Finite Group Databasebeta

← C101×#22056 #38804207

Subgroups — C101×#22056 #38804207

Order 25856.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C101C211yesmaximal, characteristic
2C101×#2324C211yesmaximal, characteristic, complemented
3C101×#2309C211yesmaximal, characteristic, complemented
4C101×#1972C211yesmaximal, characteristic, complemented
5C101×#1970C211yesmaximal, characteristic, complemented
6C101×#1936C211yesmaximal, characteristic, complemented
7C101×#1934C211yesmaximal, characteristic, complemented
8C101×#1926C211yesmaximal, characteristic, complemented
9C101×#1925C211yesmaximal, characteristic, complemented
10C101×#1879C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic, complemented
12C101×#1875C211yesmaximal, characteristic, complemented
13C101×#1854C211yesmaximal, characteristic, complemented
14C101×#1786C211yesmaximal, characteristic, complemented
15C101×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C2×#121×C101C2211yescharacteristic
20C2×C4×D4×C101C2211yescharacteristic, complemented
21C2×#117×C101C2211yescharacteristic
22C2×#117×C101C2211yescharacteristic
23#447×C101C418yescomplemented
24C2×#107×C101C2211yescharacteristic, complemented
25C2×#106×C101C2211yescharacteristic, complemented
26C2×#102×C101C2211yescharacteristic
27C2×#102×C101C2211yescharacteristic
28C2×#102×C101C2211yescharacteristic
29C2×#102×C101C2211yescharacteristic
30C2×#102×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic, complemented
33C2×#102×C101C2211yescharacteristic, complemented
34C2×C22⋊C8×C101C2211yescharacteristic
35C2×C22⋊C8×C101C2211yescharacteristic
36C2×#97×C101C2211yescharacteristic, complemented
37C2×C4×C8×C101C2211yescharacteristic, complemented
38#390×C101—21no—
39#390×C101—21no—
40#390×C101—21no—
41#390×C101C2211yescharacteristic
42#390×C101C2211yescharacteristic
43#390×C101C2211yescharacteristic
44#390×C101C2211yescharacteristic
45#390×C101C2211yescharacteristic, complemented
46#389×C101C2211yescharacteristic, complemented
47#388×C101—21no—
48#386×C101—21no—
49#385×C101—21no—
50#380×C101C2211yescharacteristic
51#379×C101—21no—
52#379×C101—21no—
53C4×C4⋊C4×C101C2211yescharacteristic, complemented
54#340×C101C2211yescharacteristic, complemented
55#340×C101C2211yescharacteristic, complemented
56#340×C101C2211yescharacteristic, complemented
57#340×C101C2211yescharacteristic, complemented
58#336×C101C2211yescharacteristic, complemented
59#336×C101C2211yescharacteristic, complemented
60C25×C101—21no—
61C22×D4×C101—21no—
62C22×D4×C101—21no—
63C22×D4×C101—22no—
64C22×D4×C101—41no—
65C22×D4×C101—41no—
66C22×D4×C101—41no—
67C22×D4×C101—41no—
68C22×D4×C101C2×C414yescomplemented
69C22×D4×C101C2311yescharacteristic
70C22×D4×C101C2311yescharacteristic
71C22×D4×C101C2311yescharacteristic
72C23×C4×C101—21no—
73C23×C4×C101C2311yescharacteristic
74C2×D8×C101—41no—
75C2×D8×C101—41no—
76C2×D8×C101—41no—
77C2×D8×C101—41no—
78C2×D8×C101C2×C414yes—
79C2×D8×C101C2×C414yes—
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83C22×C8×C101C2311yescharacteristic
84#121×C101—22no—
85#121×C101C2×C414yes—
86C4×D4×C101—41no—
87C4×D4×C101—41no—
88#117×C101—41no—
89#117×C101—41no—
90#117×C101—41no—
91#117×C101—41no—
92C2×C4⋊C4×C101—21no—
93C2×C4⋊C4×C101D411yescharacteristic
94C2×C4⋊C4×C101D411yescharacteristic
95C2×C4⋊C4×C101C2311yescharacteristic
96C2×C4⋊C4×C101C2311yescharacteristic
97C2×C4⋊C4×C101C2311yescharacteristic
98C2×C4⋊C4×C101C2311yescharacteristic
99C2×C4⋊C4×C101C2311yescharacteristic
100C2×C22⋊C4×C101—21no—
101C2×C22⋊C4×C101—21no—
102C2×C22⋊C4×C101—21no—
103C2×C22⋊C4×C101—21no—
104C2×C22⋊C4×C101—21no—
105C2×C22⋊C4×C101—21no—
106C2×C22⋊C4×C101—21no—
107C2×C22⋊C4×C101—21no—
108C2×C22⋊C4×C101—21no—
109C2×C22⋊C4×C101—21no—
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101—21no—
113C2×C22⋊C4×C101—21no—
114C2×C22⋊C4×C101D411yescharacteristic
115C2×C22⋊C4×C101D411yescharacteristic
116C2×C42×C101—21no—
117C2×C42×C101—21no—
118C2×C42×C101C2311yescharacteristic
119C2×C42×C101C2311yescharacteristic
120#107×C101—41no—
121#106×C101—41no—
122#102×C101—41no—
123#102×C101—41no—
124#102×C101—41no—
125#102×C101—41no—
126#102×C101—41no—
127#102×C101—41no—
128#102×C101C2×C414yescomplemented
129#102×C101C2×C414yescomplemented
130C22⋊C8×C101—22no—
131C22⋊C8×C101C2×C414yescomplemented
132#97×C101—41no—
133C4×C8×C101—41no—
134#95×C101—21no—
135#95×C101—21no—
136#95×C101—21no—
137C24×C101—21no—
138C24×C101—21no—
139C24×C101—21no—
140C24×C101—24no—
141C24×C101—42no—
142C24×C101—42no—
143C24×C101—81no—
144C24×C101—81no—
145C24×C101—81no—
146C24×C101—81no—
147C24×C101C2×D411yescharacteristic
148C2×D4×C101—24no—
149C2×D4×C101—24no—
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—21no—
163C2×D4×C101—21no—
164C2×D4×C101—21no—
165C2×D4×C101—44no—
166C2×D4×C101—44no—
167C2×D4×C101—42no—
168C2×D4×C101—42no—
169C2×D4×C101—44no—
170C2×D4×C101—44no—
171C2×D4×C101—81no—
172C2×D4×C101—81no—
173C2×D4×C101C22×C412yes—
174C2×D4×C101C22×C412yes—
175C2×D4×C101C22×C412yes—
176C22×C4×C101—21no—
177C22×C4×C101—21no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—42no—
186C22×C4×C101—81no—
187C22×C4×C101—81no—
188C22×C4×C101C22×C412yes—
189C22×C4×C101C2×D411yescharacteristic
190C22×C4×C101C2×D411yescharacteristic
191C22×C4×C101C2×D411yescharacteristic
192C22×C4×C101C2×D411yescharacteristic
193C22×C4×C101C2×D411yescharacteristic
194C22×C4×C101#4112yes—
195C22×C4×C101C2411yescharacteristic
196D8×C101—44no—
197D8×C101—44no—
198C2×C8×C101—21no—
199C2×C8×C101—21no—
200C2×C8×C101—21no—
201C2×C8×C101—21no—
202C2×C8×C101—21no—
203C2×C8×C101—21no—
204C2×C8×C101—21no—
205C2×C8×C101—21no—
206C2×C8×C101—21no—
207C2×C8×C101—21no—
208C2×C8×C101C22×C412yes—
209C2×C8×C101C22×C412yes—
210C4⋊C4×C101—21no—
211C4⋊C4×C101—21no—
212C4⋊C4×C101—21no—
213C4⋊C4×C101—21no—
214C4⋊C4×C101—21no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101—41no—
220C4⋊C4×C101—41no—
221C4⋊C4×C101—81no—
222C4⋊C4×C101C22×C412yes—
223C22⋊C4×C101—24no—
224C22⋊C4×C101—41no—
225C22⋊C4×C101—41no—
226C22⋊C4×C101—42no—
227C22⋊C4×C101—42no—
228C22⋊C4×C101—81no—
229C22⋊C4×C101—81no—
230C22⋊C4×C101—81no—
231C22⋊C4×C101—81no—
232C22⋊C4×C101—81no—
233C22⋊C4×C101—81no—
234C22⋊C4×C101—81no—
235C22⋊C4×C101—81no—
236C22⋊C4×C101—81no—
237C22⋊C4×C101—81no—
238C22⋊C4×C101—81no—
239C42×C101—21no—
240C42×C101—21no—
241C42×C101—21no—
242C42×C101—21no—
243C42×C101—42no—
244C42×C101—81no—
245C23×C101—21no—
246C23×C101—21no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—22no—
252C23×C101—22no—
253C23×C101—22no—
254C23×C101—48no—
255C23×C101—41no—
256C23×C101—41no—
257C23×C101—41no—
258C23×C101—41no—
259C23×C101—41no—
260C23×C101—41no—
261C23×C101—41no—
262C23×C101—41no—
263C23×C101—41no—
264C23×C101—41no—
265C23×C101—41no—
266C23×C101—41no—
267C23×C101—41no—
268C23×C101—41no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—84no—
274C23×C101—84no—
275C23×C101—84no—
276C23×C101—84no—
277C23×C101—84no—
278C23×C101—84no—
279C23×C101C4×D412yes—
280C23×C101C22×D411yescharacteristic
281D4×C101—22no—
282D4×C101—22no—
283D4×C101—22no—
284D4×C101—22no—
285D4×C101—22no—
286D4×C101—22no—
287D4×C101—48no—
288D4×C101—41no—
289D4×C101—41no—
290D4×C101—41no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—41no—
294D4×C101—84no—
295C2×C4×C101—21no—
296C2×C4×C101—21no—
297C2×C4×C101—22no—
298C2×C4×C101—22no—
299C2×C4×C101—22no—
300C2×C4×C101—22no—
301C2×C4×C101—22no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—21no—
306C2×C4×C101—21no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—41no—
315C2×C4×C101—41no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—41no—
323C2×C4×C101—41no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—84no—
329C2×C4×C101C4×D412yes—
330C2×C4×C101C23×C411yescharacteristic
331C2×C4×C101C2×#4111yescharacteristic
332C2×C4×C101H(5,𝔽2)11yescharacteristic
333C2×C4×C101H(5,𝔽2)11yescharacteristic
334C2×C4×C101H(5,𝔽2)11yescharacteristic
335C2×C4×C101H(5,𝔽2)11yescharacteristic
336C8×C101—22no—
337C8×C101—22no—
338C8×C101—41no—
339C8×C101—41no—
340C22×C101—22no—
341C22×C101—22no—
342C22×C101—22no—
343C22×C101—41no—
344C22×C101—41no—
345C22×C101—41no—
346C22×C101—41no—
347C22×C101—42no—
348C22×C101—42no—
349C22×C101—42no—
350C22×C101—42no—
351C22×C101—42no—
352C22×C101—42no—
353C22×C101—42no—
354C22×C101—42no—
355C22×C101—42no—
356C22×C101—816no—
357C22×C101—81no—
358C22×C101—81no—
359C22×C101—81no—
360C22×C101—81no—
361C22×C101—81no—
362C22×C101—81no—
363C22×C101—81no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101—81no—
368C22×C101—81no—
369C22×C101C2×C4×D411yescharacteristic
370C22×C101#53411yescharacteristic
371C22×C101#53511yescharacteristic
372C22×C101#57611yescharacteristic
373C22×C101#57611yescharacteristic
374C22×C101#57611yescharacteristic
375C22×C101#57711yescharacteristic
376C4×C101—22no—
377C4×C101—41no—
378C4×C101—41no—
379C4×C101—41no—
380C4×C101—41no—
381C4×C101—42no—
382C4×C101—81no—
383C4×C101—81no—
384C4×C101—81no—
385C4×C101—81no—
386C4×C101#51811yescharacteristic
387C4×C101#51811yescharacteristic
388C4×C101#53811yescharacteristic
389C4×C101#53811yescharacteristic
390#22056C10111yesmaximal, characteristic, direct product factor, Sylow
391C2×C101—42no—
392C2×C101—82no—
393C2×C101—82no—
394C2×C101—82no—
395C2×C101#232111yescharacteristic
396C2×C101#294611yescharacteristic
397C2×C101#294811yescharacteristic
398C2×C101#319811yescharacteristic
399C2×C101#319911yescharacteristic
400C2×C101#322011yescharacteristic
401C2×C101#322411yescharacteristic
402C2×#447C2×C10111yescharacteristic
403#2324C2×C10111yescharacteristic, complemented
404#2309C2×C10111yescharacteristic, complemented
405#1972C2×C10111yescharacteristic, complemented
406#1970C2×C10111yescharacteristic, complemented
407#1936C2×C10111yescharacteristic, complemented
408#1934C2×C10111yescharacteristic, complemented
409#1926C2×C10111yescharacteristic, complemented
410#1925C2×C10111yescharacteristic, complemented
411#1879C2×C10111yescharacteristic, complemented
412#1879C2×C10111yescharacteristic, complemented
413#1875C2×C10111yescharacteristic, complemented
414#1854C2×C10111yescharacteristic, complemented
415#1786C2×C10111yescharacteristic, complemented
416#1750C2×C10111yescharacteristic, complemented
417C101#2205611yescharacteristic, direct product factor, Sylow
418C23×D4C22×C10111yescharacteristic
419C22×D8C22×C10111yescharacteristic
420C22×D8C22×C10111yescharacteristic
421C2×#121C22×C10111yescharacteristic
422C2×C4×D4C22×C10111yescharacteristic, complemented
423C2×#117C22×C10111yescharacteristic
424C2×#117C22×C10111yescharacteristic
425#447C4×C10118yescomplemented
426C2×#107C22×C10111yescharacteristic, complemented
427C2×#106C22×C10111yescharacteristic, complemented
428C2×#102C22×C10111yescharacteristic
429C2×#102C22×C10111yescharacteristic
430C2×#102C22×C10111yescharacteristic
431C2×#102C22×C10111yescharacteristic
432C2×#102C22×C10111yescharacteristic
433C2×#102C22×C10111yescharacteristic
434C2×#102C22×C10111yescharacteristic, complemented
435C2×#102C22×C10111yescharacteristic, complemented
436C2×C22⋊C8C22×C10111yescharacteristic
437C2×C22⋊C8C22×C10111yescharacteristic
438C2×#97C22×C10111yescharacteristic, complemented
439C2×C4×C8C22×C10111yescharacteristic, complemented
440#390—21no—
441#390—21no—
442#390—21no—
443#390C22×C10111yescharacteristic
444#390C22×C10111yescharacteristic
445#390C22×C10111yescharacteristic
446#390C22×C10111yescharacteristic
447#390C22×C10111yescharacteristic, complemented
448#389C22×C10111yescharacteristic, complemented
449#388—21no—
450#386—21no—
451#385—21no—
452#380C22×C10111yescharacteristic
453#379—21no—
454#379—21no—
455C4×C4⋊C4C22×C10111yescharacteristic, complemented
456#340C22×C10111yescharacteristic, complemented
457#340C22×C10111yescharacteristic, complemented
458#340C22×C10111yescharacteristic, complemented
459#340C22×C10111yescharacteristic, complemented
460#336C22×C10111yescharacteristic, complemented
461#336C22×C10111yescharacteristic, complemented
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×C4×C10114yescomplemented
471C22×D4C23×C10111yescharacteristic
472C22×D4C23×C10111yescharacteristic
473C22×D4C23×C10111yescharacteristic
474C23×C4—21no—
475C23×C4C23×C10111yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×C4×C10114yes—
481C2×D8C2×C4×C10114yes—
482C22×C8C23×C10111yescharacteristic
483C22×C8C23×C10111yescharacteristic
484C22×C8C23×C10111yescharacteristic
485C22×C8C23×C10111yescharacteristic
486#121—22no—
487#121C2×C4×C10114yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4D4×C10111yescharacteristic
496C2×C4⋊C4D4×C10111yescharacteristic
497C2×C4⋊C4C23×C10111yescharacteristic
498C2×C4⋊C4C23×C10111yescharacteristic
499C2×C4⋊C4C23×C10111yescharacteristic
500C2×C4⋊C4C23×C10111yescharacteristic
501C2×C4⋊C4C23×C10111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C10111yescharacteristic
517C2×C22⋊C4D4×C10111yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C10111yescharacteristic
521C2×C42C23×C10111yescharacteristic
522#107—41no—
523#106—41no—
524#102—41no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102C2×C4×C10114yescomplemented
531#102C2×C4×C10114yescomplemented
532C22⋊C8—22no—
533C22⋊C8C2×C4×C10114yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24C2×D4×C10111yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×C4×C10112yes—
576C2×D4C22×C4×C10112yes—
577C2×D4C22×C4×C10112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×C4×C10112yes—
591C22×C4C2×D4×C10111yescharacteristic
592C22×C4C2×D4×C10111yescharacteristic
593C22×C4C2×D4×C10111yescharacteristic
594C22×C4C2×D4×C10111yescharacteristic
595C22×C4C2×D4×C10111yescharacteristic
596C22×C4#41×C10112yes—
597C22×C4C24×C10111yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C22×C4×C10112yes—
611C2×C8C22×C4×C10112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—81no—
624C4⋊C4C22×C4×C10112yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C4×D4×C10112yes—
682C23C22×D4×C10111yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4C4×D4×C10112yes—
732C2×C4C23×C4×C10111yescharacteristic
733C2×C4C2×#41×C10111yescharacteristic
734C2×C4H(5,𝔽2)×C10111yescharacteristic
735C2×C4H(5,𝔽2)×C10111yescharacteristic
736C2×C4H(5,𝔽2)×C10111yescharacteristic
737C2×C4H(5,𝔽2)×C10111yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C4×D4×C10111yescharacteristic
772C22#534×C10111yescharacteristic
773C22#535×C10111yescharacteristic
774C22#576×C10111yescharacteristic
775C22#576×C10111yescharacteristic
776C22#576×C10111yescharacteristic
777C22#577×C10111yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4#518×C10111yescharacteristic
789C4#518×C10111yescharacteristic
790C4#538×C10111yescharacteristic
791C4#538×C10111yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2C101×#232111yescharacteristic
797C2C101×#294611yescharacteristic
798C2C101×#294811yescharacteristic
799C2C101×#319811yescharacteristic
800C2C101×#319911yescharacteristic
801C2C101×#322011yescharacteristic
802C2C101×#322411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#447×C101C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×#117×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2324C2semidirect
3. C101×#2309C2semidirect
4. C101×#1972C2semidirect
5. C101×#1970C2semidirect
6. C101×#1936C2semidirect
7. C101×#1934C2semidirect
8. C101×#1926C2semidirect
9. C101×#1925C2semidirect
10. C101×#1879C2semidirect
11. C101×#1879C2semidirect
12. C101×#1875C2semidirect
13. C101×#1854C2semidirect
14. C101×#1786C2semidirect
15. C101×#1750C2semidirect
20. C2×C4×D4×C101C22semidirect
23. #447×C101C4semidirect
24. C2×#107×C101C22semidirect
25. C2×#106×C101C22semidirect
32. C2×#102×C101C22semidirect
33. C2×#102×C101C22semidirect
36. C2×#97×C101C22semidirect
37. C2×C4×C8×C101C22semidirect
45. #390×C101C22semidirect
46. #389×C101C22semidirect
53. C4×C4⋊C4×C101C22semidirect
54. #340×C101C22semidirect
55. #340×C101C22semidirect
56. #340×C101C22semidirect
57. #340×C101C22semidirect
58. #336×C101C22semidirect
59. #336×C101C22semidirect
68. C22×D4×C101C2×C4semidirect
128. #102×C101C2×C4semidirect
129. #102×C101C2×C4semidirect
131. C22⋊C8×C101C2×C4semidirect
390. #22056C101direct (N × H)
403. #2324C2×C101semidirect
404. #2309C2×C101semidirect
405. #1972C2×C101semidirect
406. #1970C2×C101semidirect
407. #1936C2×C101semidirect
408. #1934C2×C101semidirect
409. #1926C2×C101semidirect
410. #1925C2×C101semidirect
411. #1879C2×C101semidirect
412. #1879C2×C101semidirect
413. #1875C2×C101semidirect
414. #1854C2×C101semidirect
415. #1786C2×C101semidirect
416. #1750C2×C101semidirect
417. C101#22056direct (N × H)
422. C2×C4×D4C22×C101semidirect
425. #447C4×C101semidirect
426. C2×#107C22×C101semidirect
427. C2×#106C22×C101semidirect
434. C2×#102C22×C101semidirect
435. C2×#102C22×C101semidirect
438. C2×#97C22×C101semidirect
439. C2×C4×C8C22×C101semidirect
447. #390C22×C101semidirect
448. #389C22×C101semidirect
455. C4×C4⋊C4C22×C101semidirect
456. #340C22×C101semidirect
457. #340C22×C101semidirect
458. #340C22×C101semidirect
459. #340C22×C101semidirect
460. #336C22×C101semidirect
461. #336C22×C101semidirect
470. C22×D4C2×C4×C101semidirect
530. #102C2×C4×C101semidirect
531. #102C2×C4×C101semidirect
533. C22⋊C8C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1012
C101×#23242
C101×#23092
C101×#19722
C101×#19702
C101×#19362
C101×#19342
C101×#19262
C101×#19252
C101×#18792
C101×#18752
C101×#18542
C101×#17862
C101×#17502
#22056101