Finite Group Databasebeta

← C101×#24428 #38806579

Subgroups — C101×#24428 #38806579

Order 25856.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic, complemented
2C2×#466×C101C211yesmaximal, characteristic, complemented
3C2×#449×C101C211yesmaximal, characteristic, complemented
4C2×#447×C101C211yesmaximal, characteristic, complemented
5C2×#416×C101C211yesmaximal, characteristic, complemented
6C101×#2414C211yesmaximal, characteristic, complemented
7C101×#2042C211yesmaximal, characteristic, complemented
8C101×#2036C211yesmaximal, characteristic, complemented
9C101×#2012C211yesmaximal, characteristic, complemented
10C101×#2000C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic, complemented
12C101×#1875C211yesmaximal, characteristic, complemented
13C101×#1869C211yesmaximal, characteristic, complemented
14C101×#1862C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic, complemented
19C22×D8×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21C23×C8×C101C2211yescharacteristic, complemented
22#546×C101—24no—
23#546×C101—24no—
24C2×#124×C101C2211yescharacteristic
25C2×#123×C101—21no—
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×#121×C101—21no—
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic, complemented
31C2×#120×C101—21no—
32C2×C4×D4×C101C2211yescharacteristic
33C2×C4×D4×C101C2211yescharacteristic
34C2×#117×C101C2211yescharacteristic, complemented
35C22×C22⋊C4×C101—21no—
36#466×C101—24no—
37#449×C101—24no—
38#447×C101—24no—
39C2×#107×C101C2211yescharacteristic, complemented
40#416×C101—24no—
41C2×#103×C101C2211yescharacteristic, complemented
42C2×#103×C101C2211yescharacteristic, complemented
43C2×#103×C101C2211yescharacteristic, complemented
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×#102×C101C2211yescharacteristic, complemented
51C2×C22⋊C8×C101C2211yescharacteristic
52C2×C22⋊C8×C101C2211yescharacteristic
53C2×C22⋊C8×C101C2211yescharacteristic, complemented
54#394×C101—21no—
55#392×C101—21no—
56#390×C101—21no—
57#390×C101C2211yescharacteristic, complemented
58#389×C101C2211yescharacteristic, complemented
59#388×C101—21no—
60#380×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic, complemented
62#340×C101C2211yescharacteristic, complemented
63#336×C101C2211yescharacteristic, complemented
64#336×C101C2211yescharacteristic, complemented
65C25×C101—21no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—41no—
70C2×#41×C101—41no—
71C2×#41×C101D414yescomplemented
72C22×Q8×C101C2311yescharacteristic
73C22×D4×C101—21no—
74C22×D4×C101—21no—
75C22×D4×C101—22no—
76C22×D4×C101—22no—
77C22×D4×C101—22no—
78C22×D4×C101—22no—
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—41no—
83C22×D4×C101—41no—
84C22×D4×C101D411yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C22×D4×C101C2311yescharacteristic
87C22×D4×C101C2311yescharacteristic
88C23×C4×C101—21no—
89C23×C4×C101—21no—
90C23×C4×C101C2311yescharacteristic
91C23×C4×C101C2311yescharacteristic
92C2×SD16×C101—22no—
93C2×SD16×C101—41no—
94C2×SD16×C101—41no—
95C2×D8×C101—22no—
96C2×D8×C101—22no—
97C2×D8×C101—22no—
98C2×D8×C101—22no—
99C2×D8×C101—22no—
100C2×D8×C101—41no—
101C22×C8×C101—22no—
102C22×C8×C101—22no—
103C22×C8×C101—41no—
104C22×C8×C101C2311yescharacteristic
105C22×C8×C101C2311yescharacteristic
106C22×C8×C101C2311yescharacteristic
107C22×C8×C101C2311yescharacteristic
108#124×C101—22no—
109#124×C101—22no—
110#123×C101—28no—
111C22⋊Q8×C101—22no—
112C22⋊Q8×C101—22no—
113#121×C101—28no—
114#121×C101—22no—
115#121×C101—22no—
116#121×C101—22no—
117#121×C101—22no—
118#121×C101—41no—
119#121×C101D414yescomplemented
120#120×C101—28no—
121C4×D4×C101—22no—
122C4×D4×C101—22no—
123C4×D4×C101—22no—
124C4×D4×C101—22no—
125#117×C101—22no—
126#117×C101—41no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101—21no—
129C2×C4⋊C4×C101D411yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C4⋊C4×C101C2311yescharacteristic
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C4⋊C4×C101C2311yescharacteristic
134C2×C22⋊C4×C101—28no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101—21no—
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101—21no—
140C2×C22⋊C4×C101—21no—
141C2×C22⋊C4×C101—21no—
142C2×C22⋊C4×C101—21no—
143C2×C22⋊C4×C101—21no—
144C2×C22⋊C4×C101—21no—
145C2×C22⋊C4×C101—21no—
146C2×C22⋊C4×C101D411yescharacteristic
147C2×C22⋊C4×C101D411yescharacteristic
148C2×C42×C101—21no—
149C2×C42×C101C2311yescharacteristic
150#107×C101—22no—
151#103×C101—22no—
152#103×C101—22no—
153#103×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—22no—
158#102×C101—22no—
159#102×C101—41no—
160#102×C101D414yescomplemented
161C22⋊C8×C101—22no—
162C22⋊C8×C101—22no—
163C22⋊C8×C101—41no—
164#95×C101—21no—
165#95×C101—21no—
166C24×C101—21no—
167C24×C101—24no—
168C24×C101—21no—
169C24×C101—21no—
170C24×C101—42no—
171C24×C101—42no—
172C24×C101—42no—
173C24×C101—42no—
174C24×C101—81no—
175C24×C101—81no—
176C24×C101C2×D411yescharacteristic
177C24×C101C2×D411yescharacteristic
178#41×C101—28no—
179#41×C101—44no—
180#41×C101—44no—
181#41×C101—44no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101—21no—
187C2×Q8×C101C2×D412yes—
188C2×D4×C101—24no—
189C2×D4×C101—22no—
190C2×D4×C101—24no—
191C2×D4×C101—22no—
192C2×D4×C101—24no—
193C2×D4×C101—21no—
194C2×D4×C101—21no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—21no—
207C2×D4×C101—41no—
208C2×D4×C101—42no—
209C2×D4×C101—42no—
210C2×D4×C101—42no—
211C2×D4×C101—44no—
212C2×D4×C101—44no—
213C2×D4×C101—44no—
214C2×D4×C101—42no—
215C2×D4×C101—42no—
216C2×D4×C101—44no—
217C2×D4×C101—42no—
218C2×D4×C101—42no—
219C2×D4×C101—81no—
220C2×D4×C101—81no—
221C2×D4×C101—81no—
222C2×D4×C101—81no—
223C2×D4×C101—81no—
224C2×D4×C101C2×D412yes—
225C2×D4×C101C2×D412yes—
226C2×D4×C101C2×D412yes—
227C2×D4×C101#4112yes—
228C22×C4×C101—21no—
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—24no—
236C22×C4×C101—24no—
237C22×C4×C101—21no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—21no—
245C22×C4×C101—42no—
246C22×C4×C101—42no—
247C22×C4×C101—81no—
248C22×C4×C101—81no—
249C22×C4×C101C2×D411yescharacteristic
250C22×C4×C101C2×D411yescharacteristic
251C22×C4×C101C2×D411yescharacteristic
252C22×C4×C101C2×D411yescharacteristic
253C22×C4×C101C2×D412yes—
254C22×C4×C101C2×D412yes—
255C22×C4×C101C2411yescharacteristic
256SD16×C101—44no—
257D8×C101—44no—
258D8×C101—44no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C2×C8×C101—21no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—21no—
267C2×C8×C101—21no—
268C2×C8×C101—21no—
269C2×C8×C101—21no—
270C2×C8×C101—44no—
271C2×C8×C101C2×D412yes—
272C4⋊C4×C101—24no—
273C4⋊C4×C101—22no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—21no—
279C4⋊C4×C101—21no—
280C4⋊C4×C101—81no—
281C4⋊C4×C101C2×D412yes—
282C4⋊C4×C101C2×D412yes—
283C22⋊C4×C101—24no—
284C22⋊C4×C101—24no—
285C22⋊C4×C101—24no—
286C22⋊C4×C101—24no—
287C22⋊C4×C101—22no—
288C22⋊C4×C101—22no—
289C22⋊C4×C101—24no—
290C22⋊C4×C101—42no—
291C22⋊C4×C101—42no—
292C22⋊C4×C101—42no—
293C22⋊C4×C101—42no—
294C22⋊C4×C101—81no—
295C22⋊C4×C101—81no—
296C42×C101—21no—
297C42×C101—21no—
298C42×C101—42no—
299C23×C101—21no—
300C23×C101—22no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—22no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—22no—
307C23×C101—21no—
308C23×C101—21no—
309C23×C101—21no—
310C23×C101—21no—
311C23×C101—21no—
312C23×C101—21no—
313C23×C101—21no—
314C23×C101—22no—
315C23×C101—48no—
316C23×C101—48no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—41no—
321C23×C101—41no—
322C23×C101—41no—
323C23×C101—41no—
324C23×C101—41no—
325C23×C101—41no—
326C23×C101—41no—
327C23×C101—41no—
328C23×C101—41no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—41no—
333C23×C101—41no—
334C23×C101—84no—
335C23×C101—84no—
336C23×C101—84no—
337C23×C101—84no—
338C23×C101—84no—
339C23×C101#12012yes—
340C23×C101#13512yes—
341C23×C101C22×D411yescharacteristic
342Q8×C101—22no—
343Q8×C101—22no—
344Q8×C101—41no—
345Q8×C101—41no—
346D4×C101—22no—
347D4×C101—22no—
348D4×C101—22no—
349D4×C101—22no—
350D4×C101—22no—
351D4×C101—44no—
352D4×C101—48no—
353D4×C101—48no—
354D4×C101—41no—
355D4×C101—41no—
356D4×C101—41no—
357D4×C101—41no—
358D4×C101—41no—
359D4×C101—41no—
360D4×C101—84no—
361D4×C101—84no—
362D4×C101—84no—
363D4×C101#12114yes—
364C2×C4×C101—21no—
365C2×C4×C101—21no—
366C2×C4×C101—22no—
367C2×C4×C101—22no—
368C2×C4×C101—22no—
369C2×C4×C101—22no—
370C2×C4×C101—21no—
371C2×C4×C101—21no—
372C2×C4×C101—22no—
373C2×C4×C101—22no—
374C2×C4×C101—21no—
375C2×C4×C101—22no—
376C2×C4×C101—21no—
377C2×C4×C101—21no—
378C2×C4×C101—21no—
379C2×C4×C101—21no—
380C2×C4×C101—21no—
381C2×C4×C101—21no—
382C2×C4×C101—48no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—84no—
400C2×C4×C101#12012yes—
401C2×C4×C101C22×D411yescharacteristic
402C2×C4×C101C22×D411yescharacteristic
403C2×C4×C101C22×D411yescharacteristic
404C2×C4×C101C2×#4111yescharacteristic
405C2×C4×C101H(5,𝔽2)11yescharacteristic
406C2×C4×C101H(5,𝔽2)11yescharacteristic
407C8×C101—22no—
408C8×C101—41no—
409C8×C101—41no—
410C8×C101—41no—
411C22×C101—22no—
412C22×C101—24no—
413C22×C101—22no—
414C22×C101—22no—
415C22×C101—22no—
416C22×C101—22no—
417C22×C101—22no—
418C22×C101—41no—
419C22×C101—42no—
420C22×C101—42no—
421C22×C101—41no—
422C22×C101—41no—
423C22×C101—41no—
424C22×C101—42no—
425C22×C101—41no—
426C22×C101—42no—
427C22×C101—41no—
428C22×C101—42no—
429C22×C101—41no—
430C22×C101—41no—
431C22×C101—42no—
432C22×C101—42no—
433C22×C101—42no—
434C22×C101—42no—
435C22×C101—816no—
436C22×C101—81no—
437C22×C101—81no—
438C22×C101—81no—
439C22×C101—81no—
440C22×C101—81no—
441C22×C101—81no—
442C22×C101—81no—
443C22×C101—81no—
444C22×C101—81no—
445C22×C101—81no—
446C22×C101—81no—
447C22×C101C2×#12011yescharacteristic
448C22×C101D4211yescharacteristic
449C22×C101#54611yescharacteristic
450C22×C101C2×#13511yescharacteristic
451C22×C101#57511yescharacteristic
452C22×C101#57611yescharacteristic
453C22×C101#57611yescharacteristic
454C4×C101—22no—
455C4×C101—41no—
456C4×C101—42no—
457C4×C101—41no—
458C4×C101—41no—
459C4×C101—42no—
460C4×C101—42no—
461C4×C101—81no—
462C4×C101—81no—
463C4×C101C2×#12111yescharacteristic
464C4×C101#53411yescharacteristic
465C4×C101D4211yescharacteristic
466C4×C101#54611yescharacteristic
467#24428C10111yesmaximal, characteristic, direct product factor, Sylow
468C2×C101—42no—
469C2×C101—42no—
470C2×C101—44no—
471C2×C101—82no—
472C2×C101—161no—
473C2×C101#241011yescharacteristic
474C2×C101#300211yescharacteristic
475C2×C101#300811yescharacteristic
476C2×C101#326811yescharacteristic
477C2×C101#328011yescharacteristic
478C2×C101#329711yescharacteristic
479C2×C101#331911yescharacteristic
480C2×#546C2×C10111yescharacteristic, complemented
481C2×#466C2×C10111yescharacteristic, complemented
482C2×#449C2×C10111yescharacteristic, complemented
483C2×#447C2×C10111yescharacteristic, complemented
484C2×#416C2×C10111yescharacteristic, complemented
485#2414C2×C10111yescharacteristic, complemented
486#2042C2×C10111yescharacteristic, complemented
487#2036C2×C10111yescharacteristic, complemented
488#2012C2×C10111yescharacteristic, complemented
489#2000C2×C10111yescharacteristic, complemented
490#1879C2×C10111yescharacteristic, complemented
491#1875C2×C10111yescharacteristic, complemented
492#1869C2×C10111yescharacteristic, complemented
493#1862C2×C10111yescharacteristic, complemented
494#1786C2×C10111yescharacteristic, complemented
495C101#2442811yescharacteristic, direct product factor, Sylow
496C22×#41C22×C10111yescharacteristic
497C23×D4C22×C10111yescharacteristic
498C22×SD16C22×C10111yescharacteristic, complemented
499C22×D8C22×C10111yescharacteristic
500C22×D8C22×C10111yescharacteristic
501C23×C8C22×C10111yescharacteristic, complemented
502#546—24no—
503#546—24no—
504C2×#124C22×C10111yescharacteristic
505C2×#123—21no—
506C2×C22⋊Q8C22×C10111yescharacteristic
507C2×#121—21no—
508C2×#121C22×C10111yescharacteristic
509C2×#121C22×C10111yescharacteristic
510C2×#121C22×C10111yescharacteristic, complemented
511C2×#120—21no—
512C2×C4×D4C22×C10111yescharacteristic
513C2×C4×D4C22×C10111yescharacteristic
514C2×#117C22×C10111yescharacteristic, complemented
515C22×C22⋊C4—21no—
516#466—24no—
517#449—24no—
518#447—24no—
519C2×#107C22×C10111yescharacteristic, complemented
520#416—24no—
521C2×#103C22×C10111yescharacteristic, complemented
522C2×#103C22×C10111yescharacteristic, complemented
523C2×#103C22×C10111yescharacteristic, complemented
524C2×#102C22×C10111yescharacteristic
525C2×#102C22×C10111yescharacteristic
526C2×#102C22×C10111yescharacteristic
527C2×#102C22×C10111yescharacteristic
528C2×#102C22×C10111yescharacteristic
529C2×#102C22×C10111yescharacteristic
530C2×#102C22×C10111yescharacteristic, complemented
531C2×C22⋊C8C22×C10111yescharacteristic
532C2×C22⋊C8C22×C10111yescharacteristic
533C2×C22⋊C8C22×C10111yescharacteristic, complemented
534#394—21no—
535#392—21no—
536#390—21no—
537#390C22×C10111yescharacteristic, complemented
538#389C22×C10111yescharacteristic, complemented
539#388—21no—
540#380C22×C10111yescharacteristic
541#340C22×C10111yescharacteristic, complemented
542#340C22×C10111yescharacteristic, complemented
543#336C22×C10111yescharacteristic, complemented
544#336C22×C10111yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C10114yescomplemented
552C22×Q8C23×C10111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C10111yescharacteristic
565C22×D4C23×C10111yescharacteristic
566C22×D4C23×C10111yescharacteristic
567C22×D4C23×C10111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C10111yescharacteristic
571C23×C4C23×C10111yescharacteristic
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C10111yescharacteristic
585C22×C8C23×C10111yescharacteristic
586C22×C8C23×C10111yescharacteristic
587C22×C8C23×C10111yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121D4×C10114yescomplemented
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C10111yescharacteristic
610C2×C4⋊C4C23×C10111yescharacteristic
611C2×C4⋊C4C23×C10111yescharacteristic
612C2×C4⋊C4C23×C10111yescharacteristic
613C2×C4⋊C4C23×C10111yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C10111yescharacteristic
627C2×C22⋊C4D4×C10111yescharacteristic
628C2×C42—21no—
629C2×C42C23×C10111yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102D4×C10114yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C10111yescharacteristic
657C24C2×D4×C10111yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C10112yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C10112yes—
705C2×D4C2×D4×C10112yes—
706C2×D4C2×D4×C10112yes—
707C2×D4#41×C10112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C10111yescharacteristic
730C22×C4C2×D4×C10111yescharacteristic
731C22×C4C2×D4×C10111yescharacteristic
732C22×C4C2×D4×C10111yescharacteristic
733C22×C4C2×D4×C10112yes—
734C22×C4C2×D4×C10112yes—
735C22×C4C24×C10111yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8C2×D4×C10112yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C10112yes—
762C4⋊C4C2×D4×C10112yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—48no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#120×C10112yes—
820C23#135×C10112yes—
821C23C22×D4×C10111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C10114yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C10112yes—
881C2×C4C22×D4×C10111yescharacteristic
882C2×C4C22×D4×C10111yescharacteristic
883C2×C4C22×D4×C10111yescharacteristic
884C2×C4C2×#41×C10111yescharacteristic
885C2×C4H(5,𝔽2)×C10111yescharacteristic
886C2×C4H(5,𝔽2)×C10111yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C10111yescharacteristic
928C22D42×C10111yescharacteristic
929C22#546×C10111yescharacteristic
930C22C2×#135×C10111yescharacteristic
931C22#575×C10111yescharacteristic
932C22#576×C10111yescharacteristic
933C22#576×C10111yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C10111yescharacteristic
944C4#534×C10111yescharacteristic
945C4D42×C10111yescharacteristic
946C4#546×C10111yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—161no—
952C2C101×#241011yescharacteristic
953C2C101×#300211yescharacteristic
954C2C101×#300811yescharacteristic
955C2C101×#326811yescharacteristic
956C2C101×#328011yescharacteristic
957C2C101×#329711yescharacteristic
958C2C101×#331911yescharacteristic
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×#546×C101C2semidirect
2. C2×#466×C101C2semidirect
3. C2×#449×C101C2semidirect
4. C2×#447×C101C2semidirect
5. C2×#416×C101C2semidirect
6. C101×#2414C2semidirect
7. C101×#2042C2semidirect
8. C101×#2036C2semidirect
9. C101×#2012C2semidirect
10. C101×#2000C2semidirect
11. C101×#1879C2semidirect
12. C101×#1875C2semidirect
13. C101×#1869C2semidirect
14. C101×#1862C2semidirect
15. C101×#1786C2semidirect
18. C22×SD16×C101C22semidirect
21. C23×C8×C101C22semidirect
30. C2×#121×C101C22semidirect
34. C2×#117×C101C22semidirect
39. C2×#107×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
43. C2×#103×C101C22semidirect
50. C2×#102×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
57. #390×C101C22semidirect
58. #389×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
63. #336×C101C22semidirect
64. #336×C101C22semidirect
71. C2×#41×C101D4semidirect
119. #121×C101D4semidirect
160. #102×C101D4semidirect
467. #24428C101direct (N × H)
480. C2×#546C2×C101semidirect
481. C2×#466C2×C101semidirect
482. C2×#449C2×C101semidirect
483. C2×#447C2×C101semidirect
484. C2×#416C2×C101semidirect
485. #2414C2×C101semidirect
486. #2042C2×C101semidirect
487. #2036C2×C101semidirect
488. #2012C2×C101semidirect
489. #2000C2×C101semidirect
490. #1879C2×C101semidirect
491. #1875C2×C101semidirect
492. #1869C2×C101semidirect
493. #1862C2×C101semidirect
494. #1786C2×C101semidirect
495. C101#24428direct (N × H)
498. C22×SD16C22×C101semidirect
501. C23×C8C22×C101semidirect
510. C2×#121C22×C101semidirect
514. C2×#117C22×C101semidirect
519. C2×#107C22×C101semidirect
521. C2×#103C22×C101semidirect
522. C2×#103C22×C101semidirect
523. C2×#103C22×C101semidirect
530. C2×#102C22×C101semidirect
533. C2×C22⋊C8C22×C101semidirect
537. #390C22×C101semidirect
538. #389C22×C101semidirect
541. #340C22×C101semidirect
542. #340C22×C101semidirect
543. #336C22×C101semidirect
544. #336C22×C101semidirect
551. C2×#41D4×C101semidirect
599. #121D4×C101semidirect
640. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1012
C2×#466×C1012
C2×#449×C1012
C2×#447×C1012
C2×#416×C1012
C101×#24142
C101×#20422
C101×#20362
C101×#20122
C101×#20002
C101×#18792
C101×#18752
C101×#18692
C101×#18622
C101×#17862
#24428101