Finite Group Databasebeta

← C101×#25553 #38807704

Subgroups — C101×#25553 #38807704

Order 25856.

1200 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C101C211yesmaximal, characteristic, complemented
2C2×#480×C101C211yesmaximal, characteristic, complemented
3C2×#469×C101C211yesmaximal, characteristic, complemented
4C101×#2414C211yesmaximal, characteristic, complemented
5C101×#2059C211yesmaximal, characteristic, complemented
6C101×#2033C211yesmaximal, characteristic, complemented
7C101×#2025C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1879C211yesmaximal, characteristic, complemented
10C101×#1875C211yesmaximal, characteristic, complemented
11C101×#1875C211yesmaximal, characteristic, complemented
12C101×#1870C211yesmaximal, characteristic, complemented
13C101×#1862C211yesmaximal, characteristic, complemented
14C101×#1854C211yesmaximal, characteristic, complemented
15C101×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×M16×C101C2211yescharacteristic
18#553×C101—24no—
19#553×C101—24no—
20C2×#126×C101—21no—
21C2×#125×C101C2211yescharacteristic
22C2×#123×C101—21no—
23C2×#121×C101—21no—
24C2×#121×C101C2211yescharacteristic
25C2×#121×C101C2211yescharacteristic
26C2×#121×C101C2211yescharacteristic
27C2×#121×C101C2211yescharacteristic
28C2×C4×D4×C101—21no—
29C2×C4×D4×C101C2211yescharacteristic
30C2×C4×D4×C101C2211yescharacteristic
31C2×#117×C101C2211yescharacteristic
32C2×#117×C101C2211yescharacteristic
33C22×C4⋊C4×C101C2211yescharacteristic
34#480×C101—24no—
35#469×C101—24no—
36C2×#107×C101C2211yescharacteristic
37C2×#107×C101C2211yescharacteristic
38C2×#106×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×C22⋊C8×C101C2211yescharacteristic
46C2×C22⋊C8×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48#394×C101—21no—
49#392×C101—21no—
50#390×C101—21no—
51#390×C101C2211yescharacteristic
52#389×C101C2211yescharacteristic
53#388×C101—21no—
54#380×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101D411yescharacteristic
68C22×D4×C101C2311yescharacteristic
69C22×D4×C101C2311yescharacteristic
70C23×C4×C101—21no—
71C23×C4×C101—21no—
72C23×C4×C101C2311yescharacteristic
73C23×C4×C101C2311yescharacteristic
74C2×D8×C101—22no—
75C2×D8×C101—22no—
76C2×D8×C101—41no—
77C2×M16×C101—22no—
78C2×M16×C101—22no—
79C2×M16×C101—41no—
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83C22×C8×C101C2311yescharacteristic
84#126×C101—28no—
85#125×C101—22no—
86#125×C101—22no—
87#123×C101—28no—
88#121×C101—28no—
89#121×C101—22no—
90#121×C101—22no—
91#121×C101—22no—
92#121×C101—22no—
93#121×C101—22no—
94#121×C101—22no—
95#121×C101—41no—
96#121×C101D414yescomplemented
97C4×D4×C101—28no—
98C4×D4×C101—22no—
99C4×D4×C101—22no—
100C4×D4×C101—22no—
101C4×D4×C101—22no—
102#117×C101—22no—
103#117×C101—22no—
104#117×C101—22no—
105#117×C101—41no—
106C2×C4⋊C4×C101—21no—
107C2×C4⋊C4×C101—22no—
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101D411yescharacteristic
112C2×C4⋊C4×C101D414yescomplemented
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101—21no—
121C2×C22⋊C4×C101—21no—
122C2×C22⋊C4×C101—21no—
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101D411yescharacteristic
130C2×C22⋊C4×C101D411yescharacteristic
131C2×C42×C101—21no—
132C2×C42×C101—21no—
133C2×C42×C101C2311yescharacteristic
134#107×C101—22no—
135#107×C101—22no—
136#106×C101—22no—
137#102×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—41no—
143C22⋊C8×C101—22no—
144C22⋊C8×C101—22no—
145C22⋊C8×C101—41no—
146#95×C101—21no—
147#95×C101—21no—
148C24×C101—21no—
149C24×C101—21no—
150C24×C101C2×D411yescharacteristic
151C24×C101C2×D411yescharacteristic
152C2×D4×C101—22no—
153C2×D4×C101—24no—
154C2×D4×C101—24no—
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—21no—
166C2×D4×C101—41no—
167C2×D4×C101—41no—
168C2×D4×C101—42no—
169C2×D4×C101—42no—
170C2×D4×C101—42no—
171C2×D4×C101—42no—
172C2×D4×C101—42no—
173C2×D4×C101—81no—
174C2×D4×C101—81no—
175C2×D4×C101—81no—
176C2×D4×C101—81no—
177C2×D4×C101—81no—
178C2×D4×C101C2×D412yes—
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—21no—
186C22×C4×C101—21no—
187C22×C4×C101—24no—
188C22×C4×C101—24no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—81no—
198C22×C4×C101—81no—
199C22×C4×C101—81no—
200C22×C4×C101—81no—
201C22×C4×C101C2×D411yescharacteristic
202C22×C4×C101C2×D411yescharacteristic
203C22×C4×C101C2×D411yescharacteristic
204C22×C4×C101C2×D411yescharacteristic
205C22×C4×C101C2×D412yes—
206C22×C4×C101C2×D412yes—
207C22×C4×C101C2411yescharacteristic
208D8×C101—44no—
209M16×C101—44no—
210C2×C8×C101—21no—
211C2×C8×C101—21no—
212C2×C8×C101—21no—
213C2×C8×C101—21no—
214C2×C8×C101—21no—
215C2×C8×C101—21no—
216C2×C8×C101—21no—
217C2×C8×C101—21no—
218C2×C8×C101—21no—
219C2×C8×C101—21no—
220C2×C8×C101—21no—
221C2×C8×C101#4112yes—
222C4⋊C4×C101—24no—
223C4⋊C4×C101—24no—
224C4⋊C4×C101—24no—
225C4⋊C4×C101—22no—
226C4⋊C4×C101—21no—
227C4⋊C4×C101—21no—
228C4⋊C4×C101—21no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—21no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—81no—
235C4⋊C4×C101C2×D412yes—
236C4⋊C4×C101C2×D412yes—
237C4⋊C4×C101C2×D412yes—
238C4⋊C4×C101#4112yes—
239C22⋊C4×C101—24no—
240C22⋊C4×C101—24no—
241C22⋊C4×C101—24no—
242C22⋊C4×C101—22no—
243C22⋊C4×C101—24no—
244C22⋊C4×C101—22no—
245C22⋊C4×C101—42no—
246C22⋊C4×C101—42no—
247C22⋊C4×C101—42no—
248C22⋊C4×C101—42no—
249C22⋊C4×C101—81no—
250C22⋊C4×C101—81no—
251C42×C101—24no—
252C42×C101—21no—
253C42×C101—21no—
254C42×C101—42no—
255C23×C101—21no—
256C23×C101—21no—
257C23×C101—21no—
258C23×C101—21no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—21no—
262C23×C101—22no—
263C23×C101—21no—
264C23×C101—21no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—41no—
274C23×C101—41no—
275C23×C101—41no—
276C23×C101—41no—
277C23×C101—41no—
278C23×C101—41no—
279C23×C101—41no—
280C23×C101—41no—
281C23×C101—41no—
282C23×C101#12012yes—
283C23×C101C22×D411yescharacteristic
284D4×C101—22no—
285D4×C101—22no—
286D4×C101—44no—
287D4×C101—48no—
288D4×C101—41no—
289D4×C101—41no—
290D4×C101—41no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—41no—
294D4×C101—84no—
295D4×C101—84no—
296D4×C101—84no—
297C2×C4×C101—21no—
298C2×C4×C101—21no—
299C2×C4×C101—22no—
300C2×C4×C101—22no—
301C2×C4×C101—22no—
302C2×C4×C101—22no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—22no—
306C2×C4×C101—21no—
307C2×C4×C101—22no—
308C2×C4×C101—22no—
309C2×C4×C101—22no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
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—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—84no—
335C2×C4×C101—84no—
336C2×C4×C101#12012yes—
337C2×C4×C101C22×D411yescharacteristic
338C2×C4×C101C22×D411yescharacteristic
339C2×C4×C101C2×#4111yescharacteristic
340C2×C4×C101C2×#4111yescharacteristic
341C2×C4×C101H(5,𝔽2)11yescharacteristic
342C2×C4×C1012−1+411yescharacteristic
343C8×C101—22no—
344C8×C101—41no—
345C8×C101—41no—
346C8×C101—41no—
347C22×C101—22no—
348C22×C101—22no—
349C22×C101—22no—
350C22×C101—41no—
351C22×C101—41no—
352C22×C101—41no—
353C22×C101—41no—
354C22×C101—41no—
355C22×C101—41no—
356C22×C101—41no—
357C22×C101—42no—
358C22×C101—41no—
359C22×C101—42no—
360C22×C101—42no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—41no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101—81no—
368C22×C101—81no—
369C22×C101—81no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101—81no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101C2×#12011yescharacteristic
376C22×C101#54611yescharacteristic
377C22×C101#54711yescharacteristic
378C22×C101#57511yescharacteristic
379C22×C101#57511yescharacteristic
380C22×C101#57611yescharacteristic
381C22×C101#57611yescharacteristic
382C4×C101—22no—
383C4×C101—41no—
384C4×C101—41no—
385C4×C101—42no—
386C4×C101—41no—
387C4×C101—42no—
388C4×C101—42no—
389C4×C101—42no—
390C4×C101—81no—
391C4×C101—81no—
392C4×C101#53211yescharacteristic
393C4×C101#53711yescharacteristic
394C4×C101#54611yescharacteristic
395C4×C101#54711yescharacteristic
396#25553C10111yesmaximal, characteristic, direct product factor, Sylow
397C2×C101—42no—
398C2×C101—81no—
399C2×C101—82no—
400C2×C101—161no—
401C2×C101#243011yescharacteristic
402C2×C101#300511yescharacteristic
403C2×C101#300811yescharacteristic
404C2×C101#330911yescharacteristic
405C2×C101#332211yescharacteristic
406C2×C101#334711yescharacteristic
407C2×C101#335511yescharacteristic
408C2×#553C2×C10111yescharacteristic, complemented
409C2×#480C2×C10111yescharacteristic, complemented
410C2×#469C2×C10111yescharacteristic, complemented
411#2414C2×C10111yescharacteristic, complemented
412#2059C2×C10111yescharacteristic, complemented
413#2033C2×C10111yescharacteristic, complemented
414#2025C2×C10111yescharacteristic, complemented
415#1999C2×C10111yescharacteristic, complemented
416#1879C2×C10111yescharacteristic, complemented
417#1875C2×C10111yescharacteristic, complemented
418#1875C2×C10111yescharacteristic, complemented
419#1870C2×C10111yescharacteristic, complemented
420#1862C2×C10111yescharacteristic, complemented
421#1854C2×C10111yescharacteristic, complemented
422#1736C2×C10111yescharacteristic, complemented
423C101#2555311yescharacteristic, direct product factor, Sylow
424C22×D8C22×C10111yescharacteristic
425C22×M16C22×C10111yescharacteristic
426#553—24no—
427#553—24no—
428C2×#126—21no—
429C2×#125C22×C10111yescharacteristic
430C2×#123—21no—
431C2×#121—21no—
432C2×#121C22×C10111yescharacteristic
433C2×#121C22×C10111yescharacteristic
434C2×#121C22×C10111yescharacteristic
435C2×#121C22×C10111yescharacteristic
436C2×C4×D4—21no—
437C2×C4×D4C22×C10111yescharacteristic
438C2×C4×D4C22×C10111yescharacteristic
439C2×#117C22×C10111yescharacteristic
440C2×#117C22×C10111yescharacteristic
441C22×C4⋊C4C22×C10111yescharacteristic
442#480—24no—
443#469—24no—
444C2×#107C22×C10111yescharacteristic
445C2×#107C22×C10111yescharacteristic
446C2×#106C22×C10111yescharacteristic
447C2×#102C22×C10111yescharacteristic
448C2×#102C22×C10111yescharacteristic
449C2×#102C22×C10111yescharacteristic
450C2×#102C22×C10111yescharacteristic
451C2×#102C22×C10111yescharacteristic
452C2×#102C22×C10111yescharacteristic
453C2×C22⋊C8C22×C10111yescharacteristic
454C2×C22⋊C8C22×C10111yescharacteristic
455C2×C22⋊C8C22×C10111yescharacteristic
456#394—21no—
457#392—21no—
458#390—21no—
459#390C22×C10111yescharacteristic
460#389C22×C10111yescharacteristic
461#388—21no—
462#380C22×C10111yescharacteristic
463#340C22×C10111yescharacteristic
464#340C22×C10111yescharacteristic
465#340C22×C10111yescharacteristic
466#340C22×C10111yescharacteristic
467#340C22×C10111yescharacteristic
468#340C22×C10111yescharacteristic
469#336C22×C10111yescharacteristic
470#336C22×C10111yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C10111yescharacteristic
476C22×D4C23×C10111yescharacteristic
477C22×D4C23×C10111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C23×C10111yescharacteristic
481C23×C4C23×C10111yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—41no—
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C22×C8C23×C10111yescharacteristic
489C22×C8C23×C10111yescharacteristic
490C22×C8C23×C10111yescharacteristic
491C22×C8C23×C10111yescharacteristic
492#126—28no—
493#125—22no—
494#125—22no—
495#123—28no—
496#121—28no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—41no—
504#121D4×C10114yescomplemented
505C4×D4—28no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—41no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C10111yescharacteristic
520C2×C4⋊C4D4×C10114yescomplemented
521C2×C4⋊C4C23×C10111yescharacteristic
522C2×C4⋊C4C23×C10111yescharacteristic
523C2×C4⋊C4C23×C10111yescharacteristic
524C2×C4⋊C4C23×C10111yescharacteristic
525C2×C4⋊C4C23×C10111yescharacteristic
526C2×C4⋊C4C23×C10111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4D4×C10111yescharacteristic
538C2×C22⋊C4D4×C10111yescharacteristic
539C2×C42—21no—
540C2×C42—21no—
541C2×C42C23×C10111yescharacteristic
542#107—22no—
543#107—22no—
544#106—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—41no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C10111yescharacteristic
559C24C2×D4×C10111yescharacteristic
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4C2×D4×C10112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C10111yescharacteristic
610C22×C4C2×D4×C10111yescharacteristic
611C22×C4C2×D4×C10111yescharacteristic
612C22×C4C2×D4×C10111yescharacteristic
613C22×C4C2×D4×C10112yes—
614C22×C4C2×D4×C10112yes—
615C22×C4C24×C10111yescharacteristic
616D8—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8#41×C10112yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—81no—
643C4⋊C4C2×D4×C10112yes—
644C4⋊C4C2×D4×C10112yes—
645C4⋊C4C2×D4×C10112yes—
646C4⋊C4#41×C10112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23#120×C10112yes—
691C23C22×D4×C10111yescharacteristic
692D4—22no—
693D4—22no—
694D4—44no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4#120×C10112yes—
745C2×C4C22×D4×C10111yescharacteristic
746C2×C4C22×D4×C10111yescharacteristic
747C2×C4C2×#41×C10111yescharacteristic
748C2×C4C2×#41×C10111yescharacteristic
749C2×C4H(5,𝔽2)×C10111yescharacteristic
750C2×C42−1+4×C10111yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C10111yescharacteristic
784C22#546×C10111yescharacteristic
785C22#547×C10111yescharacteristic
786C22#575×C10111yescharacteristic
787C22#575×C10111yescharacteristic
788C22#576×C10111yescharacteristic
789C22#576×C10111yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4#532×C10111yescharacteristic
801C4#537×C10111yescharacteristic
802C4#546×C10111yescharacteristic
803C4#547×C10111yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—161no—
808C2C101×#243011yescharacteristic
809C2C101×#300511yescharacteristic
810C2C101×#300811yescharacteristic
811C2C101×#330911yescharacteristic
812C2C101×#332211yescharacteristic
813C2C101×#334711yescharacteristic
814C2C101×#335511yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#553×C101C2semidirect
2. C2×#480×C101C2semidirect
3. C2×#469×C101C2semidirect
4. C101×#2414C2semidirect
5. C101×#2059C2semidirect
6. C101×#2033C2semidirect
7. C101×#2025C2semidirect
8. C101×#1999C2semidirect
9. C101×#1879C2semidirect
10. C101×#1875C2semidirect
11. C101×#1875C2semidirect
12. C101×#1870C2semidirect
13. C101×#1862C2semidirect
14. C101×#1854C2semidirect
15. C101×#1736C2semidirect
96. #121×C101D4semidirect
112. C2×C4⋊C4×C101D4semidirect
396. #25553C101direct (N × H)
408. C2×#553C2×C101semidirect
409. C2×#480C2×C101semidirect
410. C2×#469C2×C101semidirect
411. #2414C2×C101semidirect
412. #2059C2×C101semidirect
413. #2033C2×C101semidirect
414. #2025C2×C101semidirect
415. #1999C2×C101semidirect
416. #1879C2×C101semidirect
417. #1875C2×C101semidirect
418. #1875C2×C101semidirect
419. #1870C2×C101semidirect
420. #1862C2×C101semidirect
421. #1854C2×C101semidirect
422. #1736C2×C101semidirect
423. C101#25553direct (N × H)
504. #121D4×C101semidirect
520. C2×C4⋊C4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1012
C2×#480×C1012
C2×#469×C1012
C101×#24142
C101×#20592
C101×#20332
C101×#20252
C101×#19992
C101×#18792
C101×#18752
C101×#18702
C101×#18622
C101×#18542
C101×#17362
#25553101