Finite Group Databasebeta

← C101×#24362 #38806513

Subgroups — C101×#24362 #38806513

Order 25856.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C101C211yesmaximal, characteristic, complemented
2C2×#464×C101C211yesmaximal, characteristic, complemented
3C2×#460×C101C211yesmaximal, characteristic, complemented
4C2×#449×C101C211yesmaximal, characteristic, complemented
5C101×#2431C211yesmaximal, characteristic, complemented
6C101×#2341C211yesmaximal, characteristic, complemented
7C101×#2055C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#2012C211yesmaximal, characteristic, complemented
10C101×#2011C211yesmaximal, characteristic, complemented
11C101×#1893C211yesmaximal, characteristic, complemented
12C101×#1880C211yesmaximal, characteristic, complemented
13C101×#1878C211yesmaximal, characteristic, complemented
14C101×#1850C211yesmaximal, characteristic, complemented
15C101×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C2×#135×C101—24no—
19C2×#135×C101—24no—
20C2×#135×C101—24no—
21C22×Q16×C101C2211yescharacteristic
22C22×SD16×C101C2211yescharacteristic
23C22×SD16×C101C2211yescharacteristic
24C22×SD16×C101C2211yescharacteristic
25C22×D8×C101C2211yescharacteristic
26C22×D8×C101C2211yescharacteristic
27C23×C8×C101C2211yescharacteristic
28C2×#127×C101C2211yescharacteristic
29C2×#124×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31C2×C4×Q8×C101C2211yescharacteristic
32C2×C4×Q8×C101C2211yescharacteristic
33#464×C101—24no—
34#460×C101—24no—
35#449×C101—24no—
36C2×C4⋊C8×C101C2211yescharacteristic
37C2×C4⋊C8×C101C2211yescharacteristic
38C2×#103×C101C2211yescharacteristic
39C2×#103×C101C2211yescharacteristic
40C2×#103×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×C22⋊C8×C101C2211yescharacteristic
47#392×C101—21no—
48#392×C101—21no—
49#391×C101C2211yescharacteristic
50#390×C101—21no—
51#390×C101—21no—
52#390×C101C2211yescharacteristic
53#390×C101C2211yescharacteristic
54#390×C101C2211yescharacteristic
55#386×C101—21no—
56#386×C101—21no—
57#380×C101—21no—
58#380×C101C2211yescharacteristic
59C4×C22⋊C4×C101—21no—
60C4×C22⋊C4×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63#336×C101C2211yescharacteristic
64#336×C101C2211yescharacteristic
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—22no—
70C2×#41×C101—22no—
71C2×#41×C101—22no—
72C2×#41×C101—41no—
73C2×#41×C101—41no—
74C2×#41×C101—41no—
75C2×#41×C101—41no—
76C2×#41×C101D414yescomplemented
77C22×Q8×C101C2311yescharacteristic
78C22×Q8×C101C2311yescharacteristic
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—21no—
83C22×D4×C101—21no—
84C22×D4×C101C2311yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C22×D4×C101C2311yescharacteristic
87C23×C4×C101—21no—
88C23×C4×C101—21no—
89C23×C4×C101C2311yescharacteristic
90#135×C101—232no—
91C2×Q16×C101—22no—
92C2×Q16×C101—22no—
93C2×Q16×C101D414yescomplemented
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—22no—
98C2×SD16×C101—22no—
99C2×SD16×C101—22no—
100C2×SD16×C101—22no—
101C2×SD16×C101—22no—
102C2×SD16×C101D414yescomplemented
103C2×D8×C101—22no—
104C2×D8×C101—22no—
105C2×D8×C101—22no—
106C2×D8×C101—22no—
107C2×D8×C101—41no—
108C2×D8×C101—41no—
109C22×C8×C101—22no—
110C22×C8×C101—22no—
111C22×C8×C101—22no—
112C22×C8×C101C2311yescharacteristic
113C22×C8×C101C2311yescharacteristic
114C22×C8×C101C2311yescharacteristic
115C22×C8×C101C2311yescharacteristic
116#127×C101—22no—
117#127×C101—41no—
118#124×C101—22no—
119#124×C101—41no—
120#121×C101—22no—
121#121×C101—22no—
122C4×Q8×C101—22no—
123C4×Q8×C101—22no—
124C4×Q8×C101—41no—
125C4×Q8×C101—41no—
126C2×C4⋊C4×C101—21no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101C2311yescharacteristic
129C2×C4⋊C4×C101C2311yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
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×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101—21no—
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101—21no—
140C2×C22⋊C4×C101—21no—
141C2×C22⋊C4×C101D411yescharacteristic
142C2×C22⋊C4×C101D411yescharacteristic
143C2×C42×C101—21no—
144C2×C42×C101—21no—
145C2×C42×C101C2311yescharacteristic
146C2×C42×C101C2311yescharacteristic
147C4⋊C8×C101—22no—
148C4⋊C8×C101—22no—
149#103×C101—22no—
150#103×C101—22no—
151#103×C101—41no—
152#102×C101—22no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—41no—
157C22⋊C8×C101—22no—
158#95×C101—21no—
159#95×C101—21no—
160#95×C101—21no—
161#95×C101D411yescharacteristic
162#95×C101D411yescharacteristic
163C24×C101—21no—
164C24×C101—21no—
165C24×C101—21no—
166C24×C101C2×D411yescharacteristic
167#41×C101—28no—
168#41×C101—28no—
169#41×C101—44no—
170#41×C101—44no—
171#41×C101—44no—
172#41×C101—44no—
173#41×C101—44no—
174#41×C101—44no—
175C2×Q8×C101—21no—
176C2×Q8×C101—21no—
177C2×Q8×C101—21no—
178C2×Q8×C101—21no—
179C2×Q8×C101—21no—
180C2×Q8×C101—21no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101C2×D412yes—
184C2×Q8×C101C2×D412yes—
185C2×Q8×C101C2×D412yes—
186C2×Q8×C101C2×D412yes—
187C2×D4×C101—24no—
188C2×D4×C101—21no—
189C2×D4×C101—21no—
190C2×D4×C101—21no—
191C2×D4×C101—21no—
192C2×D4×C101—21no—
193C2×D4×C101—21no—
194C2×D4×C101—21no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—42no—
205C2×D4×C101—42no—
206C2×D4×C101—42no—
207C2×D4×C101—42no—
208C2×D4×C101—42no—
209C2×D4×C101—42no—
210C2×D4×C101—42no—
211C2×D4×C101—42no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101—81no—
215C2×D4×C101—81no—
216C2×D4×C101—81no—
217C2×D4×C101—81no—
218C2×D4×C101C2×D412yes—
219C2×D4×C101C2×D412yes—
220C22×C4×C101—21no—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—24no—
227C22×C4×C101—21no—
228C22×C4×C101—21no—
229C22×C4×C101—21no—
230C22×C4×C101—42no—
231C22×C4×C101—42no—
232C22×C4×C101—42no—
233C22×C4×C101—42no—
234C22×C4×C101—42no—
235C22×C4×C101C2×D411yescharacteristic
236C22×C4×C101C2×D411yescharacteristic
237C22×C4×C101C2×D411yescharacteristic
238C22×C4×C101C2×D411yescharacteristic
239C22×C4×C101C2×D412yes—
240C22×C4×C101C2×D411yescharacteristic
241C22×C4×C101#4112yes—
242C22×C4×C101C2411yescharacteristic
243Q16×C101—28no—
244SD16×C101—28no—
245SD16×C101—28no—
246SD16×C101—44no—
247D8×C101—28no—
248D8×C101—44no—
249C2×C8×C101—28no—
250C2×C8×C101—21no—
251C2×C8×C101—21no—
252C2×C8×C101—21no—
253C2×C8×C101—21no—
254C2×C8×C101—21no—
255C2×C8×C101—21no—
256C2×C8×C101—21no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101C2×D412yes—
261C2×C8×C101C2×D412yes—
262C4⋊C4×C101—21no—
263C4⋊C4×C101—21no—
264C4⋊C4×C101—21no—
265C4⋊C4×C101—21no—
266C4⋊C4×C101—21no—
267C4⋊C4×C101—21no—
268C4⋊C4×C101—42no—
269C4⋊C4×C101—42no—
270C22⋊C4×C101—22no—
271C22⋊C4×C101—41no—
272C22⋊C4×C101—42no—
273C22⋊C4×C101—42no—
274C22⋊C4×C101—42no—
275C22⋊C4×C101—42no—
276C22⋊C4×C101—42no—
277C22⋊C4×C101—81no—
278C22⋊C4×C101—81no—
279C22⋊C4×C101—81no—
280C22⋊C4×C101—81no—
281C22⋊C4×C101—81no—
282C42×C101—21no—
283C42×C101—21no—
284C42×C101—21no—
285C42×C101—21no—
286C42×C101—42no—
287C42×C101—42no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—21no—
291C23×C101—21no—
292C23×C101—21no—
293C23×C101—21no—
294C23×C101—22no—
295C23×C101—22no—
296C23×C101—41no—
297C23×C101—41no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101—41no—
302C23×C101—41no—
303C23×C101—41no—
304C23×C101—41no—
305C23×C101—41no—
306C23×C101—41no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101#12112yes—
316C23×C101C22×D411yescharacteristic
317Q8×C101—22no—
318Q8×C101—22no—
319Q8×C101—22no—
320Q8×C101—22no—
321Q8×C101—22no—
322Q8×C101—41no—
323Q8×C101—41no—
324Q8×C101#12014yes—
325D4×C101—22no—
326D4×C101—22no—
327D4×C101—22no—
328D4×C101—22no—
329D4×C101—48no—
330D4×C101—48no—
331D4×C101—41no—
332D4×C101—41no—
333D4×C101—41no—
334D4×C101—41no—
335D4×C101—41no—
336D4×C101—41no—
337D4×C101—41no—
338D4×C101—41no—
339D4×C101—84no—
340D4×C101—84no—
341D4×C101—84no—
342C2×C4×C101—22no—
343C2×C4×C101—21no—
344C2×C4×C101—22no—
345C2×C4×C101—22no—
346C2×C4×C101—21no—
347C2×C4×C101—21no—
348C2×C4×C101—21no—
349C2×C4×C101—22no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—21no—
354C2×C4×C101—21no—
355C2×C4×C101—21no—
356C2×C4×C101—22no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—21no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—21no—
363C2×C4×C101—48no—
364C2×C4×C101—48no—
365C2×C4×C101—41no—
366C2×C4×C101—41no—
367C2×C4×C101—41no—
368C2×C4×C101—41no—
369C2×C4×C101—41no—
370C2×C4×C101—41no—
371C2×C4×C101—41no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101#12112yes—
377C2×C4×C101#13512yescomplemented
378C2×C4×C101C22×D411yescharacteristic
379C2×C4×C101C22×D411yescharacteristic
380C2×C4×C101C22×D411yescharacteristic
381C2×C4×C101C2×#4111yescharacteristic
382C2×C4×C101H(5,𝔽2)11yescharacteristic
383C2×C4×C101H(5,𝔽2)11yescharacteristic
384C8×C101—22no—
385C8×C101—22no—
386C8×C101—41no—
387C8×C101—41no—
388C22×C101—22no—
389C22×C101—22no—
390C22×C101—22no—
391C22×C101—41no—
392C22×C101—41no—
393C22×C101—41no—
394C22×C101—41no—
395C22×C101—42no—
396C22×C101—42no—
397C22×C101—42no—
398C22×C101—42no—
399C22×C101—42no—
400C22×C101—42no—
401C22×C101—81no—
402C22×C101—81no—
403C22×C101—81no—
404C22×C101—81no—
405C22×C101—81no—
406C22×C101—81no—
407C22×C101—81no—
408C22×C101—81no—
409C22×C101—81no—
410C22×C101—81no—
411C22×C101—81no—
412C22×C101—81no—
413C22×C101—81no—
414C22×C101—81no—
415C22×C101—81no—
416C22×C101C2×#12111yescharacteristic
417C22×C101D4211yescharacteristic
418C22×C101D4211yescharacteristic
419C22×C101C2×#13511yescharacteristic
420C22×C101#57511yescharacteristic
421C22×C101#57611yescharacteristic
422C22×C101#57711yescharacteristic
423C4×C101—22no—
424C4×C101—24no—
425C4×C101—22no—
426C4×C101—42no—
427C4×C101—41no—
428C4×C101—41no—
429C4×C101—41no—
430C4×C101—81no—
431C4×C101—81no—
432C4×C101—81no—
433C4×C101C2×#12011yescharacteristic
434C4×C101#53411yescharacteristic
435C4×C101#54611yescharacteristic
436C4×C101#54611yescharacteristic
437#24362C10111yesmaximal, characteristic, direct product factor, Sylow
438C2×C101—42no—
439C2×C101—82no—
440C2×C101—82no—
441C2×C101—161no—
442C2×C101#241011yescharacteristic
443C2×C101#303511yescharacteristic
444C2×C101#304511yescharacteristic
445C2×C101#326811yescharacteristic
446C2×C101#327111yescharacteristic
447C2×C101#328211yescharacteristic
448C2×C101#328711yescharacteristic
449C22×#135C2×C10111yescharacteristic, complemented
450C2×#464C2×C10111yescharacteristic, complemented
451C2×#460C2×C10111yescharacteristic, complemented
452C2×#449C2×C10111yescharacteristic, complemented
453#2431C2×C10111yescharacteristic, complemented
454#2341C2×C10111yescharacteristic, complemented
455#2055C2×C10111yescharacteristic, complemented
456#2054C2×C10111yescharacteristic, complemented
457#2012C2×C10111yescharacteristic, complemented
458#2011C2×C10111yescharacteristic, complemented
459#1893C2×C10111yescharacteristic, complemented
460#1880C2×C10111yescharacteristic, complemented
461#1878C2×C10111yescharacteristic, complemented
462#1850C2×C10111yescharacteristic, complemented
463#1788C2×C10111yescharacteristic, complemented
464C101#2436211yescharacteristic, direct product factor, Sylow
465C22×#41C22×C10111yescharacteristic
466C22×#41C22×C10111yescharacteristic
467C2×#135—24no—
468C2×#135—24no—
469C2×#135—24no—
470C22×Q16C22×C10111yescharacteristic
471C22×SD16C22×C10111yescharacteristic
472C22×SD16C22×C10111yescharacteristic
473C22×SD16C22×C10111yescharacteristic
474C22×D8C22×C10111yescharacteristic
475C22×D8C22×C10111yescharacteristic
476C23×C8C22×C10111yescharacteristic
477C2×#127C22×C10111yescharacteristic
478C2×#124C22×C10111yescharacteristic
479C2×#121C22×C10111yescharacteristic
480C2×C4×Q8C22×C10111yescharacteristic
481C2×C4×Q8C22×C10111yescharacteristic
482#464—24no—
483#460—24no—
484#449—24no—
485C2×C4⋊C8C22×C10111yescharacteristic
486C2×C4⋊C8C22×C10111yescharacteristic
487C2×#103C22×C10111yescharacteristic
488C2×#103C22×C10111yescharacteristic
489C2×#103C22×C10111yescharacteristic
490C2×#102C22×C10111yescharacteristic
491C2×#102C22×C10111yescharacteristic
492C2×#102C22×C10111yescharacteristic
493C2×#102C22×C10111yescharacteristic
494C2×#102C22×C10111yescharacteristic
495C2×C22⋊C8C22×C10111yescharacteristic
496#392—21no—
497#392—21no—
498#391C22×C10111yescharacteristic
499#390—21no—
500#390—21no—
501#390C22×C10111yescharacteristic
502#390C22×C10111yescharacteristic
503#390C22×C10111yescharacteristic
504#386—21no—
505#386—21no—
506#380—21no—
507#380C22×C10111yescharacteristic
508C4×C22⋊C4—21no—
509C4×C22⋊C4C22×C10111yescharacteristic
510#340C22×C10111yescharacteristic
511#340C22×C10111yescharacteristic
512#336C22×C10111yescharacteristic
513#336C22×C10111yescharacteristic
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41D4×C10114yescomplemented
526C22×Q8C23×C10111yescharacteristic
527C22×Q8C23×C10111yescharacteristic
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4C23×C10111yescharacteristic
534C22×D4C23×C10111yescharacteristic
535C22×D4C23×C10111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C23×C10111yescharacteristic
539#135—232no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16D4×C10114yescomplemented
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16D4×C10114yescomplemented
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8C23×C10111yescharacteristic
562C22×C8C23×C10111yescharacteristic
563C22×C8C23×C10111yescharacteristic
564C22×C8C23×C10111yescharacteristic
565#127—22no—
566#127—41no—
567#124—22no—
568#124—41no—
569#121—22no—
570#121—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—41no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4C23×C10111yescharacteristic
578C2×C4⋊C4C23×C10111yescharacteristic
579C2×C4⋊C4C23×C10111yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C10111yescharacteristic
591C2×C22⋊C4D4×C10111yescharacteristic
592C2×C42—21no—
593C2×C42—21no—
594C2×C42C23×C10111yescharacteristic
595C2×C42C23×C10111yescharacteristic
596C4⋊C8—22no—
597C4⋊C8—22no—
598#103—22no—
599#103—22no—
600#103—41no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—41no—
606C22⋊C8—22no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95D4×C10111yescharacteristic
611#95D4×C10111yescharacteristic
612C24—21no—
613C24—21no—
614C24—21no—
615C24C2×D4×C10111yescharacteristic
616#41—28no—
617#41—28no—
618#41—44no—
619#41—44no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×D4×C10112yes—
633C2×Q8C2×D4×C10112yes—
634C2×Q8C2×D4×C10112yes—
635C2×Q8C2×D4×C10112yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C10112yes—
668C2×D4C2×D4×C10112yes—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4C2×D4×C10111yescharacteristic
685C22×C4C2×D4×C10111yescharacteristic
686C22×C4C2×D4×C10111yescharacteristic
687C22×C4C2×D4×C10111yescharacteristic
688C22×C4C2×D4×C10112yes—
689C22×C4C2×D4×C10111yescharacteristic
690C22×C4#41×C10112yes—
691C22×C4C24×C10111yescharacteristic
692Q16—28no—
693SD16—28no—
694SD16—28no—
695SD16—44no—
696D8—28no—
697D8—44no—
698C2×C8—28no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8C2×D4×C10112yes—
710C2×C8C2×D4×C10112yes—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C22⋊C4—22no—
720C22⋊C4—41no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—81no—
727C22⋊C4—81no—
728C22⋊C4—81no—
729C22⋊C4—81no—
730C22⋊C4—81no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—42no—
736C42—42no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23#121×C10112yes—
765C23C22×D4×C10111yescharacteristic
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—41no—
772Q8—41no—
773Q8#120×C10114yes—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—48no—
779D4—48no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4—84no—
790D4—84no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4#121×C10112yes—
826C2×C4#135×C10112yescomplemented
827C2×C4C22×D4×C10111yescharacteristic
828C2×C4C22×D4×C10111yescharacteristic
829C2×C4C22×D4×C10111yescharacteristic
830C2×C4C2×#41×C10111yescharacteristic
831C2×C4H(5,𝔽2)×C10111yescharacteristic
832C2×C4H(5,𝔽2)×C10111yescharacteristic
833C8—22no—
834C8—22no—
835C8—41no—
836C8—41no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22C2×#121×C10111yescharacteristic
866C22D42×C10111yescharacteristic
867C22D42×C10111yescharacteristic
868C22C2×#135×C10111yescharacteristic
869C22#575×C10111yescharacteristic
870C22#576×C10111yescharacteristic
871C22#577×C10111yescharacteristic
872C4—22no—
873C4—24no—
874C4—22no—
875C4—42no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4C2×#120×C10111yescharacteristic
883C4#534×C10111yescharacteristic
884C4#546×C10111yescharacteristic
885C4#546×C10111yescharacteristic
886C2—42no—
887C2—82no—
888C2—82no—
889C2—161no—
890C2C101×#241011yescharacteristic
891C2C101×#303511yescharacteristic
892C2C101×#304511yescharacteristic
893C2C101×#326811yescharacteristic
894C2C101×#327111yescharacteristic
895C2C101×#328211yescharacteristic
896C2C101×#328711yescharacteristic
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. C22×#135×C101C2semidirect
2. C2×#464×C101C2semidirect
3. C2×#460×C101C2semidirect
4. C2×#449×C101C2semidirect
5. C101×#2431C2semidirect
6. C101×#2341C2semidirect
7. C101×#2055C2semidirect
8. C101×#2054C2semidirect
9. C101×#2012C2semidirect
10. C101×#2011C2semidirect
11. C101×#1893C2semidirect
12. C101×#1880C2semidirect
13. C101×#1878C2semidirect
14. C101×#1850C2semidirect
15. C101×#1788C2semidirect
76. C2×#41×C101D4semidirect
93. C2×Q16×C101D4semidirect
102. C2×SD16×C101D4semidirect
377. C2×C4×C101#135semidirect
437. #24362C101direct (N × H)
449. C22×#135C2×C101semidirect
450. C2×#464C2×C101semidirect
451. C2×#460C2×C101semidirect
452. C2×#449C2×C101semidirect
453. #2431C2×C101semidirect
454. #2341C2×C101semidirect
455. #2055C2×C101semidirect
456. #2054C2×C101semidirect
457. #2012C2×C101semidirect
458. #2011C2×C101semidirect
459. #1893C2×C101semidirect
460. #1880C2×C101semidirect
461. #1878C2×C101semidirect
462. #1850C2×C101semidirect
463. #1788C2×C101semidirect
464. C101#24362direct (N × H)
525. C2×#41D4×C101semidirect
542. C2×Q16D4×C101semidirect
551. C2×SD16D4×C101semidirect
826. C2×C4#135×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1012
C2×#464×C1012
C2×#460×C1012
C2×#449×C1012
C101×#24312
C101×#23412
C101×#20552
C101×#20542
C101×#20122
C101×#20112
C101×#18932
C101×#18802
C101×#18782
C101×#18502
C101×#17882
#24362101