Finite Group Databasebeta

← C101×#22588 #38804739

Subgroups — C101×#22588 #38804739

Order 25856.

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
1C101×#2924C211yesmaximal, characteristic, complemented
2C101×#2896C211yesmaximal, characteristic
3C101×#2880C211yesmaximal, characteristic
4C101×#1938C211yesmaximal, characteristic, complemented
5C101×#1937C211yesmaximal, characteristic, complemented
6C101×#1929C211yesmaximal, characteristic, complemented
7C101×#1929C211yesmaximal, characteristic, complemented
8C101×#1866C211yesmaximal, characteristic, complemented
9C101×#1866C211yesmaximal, characteristic, complemented
10C101×#1826C211yesmaximal, characteristic, complemented
11C101×#1811C211yesmaximal, characteristic, complemented
12C101×#1789C211yesmaximal, characteristic
13C101×#1765C211yesmaximal, characteristic, complemented
14C101×#1764C211yesmaximal, characteristic, complemented
15C101×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C2×#131×C101C2211yescharacteristic
18C2×#131×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic
20C2×#117×C101C2211yescharacteristic
21#433×C101—21no—
22#433×C101—21no—
23#432×C101—21no—
24#431×C101—21no—
25C2×#108×C101C2211yescharacteristic, complemented
26C2×#108×C101C2211yescharacteristic, complemented
27#424×C101C2211yescharacteristic, complemented
28#424×C101C2211yescharacteristic, complemented
29C2×#104×C101C2211yescharacteristic
30C2×#104×C101C2211yescharacteristic
31C2×#104×C101C2211yescharacteristic
32C2×#104×C101C2211yescharacteristic
33#419×C101C411yescharacteristic, complemented
34#419×C101C411yescharacteristic, complemented
35#418×C101C411yescharacteristic, complemented
36#418×C101C411yescharacteristic, complemented
37#417×C101C411yescharacteristic, complemented
38#417×C101C411yescharacteristic, complemented
39#417×C101C411yescharacteristic, complemented
40#417×C101C411yescharacteristic, complemented
41#416×C101C2211yescharacteristic
42#416×C101C2211yescharacteristic
43#416×C101C2211yescharacteristic
44#416×C101C2211yescharacteristic
45#408×C101—21no—
46#408×C101—21no—
47#408×C101C2211yescharacteristic
48#408×C101C2211yescharacteristic
49#407×C101—21no—
50#407×C101C2211yescharacteristic
51#407×C101C2211yescharacteristic
52C2×C22⋊C8×C101—21no—
53C2×C22⋊C8×C101C2211yescharacteristic
54#405×C101C2211yescharacteristic, complemented
55#405×C101C2211yescharacteristic, complemented
56C2×#97×C101C2211yescharacteristic, complemented
57C2×C4×C8×C101C2211yescharacteristic, complemented
58C4×C22⋊C4×C101C2211yescharacteristic
59#341×C101C2211yescharacteristic, complemented
60#341×C101C2211yescharacteristic, complemented
61#339×C101C2211yescharacteristic, complemented
62#339×C101C2211yescharacteristic, complemented
63#339×C101C2211yescharacteristic, complemented
64#339×C101C2211yescharacteristic, complemented
65#336×C101C2211yescharacteristic, complemented
66#336×C101C2211yescharacteristic, complemented
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×#41×C101—22no—
70C2×#41×C101—22no—
71C2×#41×C101—41no—
72C2×#41×C101—41no—
73C2×#41×C101C2×C411yescharacteristic
74C2×#41×C101C2×C411yescharacteristic
75C2×#41×C101C2311yescharacteristic
76C2×#41×C101C2311yescharacteristic
77C22×Q8×C101C2×C411yescharacteristic
78C22×D4×C101—21no—
79C22×D4×C101C2×C411yescharacteristic
80C23×C4×C101—21no—
81C23×C4×C101C2311yescharacteristic
82#131×C101—22no—
83#131×C101—22no—
84#131×C101—41no—
85#131×C101—41no—
86C2×M16×C101—21no—
87C2×M16×C101—21no—
88C2×M16×C101—41no—
89C2×M16×C101—41no—
90C2×M16×C101C2×C411yescharacteristic
91C2×M16×C101C2×C411yescharacteristic
92C2×M16×C101C2×C411yescharacteristic
93C2×M16×C101C2×C411yescharacteristic
94C2×M16×C101C2311yescharacteristic
95C2×M16×C101C2311yescharacteristic
96C2×M16×C101C2311yescharacteristic
97C2×M16×C101C2311yescharacteristic
98C22×C8×C101—21no—
99C22×C8×C101—21no—
100C22×C8×C101C2311yescharacteristic
101C22×C8×C101C2311yescharacteristic
102C22×C8×C101C2311yescharacteristic
103C22×C8×C101C2311yescharacteristic
104#117×C101—21no—
105#117×C101—21no—
106#117×C101C2×C411yescharacteristic
107#117×C101C2×C411yescharacteristic
108#117×C101C2311yescharacteristic
109#117×C101C2311yescharacteristic
110C2×C4⋊C4×C101C2×C411yescharacteristic
111C2×C4⋊C4×C101C2×C411yescharacteristic
112C2×C22⋊C4×C101—21no—
113C2×C22⋊C4×C101—21no—
114C2×C42×C101—21no—
115C2×C42×C101C2311yescharacteristic
116C2×C42×C101C2311yescharacteristic
117#108×C101—41no—
118#108×C101—41no—
119C4⋊C8×C101—21no—
120C4⋊C8×C101—21no—
121C4⋊C8×C101—21no—
122C4⋊C8×C101—21no—
123#104×C101—22no—
124#104×C101—22no—
125#104×C101—41no—
126#104×C101—41no—
127#103×C101C2×C411yescharacteristic
128#103×C101C2×C411yescharacteristic
129#103×C101C2×C411yescharacteristic
130#103×C101C2×C411yescharacteristic
131#103×C101C2×C411yescharacteristic
132#103×C101C2×C411yescharacteristic
133#103×C101C2×C411yescharacteristic
134#103×C101C2×C411yescharacteristic
135#102×C101C2×C411yescharacteristic
136#102×C101C2×C411yescharacteristic
137#102×C101C2×C411yescharacteristic
138#102×C101C2×C411yescharacteristic
139#102×C101C2×C411yescharacteristic
140#102×C101C2×C411yescharacteristic
141#102×C101C2×C411yescharacteristic
142#102×C101C2×C411yescharacteristic
143C22⋊C8×C101—21no—
144C22⋊C8×C101—21no—
145C22⋊C8×C101—21no—
146C22⋊C8×C101—21no—
147C22⋊C8×C101—21no—
148C22⋊C8×C101—21no—
149C22⋊C8×C101—21no—
150C22⋊C8×C101—21no—
151C22⋊C8×C101D411yescharacteristic
152C22⋊C8×C101D411yescharacteristic
153C22⋊C8×C101D411yescharacteristic
154C22⋊C8×C101D411yescharacteristic
155#97×C101—21no—
156#97×C101—21no—
157#97×C101—41no—
158C4×C8×C101—21no—
159C4×C8×C101—21no—
160C4×C8×C101—41no—
161#95×C101—21no—
162C24×C101—21no—
163C24×C101#4111yescharacteristic
164#41×C101—21no—
165#41×C101—21no—
166#41×C101—22no—
167#41×C101—22no—
168#41×C101—21no—
169#41×C101—21no—
170#41×C101—21no—
171#41×C101—21no—
172#41×C101—42no—
173#41×C101—42no—
174#41×C101—41no—
175#41×C101—41no—
176#41×C101—42no—
177#41×C101—42no—
178#41×C101#4112yes—
179#41×C101#4112yes—
180C2×Q8×C101—21no—
181C2×Q8×C101—22no—
182C2×Q8×C101—41no—
183C2×Q8×C101C22×C411yescharacteristic
184C2×Q8×C101C22×C411yescharacteristic
185C2×D4×C101—21no—
186C2×D4×C101—22no—
187C2×D4×C101—21no—
188C2×D4×C101—21no—
189C2×D4×C101—21no—
190C2×D4×C101—21no—
191C2×D4×C101—41no—
192C2×D4×C101—42no—
193C2×D4×C101—42no—
194C2×D4×C101C22×C411yescharacteristic
195C2×D4×C101C22×C411yescharacteristic
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—42no—
210C22×C4×C101—42no—
211C22×C4×C101C22×C411yescharacteristic
212C22×C4×C101C22×C411yescharacteristic
213C22×C4×C101C2×D411yescharacteristic
214C22×C4×C101C2×D411yescharacteristic
215C22×C4×C101#4111yescharacteristic
216C22×C4×C101C2411yescharacteristic
217M16×C101—21no—
218M16×C101—21no—
219M16×C101—21no—
220M16×C101—21no—
221M16×C101—21no—
222M16×C101—21no—
223M16×C101—21no—
224M16×C101—21no—
225M16×C101—41no—
226M16×C101—41no—
227M16×C101—41no—
228M16×C101—41no—
229M16×C101—42no—
230M16×C101—42no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—21no—
238C2×C8×C101—21no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101—21no—
242C2×C8×C101—21no—
243C2×C8×C101—42no—
244C2×C8×C101—42no—
245C2×C8×C101C22×C411yescharacteristic
246C2×C8×C101C22×C411yescharacteristic
247C2×C8×C101C22×C411yescharacteristic
248C2×C8×C101C22×C411yescharacteristic
249C2×C8×C101C2×D411yescharacteristic
250C2×C8×C101C2×D411yescharacteristic
251C2×C8×C101C2×D411yescharacteristic
252C2×C8×C101C2×D411yescharacteristic
253C4⋊C4×C101—21no—
254C4⋊C4×C101—21no—
255C4⋊C4×C101C22×C411yescharacteristic
256C4⋊C4×C101C22×C411yescharacteristic
257C4⋊C4×C101C22×C411yescharacteristic
258C4⋊C4×C101C22×C411yescharacteristic
259C22⋊C4×C101—21no—
260C22⋊C4×C101—21no—
261C22⋊C4×C101—21no—
262C22⋊C4×C101—21no—
263C22⋊C4×C101—42no—
264C42×C101—21no—
265C42×C101—21no—
266C42×C101—21no—
267C42×C101—21no—
268C42×C101—21no—
269C42×C101—21no—
270C42×C101—21no—
271C42×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—41no—
277C23×C101—41no—
278C23×C101—42no—
279C23×C101—42no—
280C23×C101—81no—
281C23×C101C4×D411yescharacteristic
282C23×C101C4×D411yescharacteristic
283C23×C101C2×#4111yescharacteristic
284Q8×C101—21no—
285Q8×C101—21no—
286Q8×C101—21no—
287Q8×C101—42no—
288Q8×C101#11712yes—
289D4×C101—22no—
290D4×C101—22no—
291D4×C101—21no—
292D4×C101—21no—
293D4×C101—21no—
294D4×C101—42no—
295D4×C101—42no—
296D4×C101—42no—
297D4×C101—41no—
298D4×C101—41no—
299D4×C101#11712yes—
300C2×C4×C101—21no—
301C2×C4×C101—21no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—21no—
306C2×C4×C101—21no—
307C2×C4×C101—22no—
308C2×C4×C101—22no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—22no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—42no—
320C2×C4×C101—42no—
321C2×C4×C101—42no—
322C2×C4×C101—41no—
323C2×C4×C101—42no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—81no—
331C2×C4×C101C4×D411yescharacteristic
332C2×C4×C101C4×D411yescharacteristic
333C2×C4×C101C23×C411yescharacteristic
334C2×C4×C101C22×D411yescharacteristic
335C2×C4×C101C2×#4111yescharacteristic
336C2×C4×C101C2×#4111yescharacteristic
337C2×C4×C101H(5,𝔽2)11yescharacteristic
338C2×C4×C101H(5,𝔽2)11yescharacteristic
339C8×C101—21no—
340C8×C101—21no—
341C8×C101—21no—
342C8×C101—21no—
343C8×C101—21no—
344C8×C101—21no—
345C8×C101—21no—
346C8×C101—21no—
347C8×C101—41no—
348C8×C101—41no—
349C8×C101—41no—
350C8×C101—41no—
351C22×C101—21no—
352C22×C101—21no—
353C22×C101—21no—
354C22×C101—21no—
355C22×C101—22no—
356C22×C101—21no—
357C22×C101—21no—
358C22×C101—21no—
359C22×C101—21no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—41no—
364C22×C101—41no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101—84no—
368C22×C101C2×C4×D411yescharacteristic
369C22×C101#55111yescharacteristic
370C22×C101#55111yescharacteristic
371C4×C101—21no—
372C4×C101—21no—
373C4×C101—22no—
374C4×C101—42no—
375C4×C101—41no—
376C4×C101—41no—
377C4×C101—41no—
378C4×C101—41no—
379C4×C101—41no—
380C4×C101—81no—
381C4×C101C2×#11711yescharacteristic
382C4×C101#51811yescharacteristic
383C4×C101#54611yescharacteristic
384C4×C101#54611yescharacteristic
385#22588C10111yesmaximal, characteristic, direct product factor, Sylow
386C2×C101—21no—
387C2×C101—21no—
388C2×C101—41no—
389C2×C101—41no—
390C2×C101—42no—
391C2×C101—81no—
392C2×C101#234211yescharacteristic
393C2×C101#295511yescharacteristic
394C2×C101#295611yescharacteristic
395#2924C2×C10111yescharacteristic, complemented
396#2896C2×C10111yescharacteristic
397#2880C2×C10111yescharacteristic
398#1938C2×C10111yescharacteristic, complemented
399#1937C2×C10111yescharacteristic, complemented
400#1929C2×C10111yescharacteristic, complemented
401#1929C2×C10111yescharacteristic, complemented
402#1866C2×C10111yescharacteristic, complemented
403#1866C2×C10111yescharacteristic, complemented
404#1826C2×C10111yescharacteristic, complemented
405#1811C2×C10111yescharacteristic, complemented
406#1789C2×C10111yescharacteristic
407#1765C2×C10111yescharacteristic, complemented
408#1764C2×C10111yescharacteristic, complemented
409#1753C2×C10111yescharacteristic, complemented
410C101#2258811yescharacteristic, direct product factor, Sylow
411C22×#41C22×C10111yescharacteristic
412C2×#131C22×C10111yescharacteristic
413C2×#131C22×C10111yescharacteristic
414C22×M16C22×C10111yescharacteristic
415C2×#117C22×C10111yescharacteristic
416#433—21no—
417#433—21no—
418#432—21no—
419#431—21no—
420C2×#108C22×C10111yescharacteristic, complemented
421C2×#108C22×C10111yescharacteristic, complemented
422#424C22×C10111yescharacteristic, complemented
423#424C22×C10111yescharacteristic, complemented
424C2×#104C22×C10111yescharacteristic
425C2×#104C22×C10111yescharacteristic
426C2×#104C22×C10111yescharacteristic
427C2×#104C22×C10111yescharacteristic
428#419C4×C10111yescharacteristic, complemented
429#419C4×C10111yescharacteristic, complemented
430#418C4×C10111yescharacteristic, complemented
431#418C4×C10111yescharacteristic, complemented
432#417C4×C10111yescharacteristic, complemented
433#417C4×C10111yescharacteristic, complemented
434#417C4×C10111yescharacteristic, complemented
435#417C4×C10111yescharacteristic, complemented
436#416C22×C10111yescharacteristic
437#416C22×C10111yescharacteristic
438#416C22×C10111yescharacteristic
439#416C22×C10111yescharacteristic
440#408—21no—
441#408—21no—
442#408C22×C10111yescharacteristic
443#408C22×C10111yescharacteristic
444#407—21no—
445#407C22×C10111yescharacteristic
446#407C22×C10111yescharacteristic
447C2×C22⋊C8—21no—
448C2×C22⋊C8C22×C10111yescharacteristic
449#405C22×C10111yescharacteristic, complemented
450#405C22×C10111yescharacteristic, complemented
451C2×#97C22×C10111yescharacteristic, complemented
452C2×C4×C8C22×C10111yescharacteristic, complemented
453C4×C22⋊C4C22×C10111yescharacteristic
454#341C22×C10111yescharacteristic, complemented
455#341C22×C10111yescharacteristic, complemented
456#339C22×C10111yescharacteristic, complemented
457#339C22×C10111yescharacteristic, complemented
458#339C22×C10111yescharacteristic, complemented
459#339C22×C10111yescharacteristic, complemented
460#336C22×C10111yescharacteristic, complemented
461#336C22×C10111yescharacteristic, complemented
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×C4×C10111yescharacteristic
469C2×#41C2×C4×C10111yescharacteristic
470C2×#41C23×C10111yescharacteristic
471C2×#41C23×C10111yescharacteristic
472C22×Q8C2×C4×C10111yescharacteristic
473C22×D4—21no—
474C22×D4C2×C4×C10111yescharacteristic
475C23×C4—21no—
476C23×C4C23×C10111yescharacteristic
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×C10111yescharacteristic
486C2×M16C2×C4×C10111yescharacteristic
487C2×M16C2×C4×C10111yescharacteristic
488C2×M16C2×C4×C10111yescharacteristic
489C2×M16C23×C10111yescharacteristic
490C2×M16C23×C10111yescharacteristic
491C2×M16C23×C10111yescharacteristic
492C2×M16C23×C10111yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8C23×C10111yescharacteristic
496C22×C8C23×C10111yescharacteristic
497C22×C8C23×C10111yescharacteristic
498C22×C8C23×C10111yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×C4×C10111yescharacteristic
502#117C2×C4×C10111yescharacteristic
503#117C23×C10111yescharacteristic
504#117C23×C10111yescharacteristic
505C2×C4⋊C4C2×C4×C10111yescharacteristic
506C2×C4⋊C4C2×C4×C10111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C23×C10111yescharacteristic
511C2×C42C23×C10111yescharacteristic
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×C10111yescharacteristic
523#103C2×C4×C10111yescharacteristic
524#103C2×C4×C10111yescharacteristic
525#103C2×C4×C10111yescharacteristic
526#103C2×C4×C10111yescharacteristic
527#103C2×C4×C10111yescharacteristic
528#103C2×C4×C10111yescharacteristic
529#103C2×C4×C10111yescharacteristic
530#102C2×C4×C10111yescharacteristic
531#102C2×C4×C10111yescharacteristic
532#102C2×C4×C10111yescharacteristic
533#102C2×C4×C10111yescharacteristic
534#102C2×C4×C10111yescharacteristic
535#102C2×C4×C10111yescharacteristic
536#102C2×C4×C10111yescharacteristic
537#102C2×C4×C10111yescharacteristic
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×C10111yescharacteristic
547C22⋊C8D4×C10111yescharacteristic
548C22⋊C8D4×C10111yescharacteristic
549C22⋊C8D4×C10111yescharacteristic
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×C10111yescharacteristic
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×C10112yes—
574#41#41×C10112yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×C4×C10111yescharacteristic
579C2×Q8C22×C4×C10111yescharacteristic
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×C10111yescharacteristic
590C2×D4C22×C4×C10111yescharacteristic
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×C10111yescharacteristic
607C22×C4C22×C4×C10111yescharacteristic
608C22×C4C2×D4×C10111yescharacteristic
609C22×C4C2×D4×C10111yescharacteristic
610C22×C4#41×C10111yescharacteristic
611C22×C4C24×C10111yescharacteristic
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×C10111yescharacteristic
641C2×C8C22×C4×C10111yescharacteristic
642C2×C8C22×C4×C10111yescharacteristic
643C2×C8C22×C4×C10111yescharacteristic
644C2×C8C2×D4×C10111yescharacteristic
645C2×C8C2×D4×C10111yescharacteristic
646C2×C8C2×D4×C10111yescharacteristic
647C2×C8C2×D4×C10111yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×C4×C10111yescharacteristic
651C4⋊C4C22×C4×C10111yescharacteristic
652C4⋊C4C22×C4×C10111yescharacteristic
653C4⋊C4C22×C4×C10111yescharacteristic
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×C10111yescharacteristic
677C23C4×D4×C10111yescharacteristic
678C23C2×#41×C10111yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#117×C10112yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#117×C10112yes—
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×C10111yescharacteristic
727C2×C4C4×D4×C10111yescharacteristic
728C2×C4C23×C4×C10111yescharacteristic
729C2×C4C22×D4×C10111yescharacteristic
730C2×C4C2×#41×C10111yescharacteristic
731C2×C4C2×#41×C10111yescharacteristic
732C2×C4H(5,𝔽2)×C10111yescharacteristic
733C2×C4H(5,𝔽2)×C10111yescharacteristic
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×C10111yescharacteristic
764C22#551×C10111yescharacteristic
765C22#551×C10111yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×#117×C10111yescharacteristic
777C4#518×C10111yescharacteristic
778C4#546×C10111yescharacteristic
779C4#546×C10111yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2C101×#234211yescharacteristic
787C2C101×#295511yescharacteristic
788C2C101×#295611yescharacteristic
subgroupG/H
centerC2×C4×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
socleC22×C101C2×C4×D4
prime radicalC22×#41×C101C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C2×C22⋊C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#2924C2semidirect
4. C101×#1938C2semidirect
5. C101×#1937C2semidirect
6. C101×#1929C2semidirect
7. C101×#1929C2semidirect
8. C101×#1866C2semidirect
9. C101×#1866C2semidirect
10. C101×#1826C2semidirect
11. C101×#1811C2semidirect
13. C101×#1765C2semidirect
14. C101×#1764C2semidirect
15. C101×#1753C2semidirect
25. C2×#108×C101C22semidirect
26. C2×#108×C101C22semidirect
27. #424×C101C22semidirect
28. #424×C101C22semidirect
33. #419×C101C4semidirect
34. #419×C101C4semidirect
35. #418×C101C4semidirect
36. #418×C101C4semidirect
37. #417×C101C4semidirect
38. #417×C101C4semidirect
39. #417×C101C4semidirect
40. #417×C101C4semidirect
54. #405×C101C22semidirect
55. #405×C101C22semidirect
56. C2×#97×C101C22semidirect
57. C2×C4×C8×C101C22semidirect
59. #341×C101C22semidirect
60. #341×C101C22semidirect
61. #339×C101C22semidirect
62. #339×C101C22semidirect
63. #339×C101C22semidirect
64. #339×C101C22semidirect
65. #336×C101C22semidirect
66. #336×C101C22semidirect
385. #22588C101direct (N × H)
395. #2924C2×C101semidirect
398. #1938C2×C101semidirect
399. #1937C2×C101semidirect
400. #1929C2×C101semidirect
401. #1929C2×C101semidirect
402. #1866C2×C101semidirect
403. #1866C2×C101semidirect
404. #1826C2×C101semidirect
405. #1811C2×C101semidirect
407. #1765C2×C101semidirect
408. #1764C2×C101semidirect
409. #1753C2×C101semidirect
410. C101#22588direct (N × H)
420. C2×#108C22×C101semidirect
421. C2×#108C22×C101semidirect
422. #424C22×C101semidirect
423. #424C22×C101semidirect
428. #419C4×C101semidirect
429. #419C4×C101semidirect
430. #418C4×C101semidirect
431. #418C4×C101semidirect
432. #417C4×C101semidirect
433. #417C4×C101semidirect
434. #417C4×C101semidirect
435. #417C4×C101semidirect
449. #405C22×C101semidirect
450. #405C22×C101semidirect
451. C2×#97C22×C101semidirect
452. C2×C4×C8C22×C101semidirect
454. #341C22×C101semidirect
455. #341C22×C101semidirect
456. #339C22×C101semidirect
457. #339C22×C101semidirect
458. #339C22×C101semidirect
459. #339C22×C101semidirect
460. #336C22×C101semidirect
461. #336C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#29242
C101×#28962
C101×#28802
C101×#19382
C101×#19372
C101×#19292
C101×#18662
C101×#18262
C101×#18112
C101×#17892
C101×#17652
C101×#17642
C101×#17532
#22588101