Finite Group Databasebeta

← C101×#22493 #38804644

Subgroups — C101×#22493 #38804644

Order 25856.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C101C211yesmaximal, characteristic
2C2×#435×C101C211yesmaximal, characteristic, complemented
3D4×C4⋊C4×C101C211yesmaximal, characteristic, complemented
4C101×#1992C211yesmaximal, characteristic, complemented
5C101×#1989C211yesmaximal, characteristic, complemented
6C101×#1895C211yesmaximal, characteristic, complemented
7C101×#1893C211yesmaximal, characteristic, complemented
8C101×#1874C211yesmaximal, characteristic, complemented
9C101×#1874C211yesmaximal, characteristic, complemented
10C101×#1825C211yesmaximal, characteristic, complemented
11C101×#1824C211yesmaximal, characteristic, complemented
12C101×#1802C211yesmaximal, characteristic, complemented
13C101×#1762C211yesmaximal, characteristic, complemented
14C101×#1736C211yesmaximal, characteristic, complemented
15C2×#340×C101C211yesmaximal, characteristic, complemented
16C22×M16×C101C2211yescharacteristic
17C23×C8×C101C2211yescharacteristic
18#553×C101—24no—
19#553×C101C418yescomplemented
20C2×#126×C101—21no—
21C2×#125×C101C2211yescharacteristic
22C2×#123×C101—21no—
23C2×#121×C101—21no—
24C2×#121×C101C2211yescharacteristic
25C2×#121×C101C2211yescharacteristic
26C2×C4×D4×C101—21no—
27C2×C4×D4×C101—21no—
28C2×C4×D4×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30C2×#117×C101C2211yescharacteristic
31C22×C4⋊C4×C101C2211yescharacteristic
32C22×C4⋊C4×C101C2211yescharacteristic
33C22×C4⋊C4×C101C2211yescharacteristic
34#435×C101—24no—
35C2×C4⋊C8×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×C22⋊C8×C101C2211yescharacteristic
41C2×C22⋊C8×C101C2211yescharacteristic
42C2×#97×C101C2211yescharacteristic
43#389×C101—21no—
44#385×C101—21no—
45#385×C101—21no—
46#384×C101C2211yescharacteristic
47#380×C101C2211yescharacteristic
48#380×C101C2211yescharacteristic
49C4×C4⋊C4×C101C2211yescharacteristic
50#340×C101C2211yescharacteristic
51#340×C101C2211yescharacteristic
52#340×C101C2211yescharacteristic
53#340×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
62C22×D4×C101—21no—
63C22×D4×C101—21no—
64C22×D4×C101D411yescharacteristic
65C22×D4×C101C2311yescharacteristic
66C23×C4×C101—21no—
67C23×C4×C101—21no—
68C23×C4×C101—21no—
69C23×C4×C101—21no—
70C23×C4×C101C2311yescharacteristic
71C23×C4×C101C2311yescharacteristic
72C2×M16×C101—22no—
73C2×M16×C101—22no—
74C2×M16×C101—41no—
75C22×C8×C101—22no—
76C22×C8×C101—22no—
77C22×C8×C101—41no—
78C22×C8×C101C2311yescharacteristic
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82#126×C101—28no—
83#125×C101—22no—
84#125×C101C2×C414yescomplemented
85#123×C101—28no—
86#121×C101—28no—
87#121×C101—22no—
88#121×C101—22no—
89#121×C101C2×C414yescomplemented
90#121×C101C2×C414yescomplemented
91C4×D4×C101—28no—
92C4×D4×C101—22no—
93C4×D4×C101—44no—
94C4×D4×C101C2×C414yes—
95C4×D4×C101C2×C414yescomplemented
96C4×D4×C101D414yes—
97#117×C101—22no—
98#117×C101C2×C414yescomplemented
99C2×C4⋊C4×C101—21no—
100C2×C4⋊C4×C101—22no—
101C2×C4⋊C4×C101—21no—
102C2×C4⋊C4×C101—21no—
103C2×C4⋊C4×C101—22no—
104C2×C4⋊C4×C101—22no—
105C2×C4⋊C4×C101—21no—
106C2×C4⋊C4×C101—21no—
107C2×C4⋊C4×C101—21no—
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—41no—
110C2×C4⋊C4×C101—41no—
111C2×C4⋊C4×C101C2×C414yescomplemented
112C2×C4⋊C4×C101D411yescharacteristic
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×C4⋊C4×C101C2311yescharacteristic
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×C101D411yescharacteristic
127C2×C22⋊C4×C101D411yescharacteristic
128C2×C42×C101—21no—
129C2×C42×C101—21no—
130C2×C42×C101C2311yescharacteristic
131C4⋊C8×C101—22no—
132#102×C101—22no—
133#102×C101—22no—
134#102×C101—41no—
135#102×C101—41no—
136C22⋊C8×C101—22no—
137C22⋊C8×C101—22no—
138#97×C101—22no—
139#95×C101—21no—
140#95×C101—21no—
141#95×C101—21no—
142C24×C101—21no—
143C24×C101C2×D411yescharacteristic
144C24×C101C2×D411yescharacteristic
145C2×D4×C101—22no—
146C2×D4×C101—22no—
147C2×D4×C101—24no—
148C2×D4×C101—24no—
149C2×D4×C101—21no—
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—42no—
155C2×D4×C101—42no—
156C2×D4×C101—81no—
157C2×D4×C101—81no—
158C2×D4×C101C22⋊C414yes—
159C2×D4×C101C22×C412yes—
160C22×C4×C101—21no—
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—21no—
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101—21no—
171C22×C4×C101—21no—
172C22×C4×C101—24no—
173C22×C4×C101—24no—
174C22×C4×C101—21no—
175C22×C4×C101—21no—
176C22×C4×C101—21no—
177C22×C4×C101—42no—
178C22×C4×C101—42no—
179C22×C4×C101—42no—
180C22×C4×C101—42no—
181C22×C4×C101—81no—
182C22×C4×C101—81no—
183C22×C4×C101—81no—
184C22×C4×C101—81no—
185C22×C4×C101—81no—
186C22×C4×C101—81no—
187C22×C4×C101C22×C412yes—
188C22×C4×C101C22×C412yes—
189C22×C4×C101C2×D411yescharacteristic
190C22×C4×C101C2×D411yescharacteristic
191C22×C4×C101C2×D411yescharacteristic
192C22×C4×C101C2×D411yescharacteristic
193C22×C4×C101C2×D412yes—
194C22×C4×C101C2×D412yes—
195C22×C4×C101C2411yescharacteristic
196M16×C101—44no—
197C2×C8×C101—21no—
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×C101—44no—
209C2×C8×C101#4112yes—
210C4⋊C4×C101—24no—
211C4⋊C4×C101—24no—
212C4⋊C4×C101—24no—
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—21no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—21no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—42no—
224C4⋊C4×C101—42no—
225C4⋊C4×C101—42no—
226C4⋊C4×C101—81no—
227C4⋊C4×C101C22⋊C414yes—
228C4⋊C4×C101C22×C412yes—
229C4⋊C4×C101C22×C412yes—
230C4⋊C4×C101C22×C412yes—
231C4⋊C4×C101#4112yes—
232C22⋊C4×C101—24no—
233C22⋊C4×C101—24no—
234C22⋊C4×C101—24no—
235C22⋊C4×C101—24no—
236C22⋊C4×C101—42no—
237C22⋊C4×C101—42no—
238C22⋊C4×C101C22⋊C414yes—
239C22⋊C4×C101C22⋊C414yes—
240C42×C101—24no—
241C42×C101—42no—
242C42×C101C22×C412yes—
243C42×C101C2×D412yes—
244C23×C101—21no—
245C23×C101—21no—
246C23×C101—21no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—21no—
252C23×C101—21no—
253C23×C101—21no—
254C23×C101—22no—
255C23×C101—41no—
256C23×C101—41no—
257C23×C101—41no—
258C23×C101—41no—
259C23×C101—41no—
260C23×C101—41no—
261C23×C101C2×C22⋊C412yes—
262C23×C101C2×C22⋊C412yes—
263C23×C101AGL(1,ℤ/8)12yes—
264C23×C101#13712yes—
265C23×C101C22×D411yescharacteristic
266D4×C101—28no—
267D4×C101—22no—
268D4×C101—22no—
269D4×C101—48no—
270D4×C101—41no—
271D4×C101—41no—
272D4×C101—84no—
273C2×C4×C101—21no—
274C2×C4×C101—21no—
275C2×C4×C101—21no—
276C2×C4×C101—21no—
277C2×C4×C101—21no—
278C2×C4×C101—21no—
279C2×C4×C101—21no—
280C2×C4×C101—21no—
281C2×C4×C101—22no—
282C2×C4×C101—22no—
283C2×C4×C101—22no—
284C2×C4×C101—22no—
285C2×C4×C101—22no—
286C2×C4×C101—22no—
287C2×C4×C101—22no—
288C2×C4×C101—22no—
289C2×C4×C101—22no—
290C2×C4×C101—22no—
291C2×C4×C101—22no—
292C2×C4×C101—22no—
293C2×C4×C101—41no—
294C2×C4×C101—41no—
295C2×C4×C101—41no—
296C2×C4×C101—41no—
297C2×C4×C101—41no—
298C2×C4×C101—41no—
299C2×C4×C101—41no—
300C2×C4×C101—41no—
301C2×C4×C101—41no—
302C2×C4×C101—41no—
303C2×C4×C101—41no—
304C2×C4×C101—41no—
305C2×C4×C101—41no—
306C2×C4×C101—41no—
307C2×C4×C101—41no—
308C2×C4×C101—41no—
309C2×C4×C101—41no—
310C2×C4×C101—84no—
311C2×C4×C101—84no—
312C2×C4×C101—84no—
313C2×C4×C101—84no—
314C2×C4×C101C2×C22⋊C412yes—
315C2×C4×C101C2×C22⋊C412yes—
316C2×C4×C101C2×C22⋊C412yes—
317C2×C4×C101C2×C22⋊C412yes—
318C2×C4×C101C23×C411yescharacteristic
319C2×C4×C101C22×D411yescharacteristic
320C2×C4×C101C2×#4111yescharacteristic
321C2×C4×C101C2×#4111yescharacteristic
322C2×C4×C101H(5,𝔽2)11yescharacteristic
323C2×C4×C1012−1+411yescharacteristic
324C8×C101—22no—
325C8×C101—41no—
326C8×C101—41no—
327C8×C101—41no—
328C22×C101—22no—
329C22×C101—22no—
330C22×C101—22no—
331C22×C101—22no—
332C22×C101—22no—
333C22×C101—22no—
334C22×C101—22no—
335C22×C101—22no—
336C22×C101—22no—
337C22×C101—41no—
338C22×C101—41no—
339C22×C101—41no—
340C22×C101—41no—
341C22×C101—42no—
342C22×C101—42no—
343C22×C101—42no—
344C22×C101—81no—
345C22×C101—81no—
346C22×C101—81no—
347C22×C101—81no—
348C22×C101#41714yes—
349C22×C101C22×C22⋊C411yescharacteristic
350C22×C101#54611yescharacteristic
351C22×C101#54711yescharacteristic
352C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C101C2×#13711yescharacteristic
354C22×C101#57611yescharacteristic
355C22×C101#57711yescharacteristic
356C4×C101—22no—
357C4×C101—22no—
358C4×C101—22no—
359C4×C101—22no—
360C4×C101—42no—
361C4×C101—42no—
362C4×C101—42no—
363C4×C101—42no—
364C4×C101—81no—
365C4×C101—81no—
366C4×C101—81no—
367C4×C101C4×#4111yescharacteristic
368C4×C101#52011yescharacteristic
369C4×C101#54611yescharacteristic
370C4×C101#54711yescharacteristic
371#22493C10111yesmaximal, characteristic, direct product factor, Sylow
372C2×C101—24no—
373C2×C101—42no—
374C2×C101—82no—
375C2×C101#233911yescharacteristic
376C2×C101C2×#41711yescharacteristic
377C2×C101#289711yescharacteristic
378C2×C101#331811yescharacteristic
379C2×C101#332011yescharacteristic
380C2×C101#334511yescharacteristic
381C2×C101#334611yescharacteristic
382C2×#553C2×C10111yescharacteristic
383C2×#435C2×C10111yescharacteristic, complemented
384D4×C4⋊C4C2×C10111yescharacteristic, complemented
385#1992C2×C10111yescharacteristic, complemented
386#1989C2×C10111yescharacteristic, complemented
387#1895C2×C10111yescharacteristic, complemented
388#1893C2×C10111yescharacteristic, complemented
389#1874C2×C10111yescharacteristic, complemented
390#1874C2×C10111yescharacteristic, complemented
391#1825C2×C10111yescharacteristic, complemented
392#1824C2×C10111yescharacteristic, complemented
393#1802C2×C10111yescharacteristic, complemented
394#1762C2×C10111yescharacteristic, complemented
395#1736C2×C10111yescharacteristic, complemented
396C2×#340C2×C10111yescharacteristic, complemented
397C101#2249311yescharacteristic, direct product factor, Sylow
398C22×M16C22×C10111yescharacteristic
399C23×C8C22×C10111yescharacteristic
400#553—24no—
401#553C4×C10118yescomplemented
402C2×#126—21no—
403C2×#125C22×C10111yescharacteristic
404C2×#123—21no—
405C2×#121—21no—
406C2×#121C22×C10111yescharacteristic
407C2×#121C22×C10111yescharacteristic
408C2×C4×D4—21no—
409C2×C4×D4—21no—
410C2×C4×D4C22×C10111yescharacteristic
411C2×C4×D4C22×C10111yescharacteristic
412C2×#117C22×C10111yescharacteristic
413C22×C4⋊C4C22×C10111yescharacteristic
414C22×C4⋊C4C22×C10111yescharacteristic
415C22×C4⋊C4C22×C10111yescharacteristic
416#435—24no—
417C2×C4⋊C8C22×C10111yescharacteristic
418C2×#102C22×C10111yescharacteristic
419C2×#102C22×C10111yescharacteristic
420C2×#102C22×C10111yescharacteristic
421C2×#102C22×C10111yescharacteristic
422C2×C22⋊C8C22×C10111yescharacteristic
423C2×C22⋊C8C22×C10111yescharacteristic
424C2×#97C22×C10111yescharacteristic
425#389—21no—
426#385—21no—
427#385—21no—
428#384C22×C10111yescharacteristic
429#380C22×C10111yescharacteristic
430#380C22×C10111yescharacteristic
431C4×C4⋊C4C22×C10111yescharacteristic
432#340C22×C10111yescharacteristic
433#340C22×C10111yescharacteristic
434#340C22×C10111yescharacteristic
435#340C22×C10111yescharacteristic
436#340C22×C10111yescharacteristic
437#340C22×C10111yescharacteristic
438#340C22×C10111yescharacteristic
439#340C22×C10111yescharacteristic
440#340C22×C10111yescharacteristic
441#340C22×C10111yescharacteristic
442#340C22×C10111yescharacteristic
443#340C22×C10111yescharacteristic
444C22×D4—21no—
445C22×D4—21no—
446C22×D4D4×C10111yescharacteristic
447C22×D4C23×C10111yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4C23×C10111yescharacteristic
453C23×C4C23×C10111yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8C23×C10111yescharacteristic
461C22×C8C23×C10111yescharacteristic
462C22×C8C23×C10111yescharacteristic
463C22×C8C23×C10111yescharacteristic
464#126—28no—
465#125—22no—
466#125C2×C4×C10114yescomplemented
467#123—28no—
468#121—28no—
469#121—22no—
470#121—22no—
471#121C2×C4×C10114yescomplemented
472#121C2×C4×C10114yescomplemented
473C4×D4—28no—
474C4×D4—22no—
475C4×D4—44no—
476C4×D4C2×C4×C10114yes—
477C4×D4C2×C4×C10114yescomplemented
478C4×D4D4×C10114yes—
479#117—22no—
480#117C2×C4×C10114yescomplemented
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4C2×C4×C10114yescomplemented
494C2×C4⋊C4D4×C10111yescharacteristic
495C2×C4⋊C4C23×C10111yescharacteristic
496C2×C4⋊C4C23×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⋊C4D4×C10111yescharacteristic
509C2×C22⋊C4D4×C10111yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42C23×C10111yescharacteristic
513C4⋊C8—22no—
514#102—22no—
515#102—22no—
516#102—41no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#97—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524C24—21no—
525C24C2×D4×C10111yescharacteristic
526C24C2×D4×C10111yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4C22⋊C4×C10114yes—
541C2×D4C22×C4×C10112yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—81no—
569C22×C4C22×C4×C10112yes—
570C22×C4C22×C4×C10112yes—
571C22×C4C2×D4×C10111yescharacteristic
572C22×C4C2×D4×C10111yescharacteristic
573C22×C4C2×D4×C10111yescharacteristic
574C22×C4C2×D4×C10111yescharacteristic
575C22×C4C2×D4×C10112yes—
576C22×C4C2×D4×C10112yes—
577C22×C4C24×C10111yescharacteristic
578M16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8#41×C10112yes—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C4⋊C4C22⋊C4×C10114yes—
610C4⋊C4C22×C4×C10112yes—
611C4⋊C4C22×C4×C10112yes—
612C4⋊C4C22×C4×C10112yes—
613C4⋊C4#41×C10112yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4C22⋊C4×C10114yes—
621C22⋊C4C22⋊C4×C10114yes—
622C42—24no—
623C42—42no—
624C42C22×C4×C10112yes—
625C42C2×D4×C10112yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23C2×C22⋊C4×C10112yes—
644C23C2×C22⋊C4×C10112yes—
645C23AGL(1,ℤ/8)×C10112yes—
646C23#137×C10112yes—
647C23C22×D4×C10111yescharacteristic
648D4—28no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4C2×C22⋊C4×C10112yes—
697C2×C4C2×C22⋊C4×C10112yes—
698C2×C4C2×C22⋊C4×C10112yes—
699C2×C4C2×C22⋊C4×C10112yes—
700C2×C4C23×C4×C10111yescharacteristic
701C2×C4C22×D4×C10111yescharacteristic
702C2×C4C2×#41×C10111yescharacteristic
703C2×C4C2×#41×C10111yescharacteristic
704C2×C4H(5,𝔽2)×C10111yescharacteristic
705C2×C42−1+4×C10111yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22#417×C10114yes—
731C22C22×C22⋊C4×C10111yescharacteristic
732C22#546×C10111yescharacteristic
733C22#547×C10111yescharacteristic
734C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
735C22C2×#137×C10111yescharacteristic
736C22#576×C10111yescharacteristic
737C22#577×C10111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C4×#41×C10111yescharacteristic
750C4#520×C10111yescharacteristic
751C4#546×C10111yescharacteristic
752C4#547×C10111yescharacteristic
753C2—24no—
754C2—42no—
755C2—82no—
756C2C101×#233911yescharacteristic
757C2C2×#417×C10111yescharacteristic
758C2C101×#289711yescharacteristic
759C2C101×#331811yescharacteristic
760C2C101×#332011yescharacteristic
761C2C101×#334511yescharacteristic
762C2C101×#334611yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#553×C101C2
LCSG ▷ C2×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
2. C2×#435×C101C2semidirect
3. D4×C4⋊C4×C101C2semidirect
4. C101×#1992C2semidirect
5. C101×#1989C2semidirect
6. C101×#1895C2semidirect
7. C101×#1893C2semidirect
8. C101×#1874C2semidirect
9. C101×#1874C2semidirect
10. C101×#1825C2semidirect
11. C101×#1824C2semidirect
12. C101×#1802C2semidirect
13. C101×#1762C2semidirect
14. C101×#1736C2semidirect
15. C2×#340×C101C2semidirect
19. #553×C101C4semidirect
84. #125×C101C2×C4semidirect
89. #121×C101C2×C4semidirect
90. #121×C101C2×C4semidirect
95. C4×D4×C101C2×C4semidirect
98. #117×C101C2×C4semidirect
111. C2×C4⋊C4×C101C2×C4semidirect
371. #22493C101direct (N × H)
383. C2×#435C2×C101semidirect
384. D4×C4⋊C4C2×C101semidirect
385. #1992C2×C101semidirect
386. #1989C2×C101semidirect
387. #1895C2×C101semidirect
388. #1893C2×C101semidirect
389. #1874C2×C101semidirect
390. #1874C2×C101semidirect
391. #1825C2×C101semidirect
392. #1824C2×C101semidirect
393. #1802C2×C101semidirect
394. #1762C2×C101semidirect
395. #1736C2×C101semidirect
396. C2×#340C2×C101semidirect
397. C101#22493direct (N × H)
401. #553C4×C101semidirect
466. #125C2×C4×C101semidirect
471. #121C2×C4×C101semidirect
472. #121C2×C4×C101semidirect
477. C4×D4C2×C4×C101semidirect
480. #117C2×C4×C101semidirect
493. 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×#553×C1012
C2×#435×C1012
D4×C4⋊C4×C1012
C101×#19922
C101×#19892
C101×#18952
C101×#18932
C101×#18742
C101×#18252
C101×#18242
C101×#18022
C101×#17622
C101×#17362
C2×#340×C1012
#22493101