Finite Group Databasebeta

← C101×#25139 #38807290

Subgroups — C101×#25139 #38807290

Order 25856.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C101C211yesmaximal, characteristic, complemented
2C2×#449×C101C211yesmaximal, characteristic, complemented
3C2×#436×C101C211yesmaximal, characteristic, complemented
4C2×#417×C101C211yesmaximal, characteristic, complemented
5C101×#2416C211yesmaximal, characteristic, complemented
6C101×#2407C211yesmaximal, characteristic, complemented
7C101×#2067C211yesmaximal, characteristic, complemented
8C101×#2055C211yesmaximal, characteristic, complemented
9C101×#2036C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1970C211yesmaximal, characteristic, complemented
12C101×#1933C211yesmaximal, characteristic, complemented
13C101×#1895C211yesmaximal, characteristic, complemented
14C101×#1895C211yesmaximal, characteristic, complemented
15C101×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic
20C22×M16×C101C2211yescharacteristic
21C2×C22⋊Q8×C101C2211yescharacteristic
22C2×#121×C101—21no—
23C2×#121×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×#121×C101C2211yescharacteristic
26C2×C4×D4×C101C2211yescharacteristic
27C22×C4⋊C4×C101C2211yescharacteristic
28#468×C101—24no—
29#449×C101—24no—
30#436×C101—24no—
31C2×#107×C101C2211yescharacteristic
32C2×#107×C101C2211yescharacteristic
33C2×C4⋊C8×C101C2211yescharacteristic
34#417×C101—24no—
35C2×#103×C101C2211yescharacteristic
36C2×#103×C101C2211yescharacteristic
37C2×#103×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×C4×C8×C101C2211yescharacteristic
46#396×C101—21no—
47#394×C101—21no—
48#394×C101—21no—
49#392×C101—21no—
50#391×C101C2211yescharacteristic
51#390×C101C2211yescharacteristic
52#390×C101C2211yescharacteristic
53#389×C101C2211yescharacteristic
54#386×C101—21no—
55#386×C101—21no—
56#385×C101—21no—
57#380×C101C2211yescharacteristic
58#380×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×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×C101D411yescharacteristic
75C22×D4×C101C2311yescharacteristic
76C22×D4×C101C2311yescharacteristic
77C23×C4×C101—21no—
78C23×C4×C101—21no—
79C23×C4×C101C2311yescharacteristic
80C23×C4×C101C2311yescharacteristic
81C2×SD16×C101—22no—
82C2×SD16×C101—22no—
83C2×SD16×C101—41no—
84C2×D8×C101—22no—
85C2×D8×C101—22no—
86C2×D8×C101—41no—
87C2×M16×C101—22no—
88C2×M16×C101—22no—
89C2×M16×C101—22no—
90C2×M16×C101—22no—
91C2×M16×C101—41no—
92C2×M16×C101—41no—
93C22×C8×C101C2311yescharacteristic
94C22×C8×C101C2311yescharacteristic
95C22×C8×C101C2311yescharacteristic
96C22×C8×C101C2311yescharacteristic
97C22⋊Q8×C101—22no—
98C22⋊Q8×C101—41no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—22no—
102#121×C101—22no—
103#121×C101—41no—
104#121×C101—41no—
105#121×C101—44no—
106C4×D4×C101—22no—
107C4×D4×C101—22no—
108C2×C4⋊C4×C101—22no—
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—41no—
113C2×C4⋊C4×C101D411yescharacteristic
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×C101C2311yescharacteristic
132#107×C101—22no—
133#107×C101—41no—
134C4⋊C8×C101—22no—
135#103×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—41no—
143C22⋊C8×C101—22no—
144C22⋊C8×C101D414yescomplemented
145C4×C8×C101—22no—
146#95×C101—21no—
147#95×C101—21no—
148#95×C101—21no—
149#95×C101—21no—
150#95×C101—21no—
151C24×C101—21no—
152C24×C101—21no—
153C24×C101C2×D411yescharacteristic
154C24×C101C2×D411yescharacteristic
155#41×C101—28no—
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×C101—21no—
163C2×Q8×C101—21no—
164C2×Q8×C101C2×D412yes—
165C2×D4×C101—22no—
166C2×D4×C101—22no—
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—41no—
179C2×D4×C101—42no—
180C2×D4×C101—42no—
181C2×D4×C101—42no—
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—81no—
190C2×D4×C101—81no—
191C2×D4×C101#4112yes—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
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—42no—
209C22×C4×C101—42no—
210C22×C4×C101—42no—
211C22×C4×C101—42no—
212C22×C4×C101—42no—
213C22×C4×C101—81no—
214C22×C4×C101C2×D411yescharacteristic
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2×D411yescharacteristic
217C22×C4×C101C2×D412yes—
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101#4112yes—
220C22×C4×C101C2411yescharacteristic
221SD16×C101—44no—
222D8×C101—44no—
223M16×C101—44no—
224M16×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×C101C2×D412yes—
235C2×C8×C101C2×D412yes—
236C2×C8×C101C2×D412yes—
237C4⋊C4×C101—22no—
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—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—42no—
248C4⋊C4×C101—42no—
249C4⋊C4×C101—42no—
250C4⋊C4×C101C2×D412yes—
251C22⋊C4×C101—22no—
252C22⋊C4×C101—22no—
253C22⋊C4×C101—42no—
254C22⋊C4×C101—42no—
255C22⋊C4×C101—42no—
256C22⋊C4×C101—42no—
257C22⋊C4×C101—42no—
258C22⋊C4×C101—42no—
259C22⋊C4×C101—42no—
260C22⋊C4×C101—81no—
261C22⋊C4×C101—81no—
262C22⋊C4×C101—81no—
263C42×C101—21no—
264C42×C101—21no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—22no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—21no—
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#12112yes—
293C23×C101C22×D411yescharacteristic
294Q8×C101—22no—
295Q8×C101—22no—
296Q8×C101—41no—
297Q8×C101—41no—
298D4×C101—22no—
299D4×C101—22no—
300D4×C101—44no—
301D4×C101—48no—
302D4×C101—41no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—84no—
309D4×C101—84no—
310D4×C101—84no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—22no—
316C2×C4×C101—22no—
317C2×C4×C101—22no—
318C2×C4×C101—22no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—22no—
323C2×C4×C101—22no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—48no—
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—41no—
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—84no—
349C2×C4×C101#12112yes—
350C2×C4×C101AGL(1,ℤ/8)12yes—
351C2×C4×C101C22×D411yescharacteristic
352C2×C4×C101C22×D411yescharacteristic
353C2×C4×C101C2×#4111yescharacteristic
354C2×C4×C101C2×#4111yescharacteristic
355C2×C4×C101H(5,𝔽2)11yescharacteristic
356C2×C4×C101H(5,𝔽2)11yescharacteristic
357C8×C101—22no—
358C8×C101—22no—
359C8×C101—22no—
360C8×C101—41no—
361C22×C101—22no—
362C22×C101—22no—
363C22×C101—22no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—42no—
370C22×C101—42no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—41no—
375C22×C101—41no—
376C22×C101—41no—
377C22×C101—42no—
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×C101C2×#12111yescharacteristic
390C22×C101D4211yescharacteristic
391C22×C101#54611yescharacteristic
392C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C101#57511yescharacteristic
394C22×C101#57611yescharacteristic
395C22×C101#57811yescharacteristic
396C4×C101—22no—
397C4×C101—22no—
398C4×C101—41no—
399C4×C101—42no—
400C4×C101—42no—
401C4×C101—41no—
402C4×C101—81no—
403C4×C101—81no—
404C4×C101—81no—
405C4×C101—81no—
406C4×C101#52511yescharacteristic
407C4×C101#53811yescharacteristic
408C4×C101D4211yescharacteristic
409C4×C101#54611yescharacteristic
410#25139C10111yesmaximal, characteristic, direct product factor, Sylow
411C2×C101—42no—
412C2×C101—81no—
413C2×C101—82no—
414C2×C101—161no—
415C2×C101#242411yescharacteristic
416C2×C101#305511yescharacteristic
417C2×C101#306111yescharacteristic
418C2×C101#327411yescharacteristic
419C2×C101#327711yescharacteristic
420C2×C101#332211yescharacteristic
421C2×C101#333011yescharacteristic
422C2×#468C2×C10111yescharacteristic, complemented
423C2×#449C2×C10111yescharacteristic, complemented
424C2×#436C2×C10111yescharacteristic, complemented
425C2×#417C2×C10111yescharacteristic, complemented
426#2416C2×C10111yescharacteristic, complemented
427#2407C2×C10111yescharacteristic, complemented
428#2067C2×C10111yescharacteristic, complemented
429#2055C2×C10111yescharacteristic, complemented
430#2036C2×C10111yescharacteristic, complemented
431#1999C2×C10111yescharacteristic, complemented
432#1970C2×C10111yescharacteristic, complemented
433#1933C2×C10111yescharacteristic, complemented
434#1895C2×C10111yescharacteristic, complemented
435#1895C2×C10111yescharacteristic, complemented
436#1852C2×C10111yescharacteristic, complemented
437C101#2513911yescharacteristic, direct product factor, Sylow
438C22×#41C22×C10111yescharacteristic
439C22×SD16C22×C10111yescharacteristic
440C22×D8C22×C10111yescharacteristic
441C22×M16C22×C10111yescharacteristic
442C22×M16C22×C10111yescharacteristic
443C2×C22⋊Q8C22×C10111yescharacteristic
444C2×#121—21no—
445C2×#121C22×C10111yescharacteristic
446C2×#121C22×C10111yescharacteristic
447C2×#121C22×C10111yescharacteristic
448C2×C4×D4C22×C10111yescharacteristic
449C22×C4⋊C4C22×C10111yescharacteristic
450#468—24no—
451#449—24no—
452#436—24no—
453C2×#107C22×C10111yescharacteristic
454C2×#107C22×C10111yescharacteristic
455C2×C4⋊C8C22×C10111yescharacteristic
456#417—24no—
457C2×#103C22×C10111yescharacteristic
458C2×#103C22×C10111yescharacteristic
459C2×#103C22×C10111yescharacteristic
460C2×#102C22×C10111yescharacteristic
461C2×#102C22×C10111yescharacteristic
462C2×#102C22×C10111yescharacteristic
463C2×#102C22×C10111yescharacteristic
464C2×#102C22×C10111yescharacteristic
465C2×C22⋊C8C22×C10111yescharacteristic
466C2×C22⋊C8C22×C10111yescharacteristic
467C2×C4×C8C22×C10111yescharacteristic
468#396—21no—
469#394—21no—
470#394—21no—
471#392—21no—
472#391C22×C10111yescharacteristic
473#390C22×C10111yescharacteristic
474#390C22×C10111yescharacteristic
475#389C22×C10111yescharacteristic
476#386—21no—
477#386—21no—
478#385—21no—
479#380C22×C10111yescharacteristic
480#380C22×C10111yescharacteristic
481#340C22×C10111yescharacteristic
482#340C22×C10111yescharacteristic
483#340C22×C10111yescharacteristic
484#340C22×C10111yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8C23×C10111yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4D4×C10111yescharacteristic
497C22×D4C23×C10111yescharacteristic
498C22×D4C23×C10111yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C23×C10111yescharacteristic
502C23×C4C23×C10111yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C23×C10111yescharacteristic
516C22×C8C23×C10111yescharacteristic
517C22×C8C23×C10111yescharacteristic
518C22×C8C23×C10111yescharacteristic
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—44no—
528C4×D4—22no—
529C4×D4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4D4×C10111yescharacteristic
536C2×C4⋊C4C23×C10111yescharacteristic
537C2×C4⋊C4C23×C10111yescharacteristic
538C2×C4⋊C4C23×C10111yescharacteristic
539C2×C4⋊C4C23×C10111yescharacteristic
540C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4—21no—
551C2×C22⋊C4D4×C10111yescharacteristic
552C2×C22⋊C4D4×C10111yescharacteristic
553C2×C42C23×C10111yescharacteristic
554#107—22no—
555#107—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#103D4×C10114yescomplemented
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—41no—
565C22⋊C8—22no—
566C22⋊C8D4×C10114yescomplemented
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573C24—21no—
574C24—21no—
575C24C2×D4×C10111yescharacteristic
576C24C2×D4×C10111yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C10112yes—
587C2×D4—22no—
588C2×D4—22no—
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—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C10112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C10111yescharacteristic
637C22×C4C2×D4×C10111yescharacteristic
638C22×C4C2×D4×C10111yescharacteristic
639C22×C4C2×D4×C10112yes—
640C22×C4C2×D4×C10111yescharacteristic
641C22×C4#41×C10112yes—
642C22×C4C24×C10111yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
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×C8C2×D4×C10112yes—
657C2×C8C2×D4×C10112yes—
658C2×C8C2×D4×C10112yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C10112yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
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#121×C10112yes—
715C23C22×D4×C10111yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
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—84no—
771C2×C4#121×C10112yes—
772C2×C4AGL(1,ℤ/8)×C10112yes—
773C2×C4C22×D4×C10111yescharacteristic
774C2×C4C22×D4×C10111yescharacteristic
775C2×C4C2×#41×C10111yescharacteristic
776C2×C4C2×#41×C10111yescharacteristic
777C2×C4H(5,𝔽2)×C10111yescharacteristic
778C2×C4H(5,𝔽2)×C10111yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×#121×C10111yescharacteristic
812C22D42×C10111yescharacteristic
813C22#546×C10111yescharacteristic
814C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
815C22#575×C10111yescharacteristic
816C22#576×C10111yescharacteristic
817C22#578×C10111yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4#525×C10111yescharacteristic
829C4#538×C10111yescharacteristic
830C4D42×C10111yescharacteristic
831C4#546×C10111yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2C101×#242411yescharacteristic
837C2C101×#305511yescharacteristic
838C2C101×#306111yescharacteristic
839C2C101×#327411yescharacteristic
840C2C101×#327711yescharacteristic
841C2C101×#332211yescharacteristic
842C2C101×#333011yescharacteristic
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×#468×C101C2semidirect
2. C2×#449×C101C2semidirect
3. C2×#436×C101C2semidirect
4. C2×#417×C101C2semidirect
5. C101×#2416C2semidirect
6. C101×#2407C2semidirect
7. C101×#2067C2semidirect
8. C101×#2055C2semidirect
9. C101×#2036C2semidirect
10. C101×#1999C2semidirect
11. C101×#1970C2semidirect
12. C101×#1933C2semidirect
13. C101×#1895C2semidirect
14. C101×#1895C2semidirect
15. C101×#1852C2semidirect
137. #103×C101D4semidirect
144. C22⋊C8×C101D4semidirect
410. #25139C101direct (N × H)
422. C2×#468C2×C101semidirect
423. C2×#449C2×C101semidirect
424. C2×#436C2×C101semidirect
425. C2×#417C2×C101semidirect
426. #2416C2×C101semidirect
427. #2407C2×C101semidirect
428. #2067C2×C101semidirect
429. #2055C2×C101semidirect
430. #2036C2×C101semidirect
431. #1999C2×C101semidirect
432. #1970C2×C101semidirect
433. #1933C2×C101semidirect
434. #1895C2×C101semidirect
435. #1895C2×C101semidirect
436. #1852C2×C101semidirect
437. C101#25139direct (N × H)
559. #103D4×C101semidirect
566. C22⋊C8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1012
C2×#449×C1012
C2×#436×C1012
C2×#417×C1012
C101×#24162
C101×#24072
C101×#20672
C101×#20552
C101×#20362
C101×#19992
C101×#19702
C101×#19332
C101×#18952
C101×#18522
#25139101