Finite Group Databasebeta

← C101×#25402 #38807553

Subgroups — C101×#25402 #38807553

Order 25856.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C101C211yesmaximal, characteristic, complemented
2C2×#465×C101C211yesmaximal, characteristic, complemented
3C2×#460×C101C211yesmaximal, characteristic, complemented
4C2×#435×C101C211yesmaximal, characteristic, complemented
5C101×#2541C211yesmaximal, characteristic
6C101×#2536C211yesmaximal, characteristic, complemented
7C101×#2034C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#2000C211yesmaximal, characteristic, complemented
10C101×#2000C211yesmaximal, characteristic, complemented
11C101×#1961C211yesmaximal, characteristic, complemented
12C101×#1949C211yesmaximal, characteristic, complemented
13C101×#1895C211yesmaximal, characteristic, complemented
14C101×#1893C211yesmaximal, characteristic, complemented
15C101×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20C2×#127×C101—21no—
21C2×#127×C101C2211yescharacteristic
22C2×C22⋊Q8×C101C2211yescharacteristic
23C2×C22⋊Q8×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×#121×C101C2211yescharacteristic
26C2×#121×C101C2211yescharacteristic
27C2×#121×C101C2211yescharacteristic
28C2×C4×Q8×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30#468×C101—24no—
31#465×C101—24no—
32#460×C101—24no—
33#435×C101—24no—
34C2×#107×C101C2211yescharacteristic
35C2×#106×C101C2211yescharacteristic
36C2×C4⋊C8×C101C2211yescharacteristic
37C2×#103×C101C2211yescharacteristic
38C2×#103×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×C22⋊C8×C101C2211yescharacteristic
46C2×C22⋊C8×C101C2211yescharacteristic
47C2×#97×C101C2211yescharacteristic
48#398×C101—21no—
49#394×C101—21no—
50#392×C101—21no—
51#392×C101—21no—
52#390×C101—21no—
53#388×C101—21no—
54#388×C101—21no—
55#382×C101C2211yescharacteristic
56#380×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic
58C4×C4⋊C4×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63C22×Q8×C101C2311yescharacteristic
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70C22×D4×C101D411yescharacteristic
71C22×D4×C101C2311yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C23×C4×C101C2311yescharacteristic
74C23×C4×C101C2311yescharacteristic
75C2×SD16×C101—22no—
76C2×SD16×C101—22no—
77C2×SD16×C101—22no—
78C2×SD16×C101—22no—
79C2×SD16×C101—41no—
80C2×SD16×C101—41no—
81C2×M16×C101—22no—
82C2×M16×C101—22no—
83C2×M16×C101—41no—
84C22×C8×C101—22no—
85C22×C8×C101—22no—
86C22×C8×C101—41no—
87C22×C8×C101C2311yescharacteristic
88C22×C8×C101C2311yescharacteristic
89C22×C8×C101C2311yescharacteristic
90C22×C8×C101C2311yescharacteristic
91#127×C101—22no—
92#127×C101—22no—
93#127×C101—44no—
94C22⋊Q8×C101—22no—
95C22⋊Q8×C101—22no—
96C22⋊Q8×C101—41no—
97C22⋊Q8×C101—41no—
98#121×C101—22no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—22no—
102#121×C101—41no—
103#121×C101—41no—
104#121×C101—41no—
105#121×C101—41no—
106C4×Q8×C101—22no—
107C4×Q8×C101—22no—
108C4×D4×C101—22no—
109C4×D4×C101—22no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—21no—
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×C101D411yescharacteristic
128C2×C22⋊C4×C101D411yescharacteristic
129C2×C42×C101—21no—
130C2×C42×C101—21no—
131C2×C42×C101C2311yescharacteristic
132#107×C101—22no—
133#106×C101—22no—
134C4⋊C8×C101D414yescomplemented
135#103×C101—22no—
136#103×C101D414yescomplemented
137#102×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—41no—
142#102×C101—41no—
143C22⋊C8×C101—22no—
144C22⋊C8×C101—22no—
145#97×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
155C2×Q8×C101—21no—
156C2×Q8×C101—21no—
157C2×Q8×C101—21no—
158C2×Q8×C101—21no—
159C2×Q8×C101—21no—
160C2×Q8×C101C2×D412yes—
161C2×D4×C101—22no—
162C2×D4×C101—22no—
163C2×D4×C101—21no—
164C2×D4×C101—21no—
165C2×D4×C101—21no—
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—41no—
176C2×D4×C101—42no—
177C2×D4×C101—42no—
178C2×D4×C101—42no—
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—81no—
189C2×D4×C101—81no—
190C2×D4×C101—81no—
191C2×D4×C101—81no—
192C2×D4×C101—81no—
193C2×D4×C101—81no—
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—21no—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2×D411yescharacteristic
214C22×C4×C101C2×D411yescharacteristic
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2411yescharacteristic
217SD16×C101—44no—
218SD16×C101—44no—
219M16×C101—44no—
220C2×C8×C101—21no—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—44no—
230C2×C8×C101C2×D412yes—
231C2×C8×C101C2×D412yes—
232C2×C8×C101C2×D412yes—
233C4⋊C4×C101—22no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—42no—
243C4⋊C4×C101—42no—
244C4⋊C4×C101—42no—
245C4⋊C4×C101C2×D412yes—
246C4⋊C4×C101#4112yes—
247C22⋊C4×C101—22no—
248C22⋊C4×C101—22no—
249C22⋊C4×C101—42no—
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—42no—
257C42×C101—42no—
258C42×C101—42no—
259C42×C101C2×D412yes—
260C42×C101#4112yes—
261C23×C101—21no—
262C23×C101—21no—
263C23×C101—21no—
264C23×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—21no—
274C23×C101—41no—
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×C101AGL(1,ℤ/8)12yes—
289C23×C101C22×D411yescharacteristic
290Q8×C101—22no—
291Q8×C101—22no—
292Q8×C101—41no—
293Q8×C101—41no—
294D4×C101—44no—
295D4×C101—41no—
296D4×C101—41no—
297D4×C101—41no—
298D4×C101—41no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—84no—
304D4×C101—84no—
305D4×C101—84no—
306D4×C101—84no—
307D4×C101—84no—
308D4×C101—84no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—22no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—22no—
319C2×C4×C101—22no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—41no—
323C2×C4×C101—41no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
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#12112yes—
346C2×C4×C101#12112yes—
347C2×C4×C101C22×D411yescharacteristic
348C2×C4×C101C22×D411yescharacteristic
349C2×C4×C101C2×#4111yescharacteristic
350C2×C4×C101C2×#4111yescharacteristic
351C2×C4×C101H(5,𝔽2)11yescharacteristic
352C2×C4×C101H(5,𝔽2)11yescharacteristic
353C8×C101—22no—
354C8×C101—22no—
355C8×C101—22no—
356C8×C101—41no—
357C22×C101—22no—
358C22×C101—22no—
359C22×C101—22no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—41no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—41no—
370C22×C101—41no—
371C22×C101—81no—
372C22×C101—81no—
373C22×C101—81no—
374C22×C101—81no—
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×C101C2×#12111yescharacteristic
386C22×C101D4211yescharacteristic
387C22×C101#54611yescharacteristic
388C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C101#57511yescharacteristic
390C22×C101#57711yescharacteristic
391C22×C101#57711yescharacteristic
392C4×C101—22no—
393C4×C101—22no—
394C4×C101—41no—
395C4×C101—41no—
396C4×C101—42no—
397C4×C101—42no—
398C4×C101—42no—
399C4×C101—81no—
400C4×C101—81no—
401C4×C101—81no—
402C4×C101#53211yescharacteristic
403C4×C101#54011yescharacteristic
404C4×C101D4211yescharacteristic
405C4×C101#55011yescharacteristic
406#25402C10111yesmaximal, characteristic, direct product factor, Sylow
407C2×C101—42no—
408C2×C101—81no—
409C2×C101—161no—
410C2×C101—161no—
411C2×C101#242811yescharacteristic
412C2×C101#305511yescharacteristic
413C2×C101#305711yescharacteristic
414C2×C101#326511yescharacteristic
415C2×C101#327111yescharacteristic
416C2×C101#331011yescharacteristic
417C2×C101#331711yescharacteristic
418C2×#468C2×C10111yescharacteristic, complemented
419C2×#465C2×C10111yescharacteristic, complemented
420C2×#460C2×C10111yescharacteristic, complemented
421C2×#435C2×C10111yescharacteristic, complemented
422#2541C2×C10111yescharacteristic
423#2536C2×C10111yescharacteristic, complemented
424#2034C2×C10111yescharacteristic, complemented
425#2033C2×C10111yescharacteristic, complemented
426#2000C2×C10111yescharacteristic, complemented
427#2000C2×C10111yescharacteristic, complemented
428#1961C2×C10111yescharacteristic, complemented
429#1949C2×C10111yescharacteristic, complemented
430#1895C2×C10111yescharacteristic, complemented
431#1893C2×C10111yescharacteristic, complemented
432#1763C2×C10111yescharacteristic, complemented
433C101#2540211yescharacteristic, direct product factor, Sylow
434C22×SD16C22×C10111yescharacteristic
435C22×SD16C22×C10111yescharacteristic
436C22×M16C22×C10111yescharacteristic
437C23×C8C22×C10111yescharacteristic
438C2×#127—21no—
439C2×#127C22×C10111yescharacteristic
440C2×C22⋊Q8C22×C10111yescharacteristic
441C2×C22⋊Q8C22×C10111yescharacteristic
442C2×#121C22×C10111yescharacteristic
443C2×#121C22×C10111yescharacteristic
444C2×#121C22×C10111yescharacteristic
445C2×#121C22×C10111yescharacteristic
446C2×C4×Q8C22×C10111yescharacteristic
447C2×C4×D4C22×C10111yescharacteristic
448#468—24no—
449#465—24no—
450#460—24no—
451#435—24no—
452C2×#107C22×C10111yescharacteristic
453C2×#106C22×C10111yescharacteristic
454C2×C4⋊C8C22×C10111yescharacteristic
455C2×#103C22×C10111yescharacteristic
456C2×#103C22×C10111yescharacteristic
457C2×#102C22×C10111yescharacteristic
458C2×#102C22×C10111yescharacteristic
459C2×#102C22×C10111yescharacteristic
460C2×#102C22×C10111yescharacteristic
461C2×#102C22×C10111yescharacteristic
462C2×#102C22×C10111yescharacteristic
463C2×C22⋊C8C22×C10111yescharacteristic
464C2×C22⋊C8C22×C10111yescharacteristic
465C2×#97C22×C10111yescharacteristic
466#398—21no—
467#394—21no—
468#392—21no—
469#392—21no—
470#390—21no—
471#388—21no—
472#388—21no—
473#382C22×C10111yescharacteristic
474#380C22×C10111yescharacteristic
475#380C22×C10111yescharacteristic
476C4×C4⋊C4C22×C10111yescharacteristic
477#340C22×C10111yescharacteristic
478#340C22×C10111yescharacteristic
479#340C22×C10111yescharacteristic
480#340C22×C10111yescharacteristic
481C22×Q8C23×C10111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C10111yescharacteristic
489C22×D4C23×C10111yescharacteristic
490C22×D4C23×C10111yescharacteristic
491C23×C4C23×C10111yescharacteristic
492C23×C4C23×C10111yescharacteristic
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—41no—
498C2×SD16—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—41no—
505C22×C8C23×C10111yescharacteristic
506C22×C8C23×C10111yescharacteristic
507C22×C8C23×C10111yescharacteristic
508C22×C8C23×C10111yescharacteristic
509#127—22no—
510#127—22no—
511#127—44no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—41no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522#121—41no—
523#121—41no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×D4—22no—
527C4×D4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4D4×C10111yescharacteristic
532C2×C4⋊C4C23×C10111yescharacteristic
533C2×C4⋊C4C23×C10111yescharacteristic
534C2×C4⋊C4C23×C10111yescharacteristic
535C2×C4⋊C4C23×C10111yescharacteristic
536C2×C4⋊C4C23×C10111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C10111yescharacteristic
546C2×C22⋊C4D4×C10111yescharacteristic
547C2×C42—21no—
548C2×C42—21no—
549C2×C42C23×C10111yescharacteristic
550#107—22no—
551#106—22no—
552C4⋊C8D4×C10114yescomplemented
553#103—22no—
554#103D4×C10114yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560#102—41no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563#97—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569C24—21no—
570C24—21no—
571C24C2×D4×C10111yescharacteristic
572C24C2×D4×C10111yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C10112yes—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—41no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C22×C4—21no—
613C22×C4—21no—
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×C4C2×D4×C10111yescharacteristic
631C22×C4C2×D4×C10111yescharacteristic
632C22×C4C2×D4×C10111yescharacteristic
633C22×C4C2×D4×C10111yescharacteristic
634C22×C4C24×C10111yescharacteristic
635SD16—44no—
636SD16—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C10112yes—
649C2×C8C2×D4×C10112yes—
650C2×C8C2×D4×C10112yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4C2×D4×C10112yes—
664C4⋊C4#41×C10112yes—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—42no—
676C42—42no—
677C42C2×D4×C10112yes—
678C42#41×C10112yes—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23AGL(1,ℤ/8)×C10112yes—
707C23C22×D4×C10111yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712D4—44no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—84no—
722D4—84no—
723D4—84no—
724D4—84no—
725D4—84no—
726D4—84no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
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#121×C10112yes—
764C2×C4#121×C10112yes—
765C2×C4C22×D4×C10111yescharacteristic
766C2×C4C22×D4×C10111yescharacteristic
767C2×C4C2×#41×C10111yescharacteristic
768C2×C4C2×#41×C10111yescharacteristic
769C2×C4H(5,𝔽2)×C10111yescharacteristic
770C2×C4H(5,𝔽2)×C10111yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C10111yescharacteristic
804C22D42×C10111yescharacteristic
805C22#546×C10111yescharacteristic
806C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
807C22#575×C10111yescharacteristic
808C22#577×C10111yescharacteristic
809C22#577×C10111yescharacteristic
810C4—22no—
811C4—22no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4#532×C10111yescharacteristic
821C4#540×C10111yescharacteristic
822C4D42×C10111yescharacteristic
823C4#550×C10111yescharacteristic
824C2—42no—
825C2—81no—
826C2—161no—
827C2—161no—
828C2C101×#242811yescharacteristic
829C2C101×#305511yescharacteristic
830C2C101×#305711yescharacteristic
831C2C101×#326511yescharacteristic
832C2C101×#327111yescharacteristic
833C2C101×#331011yescharacteristic
834C2C101×#331711yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#2541C2
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×#465×C101C2semidirect
3. C2×#460×C101C2semidirect
4. C2×#435×C101C2semidirect
6. C101×#2536C2semidirect
7. C101×#2034C2semidirect
8. C101×#2033C2semidirect
9. C101×#2000C2semidirect
10. C101×#2000C2semidirect
11. C101×#1961C2semidirect
12. C101×#1949C2semidirect
13. C101×#1895C2semidirect
14. C101×#1893C2semidirect
15. C101×#1763C2semidirect
134. C4⋊C8×C101D4semidirect
136. #103×C101D4semidirect
406. #25402C101direct (N × H)
418. C2×#468C2×C101semidirect
419. C2×#465C2×C101semidirect
420. C2×#460C2×C101semidirect
421. C2×#435C2×C101semidirect
423. #2536C2×C101semidirect
424. #2034C2×C101semidirect
425. #2033C2×C101semidirect
426. #2000C2×C101semidirect
427. #2000C2×C101semidirect
428. #1961C2×C101semidirect
429. #1949C2×C101semidirect
430. #1895C2×C101semidirect
431. #1893C2×C101semidirect
432. #1763C2×C101semidirect
433. C101#25402direct (N × H)
552. C4⋊C8D4×C101semidirect
554. #103D4×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×#465×C1012
C2×#460×C1012
C2×#435×C1012
C101×#25412
C101×#25362
C101×#20342
C101×#20332
C101×#20002
C101×#19612
C101×#19492
C101×#18952
C101×#18932
C101×#17632
#25402101