Finite Group Databasebeta

← C101×#18449 #38800600

Subgroups — C101×#18449 #38800600

Order 25856.

918 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3535C211yesmaximal, characteristic
2C101×#3195C211yesmaximal, characteristic, complemented
3C101×#3190C211yesmaximal, characteristic, complemented
4C101×#2814C211yesmaximal, characteristic, complemented
5C101×#1612C211yesmaximal, characteristic, complemented
6C101×#1611C211yesmaximal, characteristic, complemented
7C101×#1609C211yesmaximal, characteristic, complemented
8C101×#1608C211yesmaximal, characteristic, complemented
9C101×#1606C211yesmaximal, characteristic, complemented
10C101×#1605C211yesmaximal, characteristic, complemented
11C101×#1603C211yesmaximal, characteristic, complemented
12C101×#1602C211yesmaximal, characteristic, complemented
13C101×#1520C211yesmaximal, characteristic, complemented
14C101×#1513C211yesmaximal, 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×C22⋊Q8×C101C2211yescharacteristic
36#485×C101—21no—
37#483×C101—21no—
38#483×C101C2211yescharacteristic
39#483×C101C2211yescharacteristic
40#483×C101C2211yescharacteristic
41#480×C101C2211yescharacteristic
42#470×C101—21no—
43#470×C101—21no—
44#467×C101—21no—
45#465×C101—21no—
46#452×C101—21no—
47#451×C101—21no—
48#451×C101C2211yescharacteristic
49#451×C101C2211yescharacteristic
50#451×C101C2211yescharacteristic
51#448×C101C2211yescharacteristic
52#407×C101C2211yescharacteristic
53C2×C22⋊C8×C101C2211yescharacteristic
54#398×C101—21no—
55#398×C101C2211yescharacteristic
56#397×C101—21no—
57#397×C101C2211yescharacteristic
58#396×C101—21no—
59#395×C101C2211yescharacteristic
60#394×C101—21no—
61#393×C101C2211yescharacteristic
62#380×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
77C22×Q8×C101D411yescharacteristic
78C22×Q8×C101C2311yescharacteristic
79C22×D4×C101D411yescharacteristic
80C23×C4×C101C2311yescharacteristic
81C2×Q16×C101—21no—
82C2×Q16×C101—21no—
83C2×Q16×C101—21no—
84C2×SD16×C101—21no—
85C2×M16×C101—21no—
86C22×C8×C101—21no—
87C4⋊Q8×C101—21no—
88C4⋊Q8×C101—21no—
89C4⋊Q8×C101—21no—
90#126×C101—21no—
91#126×C101—21no—
92#126×C101—21no—
93#126×C101—21no—
94#126×C101—21no—
95#126×C101—21no—
96#125×C101—21no—
97#125×C101—21no—
98#125×C101—21no—
99#125×C101—21no—
100#125×C101—21no—
101#124×C101—21no—
102#124×C101—21no—
103#124×C101—21no—
104#124×C101—21no—
105#123×C101—21no—
106#123×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—
119C22⋊Q8×C101—21no—
120C22⋊Q8×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×C101—21no—
136C22⋊Q8×C101—21no—
137C22⋊Q8×C101D411yescharacteristic
138C22⋊Q8×C101D411yescharacteristic
139C22⋊Q8×C101D411yescharacteristic
140C22⋊Q8×C101C2311yescharacteristic
141C22⋊Q8×C101C2311yescharacteristic
142C22⋊Q8×C101C2311yescharacteristic
143#121×C101—21no—
144#121×C101—21no—
145#121×C101—21no—
146#121×C101—21no—
147#121×C101D411yescharacteristic
148#121×C101C2311yescharacteristic
149#120×C101—21no—
150#120×C101—21no—
151C4×Q8×C101—21no—
152C4×D4×C101—21no—
153C4×D4×C101—21no—
154C4×D4×C101—21no—
155C4×D4×C101—21no—
156C4×D4×C101—21no—
157C4×D4×C101—21no—
158C4×D4×C101—21no—
159#117×C101—21no—
160#117×C101—21no—
161#117×C101—21no—
162#117×C101D411yescharacteristic
163C2×C4⋊C4×C101—21no—
164C2×C4⋊C4×C101—21no—
165C2×C4⋊C4×C101—21no—
166C2×C4⋊C4×C101—21no—
167C2×C4⋊C4×C101—21no—
168C2×C4⋊C4×C101—21no—
169C2×C4⋊C4×C101D411yescharacteristic
170C2×C4⋊C4×C101D411yescharacteristic
171C2×C4⋊C4×C101C2311yescharacteristic
172C2×C4⋊C4×C101C2311yescharacteristic
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×C101D411yescharacteristic
180C2×C22⋊C4×C101D411yescharacteristic
181C2×C22⋊C4×C101C2311yescharacteristic
182#107×C101—21no—
183#106×C101—21no—
184#106×C101—21no—
185#106×C101—21no—
186#103×C101—21no—
187#103×C101—21no—
188#103×C101—21no—
189#103×C101—21no—
190#103×C101—21no—
191#103×C101—21no—
192#103×C101—21no—
193#102×C101—21no—
194C22⋊C8×C101—21no—
195C22⋊C8×C101—21no—
196C22⋊C8×C101C2311yescharacteristic
197C22⋊C8×C101C2311yescharacteristic
198C22⋊C8×C101C2311yescharacteristic
199C22⋊C8×C101C2311yescharacteristic
200#95×C101—21no—
201#95×C101—21no—
202#95×C101—21no—
203#95×C101—21no—
204#95×C101C2311yescharacteristic
205#95×C101C2311yescharacteristic
206C24×C101C2×D411yescharacteristic
207C24×C101C2×D411yescharacteristic
208#41×C101—82no—
209#41×C101—81no—
210C2×Q8×C101—21no—
211C2×Q8×C101—21no—
212C2×Q8×C101—21no—
213C2×Q8×C101—21no—
214C2×Q8×C101—21no—
215C2×Q8×C101—81no—
216C2×Q8×C101—81no—
217C2×Q8×C101C2×D411yescharacteristic
218C2×Q8×C101C2×D411yescharacteristic
219C2×Q8×C101C2×D411yescharacteristic
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—81no—
228C2×D4×C101C2×D411yescharacteristic
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—21no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—81no—
241C22×C4×C101C2×D411yescharacteristic
242C22×C4×C101C2×D411yescharacteristic
243C22×C4×C101C2×D411yescharacteristic
244C22×C4×C101C2×D411yescharacteristic
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2411yescharacteristic
250Q16×C101—81no—
251Q16×C101—81no—
252Q16×C101—81no—
253SD16×C101—81no—
254M16×C101—81no—
255C2×C8×C101—21no—
256C2×C8×C101—21no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—81no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—21no—
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—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—41no—
286C4⋊C4×C101—41no—
287C4⋊C4×C101—81no—
288C4⋊C4×C101—81no—
289C4⋊C4×C101—81no—
290C4⋊C4×C101C2×D411yescharacteristic
291C4⋊C4×C101C2×D411yescharacteristic
292C4⋊C4×C101C2×D411yescharacteristic
293C4⋊C4×C101C2×D411yescharacteristic
294C22⋊C4×C101—21no—
295C22⋊C4×C101—21no—
296C22⋊C4×C101—21no—
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—41no—
318C22⋊C4×C101—41no—
319C22⋊C4×C101—81no—
320C22⋊C4×C101—81no—
321C22⋊C4×C101—81no—
322C42×C101—21no—
323C42×C101—21no—
324C42×C101—21no—
325C42×C101—21no—
326C42×C101—21no—
327C23×C101—21no—
328C23×C101—21no—
329C23×C101—21no—
330C23×C101—21no—
331C23×C101—21no—
332C23×C101—21no—
333C23×C101—41no—
334C23×C101—41no—
335C23×C101—41no—
336C23×C101—41no—
337C23×C101#12011yescharacteristic
338C23×C101#12011yescharacteristic
339C23×C101C22×D411yescharacteristic
340Q8×C101—41no—
341Q8×C101—41no—
342Q8×C101—41no—
343Q8×C101—41no—
344Q8×C101—41no—
345Q8×C101—41no—
346Q8×C101—41no—
347Q8×C101—81no—
348Q8×C101—81no—
349Q8×C101—81no—
350D4×C101—41no—
351D4×C101—42no—
352D4×C101—42no—
353D4×C101—41no—
354D4×C101—41no—
355D4×C101—81no—
356D4×C101—81no—
357D4×C101—81no—
358D4×C101—81no—
359C2×C4×C101—21no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—21no—
363C2×C4×C101—21no—
364C2×C4×C101—21no—
365C2×C4×C101—21no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—21no—
369C2×C4×C101—21no—
370C2×C4×C101—21no—
371C2×C4×C101—41no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—42no—
378C2×C4×C101—41no—
379C2×C4×C101—41no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—41no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—81no—
393C2×C4×C101—81no—
394C2×C4×C101—81no—
395C2×C4×C101—81no—
396C2×C4×C101—81no—
397C2×C4×C101—81no—
398C2×C4×C101#12011yescharacteristic
399C2×C4×C101#12011yescharacteristic
400C2×C4×C101C22×D411yescharacteristic
401C2×C4×C101C22×D411yescharacteristic
402C8×C101—41no—
403C8×C101—41no—
404C8×C101—41no—
405C8×C101—41no—
406C22×C101—21no—
407C22×C101—21no—
408C22×C101—21no—
409C22×C101—21no—
410C22×C101—21no—
411C22×C101—21no—
412C22×C101—21no—
413C22×C101—21no—
414C22×C101—41no—
415C22×C101—41no—
416C22×C101—41no—
417C22×C101—41no—
418C22×C101—41no—
419C22×C101—41no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101—81no—
423C22×C101—81no—
424C22×C101C2×#12011yescharacteristic
425C22×C101#57711yescharacteristic
426C22×C101#57811yescharacteristic
427C4×C101—21no—
428C4×C101—21no—
429C4×C101—21no—
430C4×C101—21no—
431C4×C101—41no—
432C4×C101—41no—
433C4×C101—41no—
434C4×C101—41no—
435C4×C101—41no—
436C4×C101—41no—
437C4×C101—41no—
438C4×C101—41no—
439C4×C101—41no—
440C4×C101—41no—
441C4×C101—81no—
442C4×C101—81no—
443C4×C101—81no—
444C4×C101—81no—
445#18449C10111yesmaximal, characteristic, direct product factor, Sylow
446C2×C101—21no—
447C2×C101—21no—
448C2×C101—41no—
449C2×C101—41no—
450C2×C101—81no—
451C2×C101—81no—
452C2×C101#301311yescharacteristic
453C2×C101#302211yescharacteristic
454C2×C101#302611yescharacteristic
455#3535C2×C10111yescharacteristic
456#3195C2×C10111yescharacteristic, complemented
457#3190C2×C10111yescharacteristic, complemented
458#2814C2×C10111yescharacteristic, complemented
459#1612C2×C10111yescharacteristic, complemented
460#1611C2×C10111yescharacteristic, complemented
461#1609C2×C10111yescharacteristic, complemented
462#1608C2×C10111yescharacteristic, complemented
463#1606C2×C10111yescharacteristic, complemented
464#1605C2×C10111yescharacteristic, complemented
465#1603C2×C10111yescharacteristic, complemented
466#1602C2×C10111yescharacteristic, complemented
467#1520C2×C10111yescharacteristic, complemented
468#1513C2×C10111yescharacteristic, complemented
469#1468C2×C10111yescharacteristic, complemented
470C101#1844911yescharacteristic, direct product factor, Sylow
471#563—21no—
472#562—21no—
473#554—21no—
474#552—21no—
475#551—21no—
476#551—21no—
477#547—21no—
478#546—21no—
479#544C22×C10111yescharacteristic
480#543C22×C10111yescharacteristic
481#542—21no—
482#539—21no—
483#539—21no—
484#539C22×C10111yescharacteristic
485#538C22×C10111yescharacteristic
486#536—21no—
487#525C22×C10111yescharacteristic
488C2×#123C22×C10111yescharacteristic
489C2×C22⋊Q8C22×C10111yescharacteristic
490C2×C22⋊Q8C22×C10111yescharacteristic
491#485—21no—
492#483—21no—
493#483C22×C10111yescharacteristic
494#483C22×C10111yescharacteristic
495#483C22×C10111yescharacteristic
496#480C22×C10111yescharacteristic
497#470—21no—
498#470—21no—
499#467—21no—
500#465—21no—
501#452—21no—
502#451—21no—
503#451C22×C10111yescharacteristic
504#451C22×C10111yescharacteristic
505#451C22×C10111yescharacteristic
506#448C22×C10111yescharacteristic
507#407C22×C10111yescharacteristic
508C2×C22⋊C8C22×C10111yescharacteristic
509#398—21no—
510#398C22×C10111yescharacteristic
511#397—21no—
512#397C22×C10111yescharacteristic
513#396—21no—
514#395C22×C10111yescharacteristic
515#394—21no—
516#393C22×C10111yescharacteristic
517#380C22×C10111yescharacteristic
518#328C22×C10111yescharacteristic
519#328C22×C10111yescharacteristic
520#328C22×C10111yescharacteristic
521#328C22×C10111yescharacteristic
522#328C22×C10111yescharacteristic
523#328C22×C10111yescharacteristic
524#327C22×C10111yescharacteristic
525#327C22×C10111yescharacteristic
526#324C22×C10111yescharacteristic
527#324C22×C10111yescharacteristic
528#323C22×C10111yescharacteristic
529#323C22×C10111yescharacteristic
530C2×#41—21no—
531C2×#41D4×C10111yescharacteristic
532C22×Q8D4×C10111yescharacteristic
533C22×Q8C23×C10111yescharacteristic
534C22×D4D4×C10111yescharacteristic
535C23×C4C23×C10111yescharacteristic
536C2×Q16—21no—
537C2×Q16—21no—
538C2×Q16—21no—
539C2×SD16—21no—
540C2×M16—21no—
541C22×C8—21no—
542C4⋊Q8—21no—
543C4⋊Q8—21no—
544C4⋊Q8—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#126—21no—
549#126—21no—
550#126—21no—
551#125—21no—
552#125—21no—
553#125—21no—
554#125—21no—
555#125—21no—
556#124—21no—
557#124—21no—
558#124—21no—
559#124—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C10111yescharacteristic
593C22⋊Q8D4×C10111yescharacteristic
594C22⋊Q8D4×C10111yescharacteristic
595C22⋊Q8C23×C10111yescharacteristic
596C22⋊Q8C23×C10111yescharacteristic
597C22⋊Q8C23×C10111yescharacteristic
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121D4×C10111yescharacteristic
603#121C23×C10111yescharacteristic
604#120—21no—
605#120—21no—
606C4×Q8—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614#117—21no—
615#117—21no—
616#117—21no—
617#117D4×C10111yescharacteristic
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4D4×C10111yescharacteristic
625C2×C4⋊C4D4×C10111yescharacteristic
626C2×C4⋊C4C23×C10111yescharacteristic
627C2×C4⋊C4C23×C10111yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4D4×C10111yescharacteristic
635C2×C22⋊C4D4×C10111yescharacteristic
636C2×C22⋊C4C23×C10111yescharacteristic
637#107—21no—
638#106—21no—
639#106—21no—
640#106—21no—
641#103—21no—
642#103—21no—
643#103—21no—
644#103—21no—
645#103—21no—
646#103—21no—
647#103—21no—
648#102—21no—
649C22⋊C8—21no—
650C22⋊C8—21no—
651C22⋊C8C23×C10111yescharacteristic
652C22⋊C8C23×C10111yescharacteristic
653C22⋊C8C23×C10111yescharacteristic
654C22⋊C8C23×C10111yescharacteristic
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95C23×C10111yescharacteristic
660#95C23×C10111yescharacteristic
661C24C2×D4×C10111yescharacteristic
662C24C2×D4×C10111yescharacteristic
663#41—82no—
664#41—81no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—81no—
671C2×Q8—81no—
672C2×Q8C2×D4×C10111yescharacteristic
673C2×Q8C2×D4×C10111yescharacteristic
674C2×Q8C2×D4×C10111yescharacteristic
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—81no—
683C2×D4C2×D4×C10111yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—81no—
696C22×C4C2×D4×C10111yescharacteristic
697C22×C4C2×D4×C10111yescharacteristic
698C22×C4C2×D4×C10111yescharacteristic
699C22×C4C2×D4×C10111yescharacteristic
700C22×C4C2×D4×C10111yescharacteristic
701C22×C4C2×D4×C10111yescharacteristic
702C22×C4C2×D4×C10111yescharacteristic
703C22×C4C2×D4×C10111yescharacteristic
704C22×C4C24×C10111yescharacteristic
705Q16—81no—
706Q16—81no—
707Q16—81no—
708SD16—81no—
709M16—81no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—81no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—41no—
741C4⋊C4—41no—
742C4⋊C4—81no—
743C4⋊C4—81no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C10111yescharacteristic
746C4⋊C4C2×D4×C10111yescharacteristic
747C4⋊C4C2×D4×C10111yescharacteristic
748C4⋊C4C2×D4×C10111yescharacteristic
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—21no—
781C42—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23#120×C10111yescharacteristic
793C23#120×C10111yescharacteristic
794C23C22×D4×C10111yescharacteristic
795Q8—41no—
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—81no—
803Q8—81no—
804Q8—81no—
805D4—41no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4#120×C10111yescharacteristic
854C2×C4#120×C10111yescharacteristic
855C2×C4C22×D4×C10111yescharacteristic
856C2×C4C22×D4×C10111yescharacteristic
857C8—41no—
858C8—41no—
859C8—41no—
860C8—41no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×#120×C10111yescharacteristic
880C22#577×C10111yescharacteristic
881C22#578×C10111yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C2—21no—
901C2—21no—
902C2—41no—
903C2—41no—
904C2—81no—
905C2—81no—
906C2C101×#301311yescharacteristic
907C2C101×#302211yescharacteristic
908C2C101×#302611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3535C2
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
2. C101×#3195C2semidirect
3. C101×#3190C2semidirect
4. C101×#2814C2semidirect
5. C101×#1612C2semidirect
6. C101×#1611C2semidirect
7. C101×#1609C2semidirect
8. C101×#1608C2semidirect
9. C101×#1606C2semidirect
10. C101×#1605C2semidirect
11. C101×#1603C2semidirect
12. C101×#1602C2semidirect
13. C101×#1520C2semidirect
14. C101×#1513C2semidirect
15. C101×#1468C2semidirect
445. #18449C101direct (N × H)
456. #3195C2×C101semidirect
457. #3190C2×C101semidirect
458. #2814C2×C101semidirect
459. #1612C2×C101semidirect
460. #1611C2×C101semidirect
461. #1609C2×C101semidirect
462. #1608C2×C101semidirect
463. #1606C2×C101semidirect
464. #1605C2×C101semidirect
465. #1603C2×C101semidirect
466. #1602C2×C101semidirect
467. #1520C2×C101semidirect
468. #1513C2×C101semidirect
469. #1468C2×C101semidirect
470. C101#18449direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35352
C101×#31952
C101×#31902
C101×#28142
C101×#16122
C101×#16112
C101×#16092
C101×#16082
C101×#16062
C101×#16052
C101×#16032
C101×#16022
C101×#15202
C101×#15132
C101×#14682
#18449101