Finite Group Databasebeta

← C101×#21772 #38803923

Subgroups — C101×#21772 #38803923

Order 25856.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C101C211yesmaximal, characteristic
2C2×#408×C101C211yesmaximal, characteristic, complemented
3C101×#2311C211yesmaximal, characteristic, complemented
4C101×#1895C211yesmaximal, characteristic, complemented
5C101×#1894C211yesmaximal, characteristic, complemented
6C101×#1893C211yesmaximal, characteristic, complemented
7C101×#1892C211yesmaximal, characteristic, complemented
8C101×#1875C211yesmaximal, characteristic, complemented
9C101×#1874C211yesmaximal, characteristic, complemented
10C101×#1873C211yesmaximal, characteristic, complemented
11C101×#1872C211yesmaximal, characteristic, complemented
12C101×#1824C211yesmaximal, characteristic, complemented
13C101×#1823C211yesmaximal, characteristic, complemented
14C101×#1788C211yesmaximal, characteristic, complemented
15C101×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20#537×C101—24no—
21#537×C101C418yescomplemented
22C2×C22⋊Q8×C101—21no—
23C2×C22⋊Q8×C101C2211yescharacteristic
24C2×C22⋊Q8×C101C2211yescharacteristic
25C2×#121×C101—21no—
26C2×#121×C101—21no—
27C2×#121×C101—21no—
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×#117×C101C2211yescharacteristic
31C22×C4⋊C4×C101C2211yescharacteristic
32C22×C4⋊C4×C101C2211yescharacteristic
33C2×#103×C101C2211yescharacteristic
34C2×#103×C101C2211yescharacteristic
35C2×#103×C101C2211yescharacteristic
36C2×#103×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41#408×C101—24no—
42C2×C22⋊C8×C101C2211yescharacteristic
43C2×C22⋊C8×C101C2211yescharacteristic
44C2×C22⋊C8×C101C2211yescharacteristic
45C2×C22⋊C8×C101C2211yescharacteristic
46#391×C101—21no—
47#390×C101—21no—
48#386×C101—21no—
49#386×C101—21no—
50#380×C101C2211yescharacteristic
51#380×C101C2211yescharacteristic
52#380×C101C2211yescharacteristic
53#380×C101C2211yescharacteristic
54#340×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62C2×#41×C101—22no—
63C2×#41×C101—41no—
64C2×#41×C101—41no—
65C2×#41×C101—41no—
66C2×#41×C101—41no—
67C2×#41×C101—41no—
68C2×#41×C101—41no—
69C2×#41×C101—41no—
70C2×#41×C101—41no—
71C2×#41×C101C2×C414yes—
72C2×#41×C101C2×C414yescomplemented
73C2×#41×C101D414yes—
74C22×Q8×C101D411yescharacteristic
75C22×Q8×C101C2311yescharacteristic
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101D411yescharacteristic
80C22×D4×C101D411yescharacteristic
81C22×D4×C101D411yescharacteristic
82C22×D4×C101C2311yescharacteristic
83C23×C4×C101—21no—
84C23×C4×C101—21no—
85C23×C4×C101—21no—
86C23×C4×C101C2311yescharacteristic
87C23×C4×C101C2311yescharacteristic
88C23×C4×C101C2311yescharacteristic
89C2×M16×C101—22no—
90C2×M16×C101—41no—
91C2×M16×C101—41no—
92C22×C8×C101—22no—
93C22×C8×C101—41no—
94C22×C8×C101—41no—
95C22×C8×C101C2311yescharacteristic
96C22×C8×C101C2311yescharacteristic
97C22×C8×C101C2311yescharacteristic
98C22×C8×C101C2311yescharacteristic
99C22⋊Q8×C101—28no—
100C22⋊Q8×C101—22no—
101C22⋊Q8×C101—22no—
102C22⋊Q8×C101C2×C414yes—
103C22⋊Q8×C101C2×C414yescomplemented
104#121×C101—28no—
105#121×C101—28no—
106#121×C101—28no—
107#121×C101—22no—
108#121×C101—22no—
109#121×C101C2×C414yes—
110#121×C101C2×C414yescomplemented
111#117×C101—41no—
112#117×C101—41no—
113C2×C4⋊C4×C101—21no—
114C2×C4⋊C4×C101—22no—
115C2×C4⋊C4×C101—21no—
116C2×C4⋊C4×C101—21no—
117C2×C4⋊C4×C101—21no—
118C2×C4⋊C4×C101—41no—
119C2×C4⋊C4×C101—41no—
120C2×C4⋊C4×C101C2×C414yescomplemented
121C2×C4⋊C4×C101C2311yescharacteristic
122C2×C4⋊C4×C101C2311yescharacteristic
123C2×C4⋊C4×C101C2311yescharacteristic
124C2×C4⋊C4×C101C2311yescharacteristic
125C2×C4⋊C4×C101C2311yescharacteristic
126C2×C4⋊C4×C101C2311yescharacteristic
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—21no—
136C2×C42×C101—21no—
137#103×C101—41no—
138#103×C101—41no—
139#103×C101—41no—
140#103×C101—41no—
141#102×C101—41no—
142#102×C101—41no—
143#102×C101—41no—
144#102×C101—41no—
145C22⋊C8×C101—22no—
146C22⋊C8×C101—22no—
147C22⋊C8×C101—22no—
148C22⋊C8×C101—22no—
149#95×C101—21no—
150#95×C101—21no—
151#95×C101—21no—
152#95×C101—21no—
153C24×C101—21no—
154C24×C101C2×D411yescharacteristic
155C24×C101C2×D411yescharacteristic
156C24×C101C2×D411yescharacteristic
157#41×C101—44no—
158#41×C101—44no—
159#41×C101—44no—
160#41×C101—44no—
161#41×C101—44no—
162#41×C101—44no—
163#41×C101—44no—
164#41×C101—44no—
165C2×Q8×C101—21no—
166C2×Q8×C101—21no—
167C2×Q8×C101—21no—
168C2×Q8×C101—21no—
169C2×Q8×C101—21no—
170C2×Q8×C101—41no—
171C2×Q8×C101—41no—
172C2×Q8×C101C22⋊C414yes—
173C2×Q8×C101C22×C412yes—
174C2×D4×C101—24no—
175C2×D4×C101—24no—
176C2×D4×C101—24no—
177C2×D4×C101—21no—
178C2×D4×C101—21no—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—41no—
183C2×D4×C101—41no—
184C2×D4×C101—41no—
185C2×D4×C101—41no—
186C2×D4×C101—41no—
187C2×D4×C101—41no—
188C2×D4×C101—42no—
189C2×D4×C101—42no—
190C2×D4×C101—81no—
191C2×D4×C101—81no—
192C2×D4×C101—81no—
193C2×D4×C101—81no—
194C2×D4×C101C22⋊C414yes—
195C2×D4×C101C22⋊C414yes—
196C2×D4×C101C22⋊C414yes—
197C2×D4×C101C22×C412yes—
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—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—24no—
214C22×C4×C101—24no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—21no—
219C22×C4×C101—42no—
220C22×C4×C101—42no—
221C22×C4×C101—42no—
222C22×C4×C101—81no—
223C22×C4×C101—81no—
224C22×C4×C101—81no—
225C22×C4×C101—81no—
226C22×C4×C101C22×C412yes—
227C22×C4×C101C22×C412yes—
228C22×C4×C101C22×C412yes—
229C22×C4×C101C2×D411yescharacteristic
230C22×C4×C101C2×D411yescharacteristic
231C22×C4×C101C2×D411yescharacteristic
232C22×C4×C101C2×D412yes—
233C22×C4×C101C2×D412yes—
234C22×C4×C101C2×D412yes—
235C22×C4×C101C2411yescharacteristic
236M16×C101—44no—
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—21no—
244C2×C8×C101—21no—
245C2×C8×C101—21no—
246C2×C8×C101—21no—
247C2×C8×C101—21no—
248C2×C8×C101—21no—
249C2×C8×C101—44no—
250C4⋊C4×C101—24no—
251C4⋊C4×C101—24no—
252C4⋊C4×C101—24no—
253C4⋊C4×C101—21no—
254C4⋊C4×C101—21no—
255C4⋊C4×C101—21no—
256C4⋊C4×C101—21no—
257C4⋊C4×C101—21no—
258C4⋊C4×C101—21no—
259C4⋊C4×C101—21no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—21no—
262C4⋊C4×C101—21no—
263C4⋊C4×C101—42no—
264C4⋊C4×C101C22×C412yes—
265C4⋊C4×C101C22×C412yes—
266C22⋊C4×C101—24no—
267C22⋊C4×C101—24no—
268C22⋊C4×C101—24no—
269C22⋊C4×C101—24no—
270C22⋊C4×C101—42no—
271C22⋊C4×C101—81no—
272C22⋊C4×C101—81no—
273C22⋊C4×C101—81no—
274C22⋊C4×C101—81no—
275C42×C101—42no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—21no—
283C23×C101—21no—
284C23×C101—21no—
285C23×C101—21no—
286C23×C101—21no—
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—21no—
291C23×C101—21no—
292C23×C101—21no—
293C23×C101—21no—
294C23×C101—22no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—41no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101C2×C22⋊C412yes—
302C23×C101C2×C22⋊C412yes—
303C23×C101C2×C22⋊C412yes—
304C23×C101C22×D411yescharacteristic
305Q8×C101—22no—
306Q8×C101—22no—
307Q8×C101—44no—
308Q8×C101—41no—
309Q8×C101—41no—
310D4×C101—22no—
311D4×C101—22no—
312D4×C101—44no—
313D4×C101—44no—
314D4×C101—44no—
315D4×C101—48no—
316D4×C101—41no—
317D4×C101—41no—
318D4×C101—84no—
319D4×C101—84no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—22no—
327C2×C4×C101—22no—
328C2×C4×C101—22no—
329C2×C4×C101—22no—
330C2×C4×C101—22no—
331C2×C4×C101—22no—
332C2×C4×C101—22no—
333C2×C4×C101—22no—
334C2×C4×C101—22no—
335C2×C4×C101—22no—
336C2×C4×C101—22no—
337C2×C4×C101—22no—
338C2×C4×C101—22no—
339C2×C4×C101—22no—
340C2×C4×C101—22no—
341C2×C4×C101—48no—
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—41no—
351C2×C4×C101—41no—
352C2×C4×C101—41no—
353C2×C4×C101—41no—
354C2×C4×C101—41no—
355C2×C4×C101—41no—
356C2×C4×C101—41no—
357C2×C4×C101—41no—
358C2×C4×C101—41no—
359C2×C4×C101—41no—
360C2×C4×C101—84no—
361C2×C4×C101—84no—
362C2×C4×C101C2×C22⋊C412yes—
363C2×C4×C101C2×C22⋊C412yes—
364C2×C4×C101C2×C22⋊C412yes—
365C2×C4×C101C23×C411yescharacteristic
366C2×C4×C101C22×D411yescharacteristic
367C2×C4×C101H(5,𝔽2)11yescharacteristic
368C2×C4×C101H(5,𝔽2)11yescharacteristic
369C2×C4×C101H(5,𝔽2)11yescharacteristic
370C2×C4×C101H(5,𝔽2)11yescharacteristic
371C8×C101—41no—
372C8×C101—41no—
373C8×C101—41no—
374C8×C101—41no—
375C22×C101—22no—
376C22×C101—22no—
377C22×C101—22no—
378C22×C101—22no—
379C22×C101—22no—
380C22×C101—22no—
381C22×C101—22no—
382C22×C101—22no—
383C22×C101—22no—
384C22×C101—41no—
385C22×C101—41no—
386C22×C101—41no—
387C22×C101—41no—
388C22×C101—41no—
389C22×C101—41no—
390C22×C101—41no—
391C22×C101—41no—
392C22×C101—41no—
393C22×C101—41no—
394C22×C101—41no—
395C22×C101—41no—
396C22×C101—42no—
397C22×C101—42no—
398C22×C101—42no—
399C22×C101—81no—
400C22×C101—81no—
401C22×C101—81no—
402C22×C101—81no—
403C22×C101C22×C22⋊C411yescharacteristic
404C22×C101#53411yescharacteristic
405C22×C101#53411yescharacteristic
406C22×C101#57611yescharacteristic
407C22×C101#57711yescharacteristic
408C22×C101#57711yescharacteristic
409C22×C101#57811yescharacteristic
410C4×C101—22no—
411C4×C101—22no—
412C4×C101—22no—
413C4×C101—42no—
414C4×C101—42no—
415C4×C101—42no—
416C4×C101—81no—
417C4×C101—81no—
418C4×C101—81no—
419C4×C101—81no—
420C4×C101#51811yescharacteristic
421C4×C101#51811yescharacteristic
422C4×C101#53411yescharacteristic
423C4×C101#53411yescharacteristic
424#21772C10111yesmaximal, characteristic, direct product factor, Sylow
425C2×C101—42no—
426C2×C101—42no—
427C2×C101—42no—
428C2×C101—82no—
429C2×C101#230811yescharacteristic
430C2×C101#289711yescharacteristic
431C2×C101#289811yescharacteristic
432C2×C101#319811yescharacteristic
433C2×C101#320111yescharacteristic
434C2×C101#320311yescharacteristic
435C2×C101#320411yescharacteristic
436C2×#537C2×C10111yescharacteristic
437C2×#408C2×C10111yescharacteristic, complemented
438#2311C2×C10111yescharacteristic, complemented
439#1895C2×C10111yescharacteristic, complemented
440#1894C2×C10111yescharacteristic, complemented
441#1893C2×C10111yescharacteristic, complemented
442#1892C2×C10111yescharacteristic, complemented
443#1875C2×C10111yescharacteristic, complemented
444#1874C2×C10111yescharacteristic, complemented
445#1873C2×C10111yescharacteristic, complemented
446#1872C2×C10111yescharacteristic, complemented
447#1824C2×C10111yescharacteristic, complemented
448#1823C2×C10111yescharacteristic, complemented
449#1788C2×C10111yescharacteristic, complemented
450#1788C2×C10111yescharacteristic, complemented
451C101#2177211yescharacteristic, direct product factor, Sylow
452C22×#41C22×C10111yescharacteristic
453C22×#41C22×C10111yescharacteristic
454C22×M16C22×C10111yescharacteristic
455C23×C8C22×C10111yescharacteristic
456#537—24no—
457#537C4×C10118yescomplemented
458C2×C22⋊Q8—21no—
459C2×C22⋊Q8C22×C10111yescharacteristic
460C2×C22⋊Q8C22×C10111yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C22×C10111yescharacteristic
465C2×#121C22×C10111yescharacteristic
466C2×#117C22×C10111yescharacteristic
467C22×C4⋊C4C22×C10111yescharacteristic
468C22×C4⋊C4C22×C10111yescharacteristic
469C2×#103C22×C10111yescharacteristic
470C2×#103C22×C10111yescharacteristic
471C2×#103C22×C10111yescharacteristic
472C2×#103C22×C10111yescharacteristic
473C2×#102C22×C10111yescharacteristic
474C2×#102C22×C10111yescharacteristic
475C2×#102C22×C10111yescharacteristic
476C2×#102C22×C10111yescharacteristic
477#408—24no—
478C2×C22⋊C8C22×C10111yescharacteristic
479C2×C22⋊C8C22×C10111yescharacteristic
480C2×C22⋊C8C22×C10111yescharacteristic
481C2×C22⋊C8C22×C10111yescharacteristic
482#391—21no—
483#390—21no—
484#386—21no—
485#386—21no—
486#380C22×C10111yescharacteristic
487#380C22×C10111yescharacteristic
488#380C22×C10111yescharacteristic
489#380C22×C10111yescharacteristic
490#340C22×C10111yescharacteristic
491#340C22×C10111yescharacteristic
492#340C22×C10111yescharacteristic
493#340C22×C10111yescharacteristic
494#340C22×C10111yescharacteristic
495#340C22×C10111yescharacteristic
496#340C22×C10111yescharacteristic
497#340C22×C10111yescharacteristic
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C10114yes—
508C2×#41C2×C4×C10114yescomplemented
509C2×#41D4×C10114yes—
510C22×Q8D4×C10111yescharacteristic
511C22×Q8C23×C10111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C10111yescharacteristic
516C22×D4D4×C10111yescharacteristic
517C22×D4D4×C10111yescharacteristic
518C22×D4C23×C10111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C10111yescharacteristic
523C23×C4C23×C10111yescharacteristic
524C23×C4C23×C10111yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C10111yescharacteristic
532C22×C8C23×C10111yescharacteristic
533C22×C8C23×C10111yescharacteristic
534C22×C8C23×C10111yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C10114yes—
539C22⋊Q8C2×C4×C10114yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C10114yes—
546#121C2×C4×C10114yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C10114yescomplemented
557C2×C4⋊C4C23×C10111yescharacteristic
558C2×C4⋊C4C23×C10111yescharacteristic
559C2×C4⋊C4C23×C10111yescharacteristic
560C2×C4⋊C4C23×C10111yescharacteristic
561C2×C4⋊C4C23×C10111yescharacteristic
562C2×C4⋊C4C23×C10111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C10111yescharacteristic
591C24C2×D4×C10111yescharacteristic
592C24C2×D4×C10111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C10114yes—
609C2×Q8C22×C4×C10112yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C10114yes—
631C2×D4C22⋊C4×C10114yes—
632C2×D4C22⋊C4×C10114yes—
633C2×D4C22×C4×C10112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C10112yes—
663C22×C4C22×C4×C10112yes—
664C22×C4C22×C4×C10112yes—
665C22×C4C2×D4×C10111yescharacteristic
666C22×C4C2×D4×C10111yescharacteristic
667C22×C4C2×D4×C10111yescharacteristic
668C22×C4C2×D4×C10112yes—
669C22×C4C2×D4×C10112yes—
670C22×C4C2×D4×C10112yes—
671C22×C4C24×C10111yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C10112yes—
701C4⋊C4C22×C4×C10112yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C10112yes—
738C23C2×C22⋊C4×C10112yes—
739C23C2×C22⋊C4×C10112yes—
740C23C22×D4×C10111yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C10112yes—
799C2×C4C2×C22⋊C4×C10112yes—
800C2×C4C2×C22⋊C4×C10112yes—
801C2×C4C23×C4×C10111yescharacteristic
802C2×C4C22×D4×C10111yescharacteristic
803C2×C4H(5,𝔽2)×C10111yescharacteristic
804C2×C4H(5,𝔽2)×C10111yescharacteristic
805C2×C4H(5,𝔽2)×C10111yescharacteristic
806C2×C4H(5,𝔽2)×C10111yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C10111yescharacteristic
840C22#534×C10111yescharacteristic
841C22#534×C10111yescharacteristic
842C22#576×C10111yescharacteristic
843C22#577×C10111yescharacteristic
844C22#577×C10111yescharacteristic
845C22#578×C10111yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4#518×C10111yescharacteristic
857C4#518×C10111yescharacteristic
858C4#534×C10111yescharacteristic
859C4#534×C10111yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2C101×#230811yescharacteristic
865C2C101×#289711yescharacteristic
866C2C101×#289811yescharacteristic
867C2C101×#319811yescharacteristic
868C2C101×#320111yescharacteristic
869C2C101×#320311yescharacteristic
870C2C101×#320411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#537×C101C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C22×#41×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#408×C101C2semidirect
3. C101×#2311C2semidirect
4. C101×#1895C2semidirect
5. C101×#1894C2semidirect
6. C101×#1893C2semidirect
7. C101×#1892C2semidirect
8. C101×#1875C2semidirect
9. C101×#1874C2semidirect
10. C101×#1873C2semidirect
11. C101×#1872C2semidirect
12. C101×#1824C2semidirect
13. C101×#1823C2semidirect
14. C101×#1788C2semidirect
15. C101×#1788C2semidirect
21. #537×C101C4semidirect
72. C2×#41×C101C2×C4semidirect
103. C22⋊Q8×C101C2×C4semidirect
110. #121×C101C2×C4semidirect
120. C2×C4⋊C4×C101C2×C4semidirect
424. #21772C101direct (N × H)
437. C2×#408C2×C101semidirect
438. #2311C2×C101semidirect
439. #1895C2×C101semidirect
440. #1894C2×C101semidirect
441. #1893C2×C101semidirect
442. #1892C2×C101semidirect
443. #1875C2×C101semidirect
444. #1874C2×C101semidirect
445. #1873C2×C101semidirect
446. #1872C2×C101semidirect
447. #1824C2×C101semidirect
448. #1823C2×C101semidirect
449. #1788C2×C101semidirect
450. #1788C2×C101semidirect
451. C101#21772direct (N × H)
457. #537C4×C101semidirect
508. C2×#41C2×C4×C101semidirect
539. C22⋊Q8C2×C4×C101semidirect
546. #121C2×C4×C101semidirect
556. C2×C4⋊C4C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1012
C2×#408×C1012
C101×#23112
C101×#18952
C101×#18942
C101×#18932
C101×#18922
C101×#18752
C101×#18742
C101×#18732
C101×#18722
C101×#18242
C101×#18232
C101×#17882
#21772101