacteristic
733C2×C4H(5,𝔽2)×C10711yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×D4×C10711yescharacteristic
764C22#551×C10711yescharacteristic
765C22#551×C10711yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×#117×C10711yescharacteristic
777C4#518×C10711yescharacteristic
778C4#546×C10711yescharacteristic
779C4#546×C10711yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2C107×#234211yescharacteristic
787C2C107×#295511yescharacteristic
788C2C107×#295611yescharacteristic
subgroupG/H
centerC2×C4×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
socleC22×C107C2×C4×D4
prime radicalC22×#41×C107C22
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
1. C107×#2924C2semidirect
4. C107×#1938C2semidirect
5. C107×#1937C2semidirect
6. C107×#1929C2semidirect
7. C107×#1929C2semidirect
8. C107×#1866C2semidirect
9. C107×#1866C2semidirect
10. C107×#1826C2semidirect
11. C107×#1811C2semidirect
13. C107×#1765C2semidirect
14. C107×#1764C2semidirect
15. C107×#1753C2semidirect
25. C2×#108×C107C22semidirect
26. C2×#108×C107C22semidirect
27. #424×C107C22semidirect
28. #424×C107C22semidirect
33. #419×C107C4semidirect
34. #419×C107C4semidirect
35. #418×C107C4semidirect
36. #418×C107C4semidirect
37. #417×C107C4semidirect
38. #417×C107C4semidirect
39. #417×C107C4semidirect
40. #417×C107C4semidirect
54. #405×C107C22semidirect
55. #405×C107C22semidirect
56. C2×#97×C107C22semidirect
57. C2×C4×C8×C107C22semidirect
59. #341×C107C22semidirect
60. #341×C107C22semidirect
61. #339×C107C22semidirect
62. #339×C107C22semidirect
63. #339×C107C22semidirect
64. #339×C107C22semidirect
65. #336×C107C22semidirect
66. #336×C107C22semidirect
385. #22588C107direct (N × H)
395. #2924C2×C107semidirect
398. #1938C2×C107semidirect
399. #1937C2×C107semidirect
400. #1929C2×C107semidirect
401. #1929C2×C107semidirect
402. #1866C2×C107semidirect
403. #1866C2×C107semidirect
404. #1826C2×C107semidirect
405. #1811C2×C107semidirect
407. #1765C2×C107semidirect
408. #1764C2×C107semidirect
409. #1753C2×C107semidirect
410. C107#22588direct (N × H)
420. C2×#108C22×C107semidirect
421. C2×#108C22×C107semidirect
422. #424C22×C107semidirect
423. #424C22×C107semidirect
428. #419C4×C107semidirect
429. #419C4×C107semidirect
430. #418C4×C107semidirect
431. #418C4×C107semidirect
432. #417C4×C107semidirect
433. #417C4×C107semidirect
434. #417C4×C107semidirect
435. #417C4×C107semidirect
449. #405C22×C107semidirect
450. #405C22×C107semidirect
451. C2×#97C22×C107semidirect
452. C2×C4×C8C22×C107semidirect
454. #341C22×C107semidirect
455. #341C22×C107semidirect
456. #339C22×C107semidirect
457. #339C22×C107semidirect
458. #339C22×C107semidirect
459. #339C22×C107semidirect
460. #336C22×C107semidirect
461. #336C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#29242
C107×#28962
C107×#28802
C107×#19382
C107×#19372
C107×#19292
C107×#18662
C107×#18262
C107×#18112
C107×#17892
C107×#17652
C107×#17642
C107×#17532
#22588107