Finite Group Databasebeta

← C101×#18416 #38800567

Subgroups — C101×#18416 #38800567

Order 25856.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3535C211yesmaximal, characteristic, complemented
2C101×#3194C211yesmaximal, characteristic, complemented
3C101×#3187C211yesmaximal, characteristic, complemented
4C101×#2661C211yesmaximal, characteristic, complemented
5C101×#1612C211yesmaximal, characteristic, complemented
6C101×#1611C211yesmaximal, characteristic, complemented
7C101×#1609C211yesmaximal, characteristic, complemented
8C101×#1608C211yesmaximal, characteristic, complemented
9C101×#1600C211yesmaximal, characteristic, complemented
10C101×#1599C211yesmaximal, characteristic, complemented
11C101×#1597C211yesmaximal, characteristic, complemented
12C101×#1596C211yesmaximal, characteristic, complemented
13C101×#1508C211yesmaximal, characteristic, complemented
14C101×#1501C211yesmaximal, characteristic, complemented
15C101×#1468C211yesmaximal, characteristic, complemented
16#563×C101—21no—
17#562×C101—21no—
18#554×C101—21no—
19#552×C101—21no—
20#551×C101—21no—
21#551×C101—21no—
22#547×C101—21no—
23#546×C101—21no—
24#544×C101C2211yescharacteristic
25#543×C101C2211yescharacteristic
26#542×C101—21no—
27#539×C101—21no—
28#539×C101—21no—
29#539×C101C2211yescharacteristic
30#538×C101C2211yescharacteristic
31#536×C101—21no—
32#525×C101C2211yescharacteristic
33C2×#123×C101C2211yescharacteristic
34C2×C22⋊Q8×C101C2211yescharacteristic
35C2×#121×C101C2211yescharacteristic
36#483×C101C2211yescharacteristic
37#483×C101C2211yescharacteristic
38#483×C101C2211yescharacteristic
39#482×C101—21no—
40#481×C101—21no—
41#480×C101C2211yescharacteristic
42#469×C101—21no—
43#468×C101—21no—
44#465×C101—21no—
45#465×C101—21no—
46#450×C101C2211yescharacteristic
47#450×C101C2211yescharacteristic
48#450×C101C2211yescharacteristic
49#449×C101—21no—
50#448×C101—21no—
51#447×C101C2211yescharacteristic
52#407×C101C2211yescharacteristic
53C2×C22⋊C8×C101C2211yescharacteristic
54#398×C101C2211yescharacteristic
55#397×C101C2211yescharacteristic
56#394×C101—21no—
57#394×C101C2211yescharacteristic
58#392×C101—21no—
59#392×C101C2211yescharacteristic
60#390×C101—21no—
61#388×C101—21no—
62C4×C22⋊C4×C101C2211yescharacteristic
63#328×C101C2211yescharacteristic
64#328×C101C2211yescharacteristic
65#328×C101C2211yescharacteristic
66#328×C101C2211yescharacteristic
67#328×C101C2211yescharacteristic
68#328×C101C2211yescharacteristic
69#327×C101C2211yescharacteristic
70#327×C101C2211yescharacteristic
71#324×C101C2211yescharacteristic
72#324×C101C2211yescharacteristic
73#323×C101C2211yescharacteristic
74#323×C101C2211yescharacteristic
75C2×#41×C101—21no—
76C2×#41×C101D411yescharacteristic, complemented
77C22×Q8×C101D411yescharacteristic, complemented
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101D411yescharacteristic
81C22×D4×C101C2311yescharacteristic
82C23×C4×C101C2311yescharacteristic
83C2×SD16×C101—21no—
84C2×SD16×C101—21no—
85C2×SD16×C101—21no—
86C2×D8×C101—21no—
87C2×M16×C101—21no—
88C22×C8×C101—21no—
89C4⋊Q8×C101—21no—
90C4⋊Q8×C101—21no—
91C4⋊Q8×C101—21no—
92#126×C101—21no—
93#126×C101—21no—
94#126×C101—21no—
95#126×C101—21no—
96#126×C101—21no—
97#126×C101—21no—
98#125×C101—21no—
99#125×C101—21no—
100#125×C101—21no—
101#125×C101—21no—
102#125×C101—21no—
103#124×C101—21no—
104#124×C101—21no—
105#124×C101—21no—
106#124×C101—21no—
107#123×C101—21no—
108#123×C101—21no—
109#123×C101—21no—
110#123×C101—21no—
111#123×C101—21no—
112#123×C101—21no—
113#123×C101—21no—
114#123×C101—21no—
115#123×C101—21no—
116#123×C101—21no—
117#123×C101—21no—
118#123×C101—21no—
119#123×C101—21no—
120#123×C101—21no—
121C22⋊Q8×C101—21no—
122C22⋊Q8×C101—21no—
123C22⋊Q8×C101—21no—
124C22⋊Q8×C101—21no—
125C22⋊Q8×C101—21no—
126C22⋊Q8×C101—21no—
127C22⋊Q8×C101—21no—
128C22⋊Q8×C101—21no—
129C22⋊Q8×C101—21no—
130C22⋊Q8×C101—21no—
131C22⋊Q8×C101—21no—
132C22⋊Q8×C101—21no—
133C22⋊Q8×C101—21no—
134C22⋊Q8×C101—21no—
135C22⋊Q8×C101D411yescharacteristic, complemented
136C22⋊Q8×C101D411yescharacteristic, complemented
137C22⋊Q8×C101D411yescharacteristic, complemented
138C22⋊Q8×C101C2311yescharacteristic
139C22⋊Q8×C101C2311yescharacteristic
140C22⋊Q8×C101C2311yescharacteristic
141#121×C101—21no—
142#121×C101—21no—
143#121×C101—21no—
144#121×C101—21no—
145#121×C101—21no—
146#121×C101—21no—
147#121×C101—21no—
148#121×C101—21no—
149#121×C101D411yescharacteristic, complemented
150#121×C101C2311yescharacteristic
151#120×C101—21no—
152#120×C101—21no—
153C4×Q8×C101—21no—
154C4×D4×C101—21no—
155C4×D4×C101—21no—
156C4×D4×C101—21no—
157C4×D4×C101—21no—
158C4×D4×C101—21no—
159C4×D4×C101—21no—
160C4×D4×C101—21no—
161#117×C101—21no—
162#117×C101—21no—
163#117×C101—21no—
164#117×C101D411yescharacteristic, complemented
165C2×C4⋊C4×C101—21no—
166C2×C4⋊C4×C101—21no—
167C2×C4⋊C4×C101—21no—
168C2×C4⋊C4×C101D411yescharacteristic
169C2×C4⋊C4×C101D411yescharacteristic, complemented
170C2×C4⋊C4×C101C2311yescharacteristic
171C2×C4⋊C4×C101C2311yescharacteristic
172C2×C22⋊C4×C101—21no—
173C2×C22⋊C4×C101—21no—
174C2×C22⋊C4×C101—21no—
175C2×C22⋊C4×C101—21no—
176C2×C22⋊C4×C101—21no—
177C2×C22⋊C4×C101—21no—
178C2×C22⋊C4×C101—21no—
179C2×C22⋊C4×C101—21no—
180C2×C22⋊C4×C101D411yescharacteristic
181C2×C22⋊C4×C101D411yescharacteristic
182C2×C22⋊C4×C101C2311yescharacteristic
183C2×C42×C101—21no—
184#107×C101—21no—
185#106×C101—21no—
186#106×C101—21no—
187#106×C101—21no—
188#103×C101—21no—
189#103×C101—21no—
190#103×C101—21no—
191#102×C101—21no—
192#102×C101—21no—
193#102×C101—21no—
194#102×C101—21no—
195#102×C101—21no—
196C22⋊C8×C101—21no—
197C22⋊C8×C101—21no—
198C22⋊C8×C101C2311yescharacteristic
199C22⋊C8×C101C2311yescharacteristic
200C22⋊C8×C101C2311yescharacteristic
201C22⋊C8×C101C2311yescharacteristic
202#95×C101—21no—
203#95×C101—21no—
204#95×C101C2311yescharacteristic
205#95×C101C2311yescharacteristic
206C24×C101—21no—
207C24×C101C2×D411yescharacteristic
208C24×C101C2×D411yescharacteristic
209#41×C101—82no—
210#41×C101—81no—
211C2×Q8×C101—21no—
212C2×Q8×C101—21no—
213C2×Q8×C101—21no—
214C2×Q8×C101—81no—
215C2×Q8×C101C2×D411yescharacteristic
216C2×Q8×C101C2×D411yescharacteristic
217C2×Q8×C101C2×D411yescharacteristic
218C2×D4×C101—21no—
219C2×D4×C101—21no—
220C2×D4×C101—21no—
221C2×D4×C101—21no—
222C2×D4×C101—21no—
223C2×D4×C101—21no—
224C2×D4×C101—21no—
225C2×D4×C101—21no—
226C2×D4×C101—21no—
227C2×D4×C101—42no—
228C2×D4×C101—41no—
229C2×D4×C101—41no—
230C2×D4×C101—81no—
231C2×D4×C101—81no—
232C2×D4×C101—81no—
233C2×D4×C101—81no—
234C2×D4×C101—81no—
235C2×D4×C101—81no—
236C2×D4×C101C2×D411yescharacteristic
237C22×C4×C101—21no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—21no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—81no—
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2×D411yescharacteristic
250C22×C4×C101C2×D411yescharacteristic
251C22×C4×C101C2×D411yescharacteristic
252C22×C4×C101C2×D411yescharacteristic
253C22×C4×C101C2×D411yescharacteristic
254C22×C4×C101C2×D411yescharacteristic
255C22×C4×C101C2×D411yescharacteristic
256C22×C4×C101C2411yescharacteristic
257SD16×C101—81no—
258SD16×C101—81no—
259SD16×C101—81no—
260D8×C101—81no—
261M16×C101—81no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—81no—
267C4⋊C4×C101—21no—
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—21no—
279C4⋊C4×C101—21no—
280C4⋊C4×C101—21no—
281C4⋊C4×C101—21no—
282C4⋊C4×C101—21no—
283C4⋊C4×C101—21no—
284C4⋊C4×C101—21no—
285C4⋊C4×C101—21no—
286C4⋊C4×C101—21no—
287C4⋊C4×C101—21no—
288C4⋊C4×C101—21no—
289C4⋊C4×C101—21no—
290C4⋊C4×C101—21no—
291C4⋊C4×C101—21no—
292C4⋊C4×C101—81no—
293C4⋊C4×C101C2×D411yescharacteristic
294C4⋊C4×C101C2×D411yescharacteristic
295C4⋊C4×C101C2×D411yescharacteristic
296C4⋊C4×C101C2×D411yescharacteristic
297C22⋊C4×C101—21no—
298C22⋊C4×C101—21no—
299C22⋊C4×C101—21no—
300C22⋊C4×C101—21no—
301C22⋊C4×C101—21no—
302C22⋊C4×C101—21no—
303C22⋊C4×C101—21no—
304C22⋊C4×C101—21no—
305C22⋊C4×C101—21no—
306C22⋊C4×C101—21no—
307C22⋊C4×C101—21no—
308C22⋊C4×C101—21no—
309C22⋊C4×C101—21no—
310C22⋊C4×C101—21no—
311C22⋊C4×C101—21no—
312C22⋊C4×C101—21no—
313C22⋊C4×C101—21no—
314C22⋊C4×C101—21no—
315C22⋊C4×C101—21no—
316C22⋊C4×C101—21no—
317C22⋊C4×C101—21no—
318C22⋊C4×C101—21no—
319C22⋊C4×C101—21no—
320C22⋊C4×C101—42no—
321C22⋊C4×C101—42no—
322C22⋊C4×C101—41no—
323C22⋊C4×C101—41no—
324C22⋊C4×C101—81no—
325C22⋊C4×C101—81no—
326C22⋊C4×C101—81no—
327C42×C101—21no—
328C42×C101—21no—
329C42×C101—21no—
330C42×C101—21no—
331C42×C101—21no—
332C42×C101—81no—
333C23×C101—21no—
334C23×C101—21no—
335C23×C101—21no—
336C23×C101—21no—
337C23×C101—21no—
338C23×C101—21no—
339C23×C101—41no—
340C23×C101—41no—
341C23×C101—41no—
342C23×C101—41no—
343C23×C101—41no—
344C23×C101—41no—
345C23×C101—41no—
346C23×C101—41no—
347C23×C101—41no—
348C23×C101—41no—
349C23×C101—41no—
350C23×C101#12011yescharacteristic
351C23×C101#12011yescharacteristic
352C23×C101C22×D411yescharacteristic
353Q8×C101—41no—
354Q8×C101—41no—
355Q8×C101—41no—
356Q8×C101—81no—
357Q8×C101—81no—
358Q8×C101—81no—
359D4×C101—41no—
360D4×C101—41no—
361D4×C101—41no—
362D4×C101—41no—
363D4×C101—41no—
364D4×C101—42no—
365D4×C101—42no—
366D4×C101—41no—
367D4×C101—41no—
368D4×C101—81no—
369D4×C101—81no—
370D4×C101—81no—
371D4×C101—81no—
372D4×C101—84no—
373D4×C101—82no—
374D4×C101—82no—
375C2×C4×C101—22no—
376C2×C4×C101—21no—
377C2×C4×C101—21no—
378C2×C4×C101—21no—
379C2×C4×C101—21no—
380C2×C4×C101—21no—
381C2×C4×C101—21no—
382C2×C4×C101—21no—
383C2×C4×C101—21no—
384C2×C4×C101—21no—
385C2×C4×C101—21no—
386C2×C4×C101—21no—
387C2×C4×C101—21no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—42no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—41no—
400C2×C4×C101—41no—
401C2×C4×C101—41no—
402C2×C4×C101—41no—
403C2×C4×C101—41no—
404C2×C4×C101—41no—
405C2×C4×C101—81no—
406C2×C4×C101—81no—
407C2×C4×C101—81no—
408C2×C4×C101—81no—
409C2×C4×C101—81no—
410C2×C4×C101—81no—
411C2×C4×C101#12011yescharacteristic
412C2×C4×C101#12011yescharacteristic
413C2×C4×C101C22×D411yescharacteristic
414C2×C4×C101C22×D411yescharacteristic
415C8×C101—41no—
416C8×C101—41no—
417C8×C101—41no—
418C8×C101—41no—
419C22×C101—21no—
420C22×C101—21no—
421C22×C101—21no—
422C22×C101—21no—
423C22×C101—21no—
424C22×C101—21no—
425C22×C101—21no—
426C22×C101—21no—
427C22×C101—41no—
428C22×C101—41no—
429C22×C101—41no—
430C22×C101—41no—
431C22×C101—41no—
432C22×C101—41no—
433C22×C101—81no—
434C22×C101—81no—
435C22×C101—81no—
436C22×C101—81no—
437C22×C101—81no—
438C22×C101—81no—
439C22×C101—81no—
440C22×C101—81no—
441C22×C101—81no—
442C22×C101—81no—
443C22×C101—81no—
444C22×C101C2×#12011yescharacteristic
445C22×C101#57711yescharacteristic
446C22×C101#57711yescharacteristic
447C4×C101—21no—
448C4×C101—21no—
449C4×C101—21no—
450C4×C101—21no—
451C4×C101—42no—
452C4×C101—41no—
453C4×C101—41no—
454C4×C101—41no—
455C4×C101—41no—
456C4×C101—41no—
457C4×C101—41no—
458C4×C101—41no—
459C4×C101—41no—
460C4×C101—41no—
461C4×C101—41no—
462C4×C101—81no—
463C4×C101—81no—
464#18416C10111yesmaximal, characteristic, direct product factor, Sylow
465C2×C101—21no—
466C2×C101—21no—
467C2×C101—41no—
468C2×C101—41no—
469C2×C101—81no—
470C2×C101—81no—
471C2×C101—161no—
472C2×C101#301011yescharacteristic
473C2×C101#301811yescharacteristic
474C2×C101#302611yescharacteristic
475#3535C2×C10111yescharacteristic, complemented
476#3194C2×C10111yescharacteristic, complemented
477#3187C2×C10111yescharacteristic, complemented
478#2661C2×C10111yescharacteristic, complemented
479#1612C2×C10111yescharacteristic, complemented
480#1611C2×C10111yescharacteristic, complemented
481#1609C2×C10111yescharacteristic, complemented
482#1608C2×C10111yescharacteristic, complemented
483#1600C2×C10111yescharacteristic, complemented
484#1599C2×C10111yescharacteristic, complemented
485#1597C2×C10111yescharacteristic, complemented
486#1596C2×C10111yescharacteristic, complemented
487#1508C2×C10111yescharacteristic, complemented
488#1501C2×C10111yescharacteristic, complemented
489#1468C2×C10111yescharacteristic, complemented
490C101#1841611yescharacteristic, direct product factor, Sylow
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C10111yescharacteristic
500#543C22×C10111yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C10111yescharacteristic
505#538C22×C10111yescharacteristic
506#536—21no—
507#525C22×C10111yescharacteristic
508C2×#123C22×C10111yescharacteristic
509C2×C22⋊Q8C22×C10111yescharacteristic
510C2×#121C22×C10111yescharacteristic
511#483C22×C10111yescharacteristic
512#483C22×C10111yescharacteristic
513#483C22×C10111yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C10111yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C10111yescharacteristic
522#450C22×C10111yescharacteristic
523#450C22×C10111yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C10111yescharacteristic
527#407C22×C10111yescharacteristic
528C2×C22⋊C8C22×C10111yescharacteristic
529#398C22×C10111yescharacteristic
530#397C22×C10111yescharacteristic
531#394—21no—
532#394C22×C10111yescharacteristic
533#392—21no—
534#392C22×C10111yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C10111yescharacteristic
538#328C22×C10111yescharacteristic
539#328C22×C10111yescharacteristic
540#328C22×C10111yescharacteristic
541#328C22×C10111yescharacteristic
542#328C22×C10111yescharacteristic
543#328C22×C10111yescharacteristic
544#327C22×C10111yescharacteristic
545#327C22×C10111yescharacteristic
546#324C22×C10111yescharacteristic
547#324C22×C10111yescharacteristic
548#323C22×C10111yescharacteristic
549#323C22×C10111yescharacteristic
550C2×#41—21no—
551C2×#41D4×C10111yescharacteristic, complemented
552C22×Q8D4×C10111yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C10111yescharacteristic
556C22×D4C23×C10111yescharacteristic
557C23×C4C23×C10111yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C10111yescharacteristic, complemented
611C22⋊Q8D4×C10111yescharacteristic, complemented
612C22⋊Q8D4×C10111yescharacteristic, complemented
613C22⋊Q8C23×C10111yescharacteristic
614C22⋊Q8C23×C10111yescharacteristic
615C22⋊Q8C23×C10111yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C10111yescharacteristic, complemented
625#121C23×C10111yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C10111yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C10111yescharacteristic
644C2×C4⋊C4D4×C10111yescharacteristic, complemented
645C2×C4⋊C4C23×C10111yescharacteristic
646C2×C4⋊C4C23×C10111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C10111yescharacteristic
656C2×C22⋊C4D4×C10111yescharacteristic
657C2×C22⋊C4C23×C10111yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C10111yescharacteristic
674C22⋊C8C23×C10111yescharacteristic
675C22⋊C8C23×C10111yescharacteristic
676C22⋊C8C23×C10111yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C10111yescharacteristic
680#95C23×C10111yescharacteristic
681C24—21no—
682C24C2×D4×C10111yescharacteristic
683C24C2×D4×C10111yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C10111yescharacteristic
691C2×Q8C2×D4×C10111yescharacteristic
692C2×Q8C2×D4×C10111yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C10111yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C10111yescharacteristic
724C22×C4C2×D4×C10111yescharacteristic
725C22×C4C2×D4×C10111yescharacteristic
726C22×C4C2×D4×C10111yescharacteristic
727C22×C4C2×D4×C10111yescharacteristic
728C22×C4C2×D4×C10111yescharacteristic
729C22×C4C2×D4×C10111yescharacteristic
730C22×C4C2×D4×C10111yescharacteristic
731C22×C4C24×C10111yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C10111yescharacteristic
769C4⋊C4C2×D4×C10111yescharacteristic
770C4⋊C4C2×D4×C10111yescharacteristic
771C4⋊C4C2×D4×C10111yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C10111yescharacteristic
826C23#120×C10111yescharacteristic
827C23C22×D4×C10111yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C10111yescharacteristic
887C2×C4#120×C10111yescharacteristic
888C2×C4C22×D4×C10111yescharacteristic
889C2×C4C22×D4×C10111yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C10111yescharacteristic
920C22#577×C10111yescharacteristic
921C22#577×C10111yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C101×#301011yescharacteristic
947C2C101×#301811yescharacteristic
948C2C101×#302611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3535C2semidirect
2. C101×#3194C2semidirect
3. C101×#3187C2semidirect
4. C101×#2661C2semidirect
5. C101×#1612C2semidirect
6. C101×#1611C2semidirect
7. C101×#1609C2semidirect
8. C101×#1608C2semidirect
9. C101×#1600C2semidirect
10. C101×#1599C2semidirect
11. C101×#1597C2semidirect
12. C101×#1596C2semidirect
13. C101×#1508C2semidirect
14. C101×#1501C2semidirect
15. C101×#1468C2semidirect
76. C2×#41×C101D4semidirect
77. C22×Q8×C101D4semidirect
135. C22⋊Q8×C101D4semidirect
136. C22⋊Q8×C101D4semidirect
137. C22⋊Q8×C101D4semidirect
149. #121×C101D4semidirect
164. #117×C101D4semidirect
169. C2×C4⋊C4×C101D4semidirect
464. #18416C101direct (N × H)
475. #3535C2×C101semidirect
476. #3194C2×C101semidirect
477. #3187C2×C101semidirect
478. #2661C2×C101semidirect
479. #1612C2×C101semidirect
480. #1611C2×C101semidirect
481. #1609C2×C101semidirect
482. #1608C2×C101semidirect
483. #1600C2×C101semidirect
484. #1599C2×C101semidirect
485. #1597C2×C101semidirect
486. #1596C2×C101semidirect
487. #1508C2×C101semidirect
488. #1501C2×C101semidirect
489. #1468C2×C101semidirect
490. C101#18416direct (N × H)
551. C2×#41D4×C101semidirect
552. C22×Q8D4×C101semidirect
610. C22⋊Q8D4×C101semidirect
611. C22⋊Q8D4×C101semidirect
612. C22⋊Q8D4×C101semidirect
624. #121D4×C101semidirect
639. #117D4×C101semidirect
644. C2×C4⋊C4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35352
C101×#31942
C101×#31872
C101×#26612
C101×#16122
C101×#16112
C101×#16092
C101×#16082
C101×#16002
C101×#15992
C101×#15972
C101×#15962
C101×#15082
C101×#15012
C101×#14682
#18416101