Finite Group Databasebeta

← C101×#25179 #38807330

Subgroups — C101×#25179 #38807330

Order 25856.

1206 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C101C211yesmaximal, characteristic, complemented
2C2×#449×C101C211yesmaximal, characteristic, complemented
3C2×#449×C101C211yesmaximal, characteristic, complemented
4C2×#440×C101C211yesmaximal, characteristic, complemented
5C101×#2428C211yesmaximal, characteristic, complemented
6C101×#2341C211yesmaximal, characteristic, complemented
7C101×#2067C211yesmaximal, characteristic, complemented
8C101×#2034C211yesmaximal, characteristic, complemented
9C101×#2033C211yesmaximal, characteristic, complemented
10C101×#2011C211yesmaximal, characteristic, complemented
11C101×#1972C211yesmaximal, characteristic, complemented
12C101×#1924C211yesmaximal, characteristic, complemented
13C101×#1880C211yesmaximal, characteristic, complemented
14C101×#1879C211yesmaximal, characteristic, complemented
15C101×#1865C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×D8×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21C2×#127×C101C2211yescharacteristic
22C2×#121×C101—21no—
23C2×#121×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×C4×Q8×C101C2211yescharacteristic
26C2×C4×Q8×C101C2211yescharacteristic
27C2×C4×D4×C101C2211yescharacteristic
28#460×C101—24no—
29#449×C101—24no—
30#449×C101—24no—
31#440×C101—24no—
32C2×#107×C101C2211yescharacteristic
33C2×#106×C101C2211yescharacteristic
34C2×C4⋊C8×C101C2211yescharacteristic
35C2×#103×C101C2211yescharacteristic
36C2×#103×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×C22⋊C8×C101C2211yescharacteristic
44C2×C22⋊C8×C101C2211yescharacteristic
45C2×#97×C101C2211yescharacteristic
46#394×C101—21no—
47#392×C101—21no—
48#390×C101—21no—
49#390×C101—21no—
50#390×C101C2211yescharacteristic
51#390×C101C2211yescharacteristic
52#390×C101C2211yescharacteristic
53#389×C101C2211yescharacteristic
54#386×C101—21no—
55#380×C101—21no—
56#380×C101C2211yescharacteristic
57C4×C22⋊C4×C101—21no—
58C4×C22⋊C4×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C2×#41×C101—22no—
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—41no—
68C2×#41×C101—41no—
69C22×Q8×C101C2311yescharacteristic
70C22×D4×C101—21no—
71C22×D4×C101—21no—
72C22×D4×C101—21no—
73C22×D4×C101—21no—
74C22×D4×C101—21no—
75C22×D4×C101C2311yescharacteristic
76C22×D4×C101C2311yescharacteristic
77C22×D4×C101C2311yescharacteristic
78C23×C4×C101—21no—
79C23×C4×C101—21no—
80C23×C4×C101C2311yescharacteristic
81C2×SD16×C101—22no—
82C2×SD16×C101—22no—
83C2×SD16×C101—22no—
84C2×SD16×C101—22no—
85C2×SD16×C101—22no—
86C2×SD16×C101D414yescomplemented
87C2×D8×C101—22no—
88C2×D8×C101—22no—
89C2×D8×C101—22no—
90C2×D8×C101—22no—
91C2×D8×C101—41no—
92C2×D8×C101—41no—
93C22×C8×C101C2311yescharacteristic
94C22×C8×C101C2311yescharacteristic
95C22×C8×C101C2311yescharacteristic
96C22×C8×C101C2311yescharacteristic
97#127×C101—22no—
98#127×C101—41no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—44no—
102#121×C101—41no—
103#121×C101—41no—
104C4×Q8×C101—22no—
105C4×Q8×C101—22no—
106C4×Q8×C101—41no—
107C4×Q8×C101—41no—
108C4×D4×C101—22no—
109C4×D4×C101—41no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—21no—
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C22⋊C4×C101—21no—
118C2×C22⋊C4×C101—21no—
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×C101D411yescharacteristic
128C2×C22⋊C4×C101D411yescharacteristic
129C2×C42×C101—21no—
130C2×C42×C101—21no—
131C2×C42×C101C2311yescharacteristic
132C2×C42×C101C2311yescharacteristic
133#107×C101—22no—
134#106×C101—41no—
135C4⋊C8×C101—22no—
136#103×C101—22no—
137#103×C101D414yescomplemented
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—41no—
144C22⋊C8×C101—22no—
145C22⋊C8×C101—22no—
146#97×C101—22no—
147#95×C101—21no—
148#95×C101—21no—
149#95×C101D411yescharacteristic
150#95×C101D411yescharacteristic
151C24×C101—21no—
152C24×C101—21no—
153C24×C101—21no—
154C24×C101C2×D411yescharacteristic
155#41×C101—44no—
156#41×C101—44no—
157#41×C101—44no—
158#41×C101—44no—
159C2×Q8×C101—21no—
160C2×Q8×C101—21no—
161C2×Q8×C101—21no—
162C2×Q8×C101C2×D412yes—
163C2×Q8×C101C2×D412yes—
164C2×Q8×C101#4112yes—
165C2×D4×C101—24no—
166C2×D4×C101—21no—
167C2×D4×C101—21no—
168C2×D4×C101—21no—
169C2×D4×C101—21no—
170C2×D4×C101—21no—
171C2×D4×C101—21no—
172C2×D4×C101—21no—
173C2×D4×C101—21no—
174C2×D4×C101—21no—
175C2×D4×C101—21no—
176C2×D4×C101—21no—
177C2×D4×C101—21no—
178C2×D4×C101—21no—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—42no—
183C2×D4×C101—42no—
184C2×D4×C101—42no—
185C2×D4×C101—42no—
186C2×D4×C101—42no—
187C2×D4×C101—42no—
188C2×D4×C101—42no—
189C2×D4×C101—42no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—81no—
193C2×D4×C101—81no—
194C2×D4×C101—81no—
195C2×D4×C101—81no—
196C2×D4×C101C2×D412yes—
197C2×D4×C101#4112yes—
198C22×C4×C101—21no—
199C22×C4×C101—24no—
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—21no—
210C22×C4×C101—42no—
211C22×C4×C101—42no—
212C22×C4×C101—42no—
213C22×C4×C101—42no—
214C22×C4×C101—81no—
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2×D411yescharacteristic
217C22×C4×C101C2×D411yescharacteristic
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2411yescharacteristic
221SD16×C101—28no—
222SD16×C101—44no—
223D8×C101—44no—
224D8×C101—44no—
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101C2×D412yes—
236C2×C8×C101C2×D412yes—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—42no—
245C4⋊C4×C101—42no—
246C4⋊C4×C101—42no—
247C4⋊C4×C101C2×D412yes—
248C22⋊C4×C101—22no—
249C22⋊C4×C101—41no—
250C22⋊C4×C101—42no—
251C22⋊C4×C101—42no—
252C22⋊C4×C101—42no—
253C22⋊C4×C101—42no—
254C22⋊C4×C101—42no—
255C22⋊C4×C101—42no—
256C22⋊C4×C101—81no—
257C22⋊C4×C101—81no—
258C22⋊C4×C101—81no—
259C22⋊C4×C101—81no—
260C42×C101—21no—
261C42×C101—21no—
262C42×C101—21no—
263C42×C101—21no—
264C42×C101—42no—
265C42×C101—42no—
266C23×C101—21no—
267C23×C101—22no—
268C23×C101—22no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—21no—
275C23×C101—41no—
276C23×C101—41no—
277C23×C101—41no—
278C23×C101—41no—
279C23×C101—41no—
280C23×C101—41no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—41no—
285C23×C101—41no—
286C23×C101—41no—
287C23×C101—41no—
288C23×C101—41no—
289C23×C101—41no—
290C23×C101—41no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101C22×D411yescharacteristic
295Q8×C101—22no—
296Q8×C101—22no—
297Q8×C101—22no—
298Q8×C101#12114yescomplemented
299D4×C101—22no—
300D4×C101—22no—
301D4×C101—22no—
302D4×C101—22no—
303D4×C101—48no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—41no—
310D4×C101—41no—
311D4×C101—41no—
312D4×C101—84no—
313D4×C101—84no—
314D4×C101—84no—
315D4×C101—84no—
316C2×C4×C101—22no—
317C2×C4×C101—21no—
318C2×C4×C101—22no—
319C2×C4×C101—22no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—22no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
329C2×C4×C101—21no—
330C2×C4×C101—21no—
331C2×C4×C101—21no—
332C2×C4×C101—21no—
333C2×C4×C101—21no—
334C2×C4×C101—48no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—41no—
340C2×C4×C101—41no—
341C2×C4×C101—41no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—84no—
351C2×C4×C101AGL(1,ℤ/8)12yes—
352C2×C4×C101C22×D411yescharacteristic
353C2×C4×C101C22×D411yescharacteristic
354C2×C4×C101C2×#4111yescharacteristic
355C2×C4×C101C2×#4111yescharacteristic
356C2×C4×C101H(5,𝔽2)11yescharacteristic
357C2×C4×C101H(5,𝔽2)11yescharacteristic
358C8×C101—22no—
359C8×C101—22no—
360C8×C101—41no—
361C8×C101—41no—
362C22×C101—41no—
363C22×C101—42no—
364C22×C101—41no—
365C22×C101—42no—
366C22×C101—42no—
367C22×C101—41no—
368C22×C101—42no—
369C22×C101—41no—
370C22×C101—42no—
371C22×C101—42no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—41no—
375C22×C101—81no—
376C22×C101—81no—
377C22×C101—81no—
378C22×C101—81no—
379C22×C101—81no—
380C22×C101—81no—
381C22×C101—81no—
382C22×C101—81no—
383C22×C101—81no—
384C22×C101—81no—
385C22×C101—81no—
386C22×C101—81no—
387C22×C101—81no—
388C22×C101—81no—
389C22×C101—81no—
390C22×C101#52511yescharacteristic
391C22×C101D4211yescharacteristic
392C22×C101D4211yescharacteristic
393C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C101#57511yescharacteristic
395C22×C101#57611yescharacteristic
396C22×C101#57711yescharacteristic
397C4×C101—24no—
398C4×C101—22no—
399C4×C101—41no—
400C4×C101—41no—
401C4×C101—41no—
402C4×C101—41no—
403C4×C101—42no—
404C4×C101—81no—
405C4×C101—81no—
406C4×C101—81no—
407C4×C101C2×#12111yescharacteristic
408C4×C101#53811yescharacteristic
409C4×C101#54611yescharacteristic
410C4×C101#54611yescharacteristic
411#25179C10111yesmaximal, characteristic, direct product factor, Sylow
412C2×C101—81no—
413C2×C101—82no—
414C2×C101—82no—
415C2×C101—161no—
416C2×C101#242411yescharacteristic
417C2×C101#311511yescharacteristic
418C2×C101#311911yescharacteristic
419C2×C101#326511yescharacteristic
420C2×C101#326811yescharacteristic
421C2×C101#327111yescharacteristic
422C2×C101#327411yescharacteristic
423C2×#460C2×C10111yescharacteristic, complemented
424C2×#449C2×C10111yescharacteristic, complemented
425C2×#449C2×C10111yescharacteristic, complemented
426C2×#440C2×C10111yescharacteristic, complemented
427#2428C2×C10111yescharacteristic, complemented
428#2341C2×C10111yescharacteristic, complemented
429#2067C2×C10111yescharacteristic, complemented
430#2034C2×C10111yescharacteristic, complemented
431#2033C2×C10111yescharacteristic, complemented
432#2011C2×C10111yescharacteristic, complemented
433#1972C2×C10111yescharacteristic, complemented
434#1924C2×C10111yescharacteristic, complemented
435#1880C2×C10111yescharacteristic, complemented
436#1879C2×C10111yescharacteristic, complemented
437#1865C2×C10111yescharacteristic, complemented
438C101#2517911yescharacteristic, direct product factor, Sylow
439C22×#41C22×C10111yescharacteristic
440C22×SD16C22×C10111yescharacteristic
441C22×SD16C22×C10111yescharacteristic
442C22×D8C22×C10111yescharacteristic
443C22×D8C22×C10111yescharacteristic
444C2×#127C22×C10111yescharacteristic
445C2×#121—21no—
446C2×#121C22×C10111yescharacteristic
447C2×#121C22×C10111yescharacteristic
448C2×C4×Q8C22×C10111yescharacteristic
449C2×C4×Q8C22×C10111yescharacteristic
450C2×C4×D4C22×C10111yescharacteristic
451#460—24no—
452#449—24no—
453#449—24no—
454#440—24no—
455C2×#107C22×C10111yescharacteristic
456C2×#106C22×C10111yescharacteristic
457C2×C4⋊C8C22×C10111yescharacteristic
458C2×#103C22×C10111yescharacteristic
459C2×#103C22×C10111yescharacteristic
460C2×#102C22×C10111yescharacteristic
461C2×#102C22×C10111yescharacteristic
462C2×#102C22×C10111yescharacteristic
463C2×#102C22×C10111yescharacteristic
464C2×#102C22×C10111yescharacteristic
465C2×#102C22×C10111yescharacteristic
466C2×C22⋊C8C22×C10111yescharacteristic
467C2×C22⋊C8C22×C10111yescharacteristic
468C2×#97C22×C10111yescharacteristic
469#394—21no—
470#392—21no—
471#390—21no—
472#390—21no—
473#390C22×C10111yescharacteristic
474#390C22×C10111yescharacteristic
475#390C22×C10111yescharacteristic
476#389C22×C10111yescharacteristic
477#386—21no—
478#380—21no—
479#380C22×C10111yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4C22×C10111yescharacteristic
482#340C22×C10111yescharacteristic
483#340C22×C10111yescharacteristic
484#336C22×C10111yescharacteristic
485#336C22×C10111yescharacteristic
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C10111yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C10111yescharacteristic
499C22×D4C23×C10111yescharacteristic
500C22×D4C23×C10111yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C10111yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C10114yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C10111yescharacteristic
517C22×C8C23×C10111yescharacteristic
518C22×C8C23×C10111yescharacteristic
519C22×C8C23×C10111yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C10111yescharacteristic
537C2×C4⋊C4C23×C10111yescharacteristic
538C2×C4⋊C4C23×C10111yescharacteristic
539C2×C4⋊C4C23×C10111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C10111yescharacteristic
551C2×C22⋊C4D4×C10111yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C10111yescharacteristic
555C2×C42C23×C10111yescharacteristic
556#107—22no—
557#106—41no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C10114yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569#97—22no—
570#95—21no—
571#95—21no—
572#95D4×C10111yescharacteristic
573#95D4×C10111yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C10111yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C10112yes—
586C2×Q8C2×D4×C10112yes—
587C2×Q8#41×C10112yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C10112yes—
620C2×D4#41×C10112yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C10111yescharacteristic
639C22×C4C2×D4×C10111yescharacteristic
640C22×C4C2×D4×C10111yescharacteristic
641C22×C4C2×D4×C10111yescharacteristic
642C22×C4C2×D4×C10111yescharacteristic
643C22×C4C24×C10111yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C10112yes—
659C2×C8C2×D4×C10112yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C10112yes—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C10111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C10114yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4AGL(1,ℤ/8)×C10112yes—
775C2×C4C22×D4×C10111yescharacteristic
776C2×C4C22×D4×C10111yescharacteristic
777C2×C4C2×#41×C10111yescharacteristic
778C2×C4C2×#41×C10111yescharacteristic
779C2×C4H(5,𝔽2)×C10111yescharacteristic
780C2×C4H(5,𝔽2)×C10111yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—42no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—42no—
790C22—42no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22#525×C10111yescharacteristic
814C22D42×C10111yescharacteristic
815C22D42×C10111yescharacteristic
816C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
817C22#575×C10111yescharacteristic
818C22#576×C10111yescharacteristic
819C22#577×C10111yescharacteristic
820C4—24no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C10111yescharacteristic
831C4#538×C10111yescharacteristic
832C4#546×C10111yescharacteristic
833C4#546×C10111yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C101×#242411yescharacteristic
839C2C101×#311511yescharacteristic
840C2C101×#311911yescharacteristic
841C2C101×#326511yescharacteristic
842C2C101×#326811yescharacteristic
843C2C101×#327111yescharacteristic
844C2C101×#327411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#460×C101C2semidirect
2. C2×#449×C101C2semidirect
3. C2×#449×C101C2semidirect
4. C2×#440×C101C2semidirect
5. C101×#2428C2semidirect
6. C101×#2341C2semidirect
7. C101×#2067C2semidirect
8. C101×#2034C2semidirect
9. C101×#2033C2semidirect
10. C101×#2011C2semidirect
11. C101×#1972C2semidirect
12. C101×#1924C2semidirect
13. C101×#1880C2semidirect
14. C101×#1879C2semidirect
15. C101×#1865C2semidirect
86. C2×SD16×C101D4semidirect
137. #103×C101D4semidirect
298. Q8×C101#121semidirect
411. #25179C101direct (N × H)
423. C2×#460C2×C101semidirect
424. C2×#449C2×C101semidirect
425. C2×#449C2×C101semidirect
426. C2×#440C2×C101semidirect
427. #2428C2×C101semidirect
428. #2341C2×C101semidirect
429. #2067C2×C101semidirect
430. #2034C2×C101semidirect
431. #2033C2×C101semidirect
432. #2011C2×C101semidirect
433. #1972C2×C101semidirect
434. #1924C2×C101semidirect
435. #1880C2×C101semidirect
436. #1879C2×C101semidirect
437. #1865C2×C101semidirect
438. C101#25179direct (N × H)
509. C2×SD16D4×C101semidirect
560. #103D4×C101semidirect
721. Q8#121×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1012
C2×#449×C1012
C2×#440×C1012
C101×#24282
C101×#23412
C101×#20672
C101×#20342
C101×#20332
C101×#20112
C101×#19722
C101×#19242
C101×#18802
C101×#18792
C101×#18652
#25179101