Finite Group Databasebeta

← C101×#25446 #38807597

Subgroups — C101×#25446 #38807597

Order 25856.

876 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3154C211yesmaximal, characteristic, complemented
2C101×#3069C211yesmaximal, characteristic, complemented
3C101×#3068C211yesmaximal, characteristic, complemented
4C101×#3067C211yesmaximal, characteristic, complemented
5C2×#471×C101C211yesmaximal, characteristic, complemented
6C101×#2957C211yesmaximal, characteristic, complemented
7C101×#2049C211yesmaximal, characteristic, complemented
8C101×#2048C211yesmaximal, characteristic, complemented
9C101×#2009C211yesmaximal, characteristic, complemented
10C101×#2008C211yesmaximal, characteristic, complemented
11C101×#1977C211yesmaximal, characteristic, complemented
12C101×#1953C211yesmaximal, characteristic, complemented
13C101×#1915C211yesmaximal, characteristic, complemented
14C101×#1914C211yesmaximal, characteristic, complemented
15C101×#1757C211yesmaximal, characteristic, complemented
16#575×C101C2211yescharacteristic
17#575×C101C2211yescharacteristic
18C2×#137×C101C2211yescharacteristic
19C2×#137×C101C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
22C2×#135×C101C2211yescharacteristic
23C22×SD16×C101C2211yescharacteristic
24#568×C101C2211yescharacteristic
25#568×C101C2211yescharacteristic
26C2×#131×C101C2211yescharacteristic
27#536×C101C2211yescharacteristic
28#535×C101C2211yescharacteristic
29#497×C101—21no—
30#496×C101—21no—
31#495×C101—21no—
32#492×C101—21no—
33#473×C101—21no—
34#473×C101—22no—
35#472×C101—21no—
36#472×C101—22no—
37#471×C101—21no—
38#471×C101—21no—
39#471×C101—22no—
40#471×C101—22no—
41#471×C101—22no—
42#471×C101—22no—
43#444×C101—22no—
44#443×C101—22no—
45#430×C101C2211yescharacteristic
46#430×C101C2211yescharacteristic
47C2×#108×C101C2211yescharacteristic
48C2×#108×C101C2211yescharacteristic
49#421×C101C2211yescharacteristic
50#421×C101C2211yescharacteristic
51#419×C101C2211yescharacteristic
52#418×C101C2211yescharacteristic
53#413×C101C2211yescharacteristic
54#413×C101C2211yescharacteristic
55#413×C101C2211yescharacteristic
56C2×#101×C101C2211yescharacteristic
57C2×#101×C101C2211yescharacteristic
58C2×#100×C101C2211yescharacteristic
59C2×#100×C101C2211yescharacteristic
60#410×C101C2211yescharacteristic
61#405×C101C2211yescharacteristic
62#405×C101C2211yescharacteristic
63#344×C101C2211yescharacteristic
64#344×C101C2211yescharacteristic
65#344×C101C2211yescharacteristic
66#344×C101C2211yescharacteristic
67C2×#41×C101C2311yescharacteristic
68C2×#41×C101C2311yescharacteristic
69C2×#41×C101C2311yescharacteristic
70C22×Q8×C101C2311yescharacteristic
71C22×D4×C101C2311yescharacteristic
72#137×C101—21no—
73#137×C101—21no—
74#137×C101—21no—
75#137×C101—21no—
76#137×C101—22no—
77#137×C101—22no—
78#137×C101—41no—
79#137×C101—41no—
80AGL(1,ℤ/8)×C101—21no—
81AGL(1,ℤ/8)×C101—21no—
82AGL(1,ℤ/8)×C101—21no—
83AGL(1,ℤ/8)×C101—21no—
84AGL(1,ℤ/8)×C101—22no—
85AGL(1,ℤ/8)×C101—22no—
86AGL(1,ℤ/8)×C101—41no—
87AGL(1,ℤ/8)×C101—41no—
88#135×C101—21no—
89#135×C101—21no—
90#135×C101—21no—
91#135×C101—21no—
92#135×C101—41no—
93#135×C101—41no—
94C2×Q16×C101—21no—
95C2×Q16×C101—21no—
96C2×Q16×C101D411yescharacteristic
97C2×SD16×C101—21no—
98C2×SD16×C101—21no—
99C2×SD16×C101—21no—
100C2×SD16×C101—21no—
101C2×SD16×C101—21no—
102C2×SD16×C101—21no—
103C2×SD16×C101—21no—
104C2×SD16×C101—21no—
105C2×SD16×C101—21no—
106C2×SD16×C101—21no—
107C2×SD16×C101D411yescharacteristic
108C2×SD16×C101D411yescharacteristic
109C2×D8×C101—21no—
110C2×D8×C101—21no—
111C2×D8×C101D411yescharacteristic
112#131×C101—22no—
113#131×C101—22no—
114#131×C101—22no—
115#131×C101—22no—
116#131×C101—21no—
117#131×C101—21no—
118#131×C101—21no—
119#131×C101—21no—
120C2×M16×C101—21no—
121C2×M16×C101—41no—
122C2×M16×C101—41no—
123C2×M16×C101C2311yescharacteristic
124C2×M16×C101C2311yescharacteristic
125C2×M16×C101C2311yescharacteristic
126C2×M16×C101C2311yescharacteristic
127C2×M16×C101C2311yescharacteristic
128C2×M16×C101C2311yescharacteristic
129C2×M16×C101C2311yescharacteristic
130C22×C8×C101—21no—
131C22×C8×C101C2311yescharacteristic
132C4⋊Q8×C101—21no—
133#127×C101—21no—
134#124×C101—21no—
135#124×C101—21no—
136#123×C101—22no—
137C22⋊Q8×C101—41no—
138#121×C101—41no—
139#120×C101—22no—
140#117×C101C2311yescharacteristic
141#117×C101C2311yescharacteristic
142#108×C101—22no—
143#108×C101—22no—
144#108×C101—21no—
145#108×C101—21no—
146#108×C101D412yescomplemented
147#108×C101D412yescomplemented
148#104×C101—22no—
149#104×C101—22no—
150#103×C101—41no—
151#102×C101—41no—
152#101×C101—21no—
153#101×C101—21no—
154#101×C101—22no—
155#101×C101—22no—
156#101×C101D412yescomplemented
157#100×C101—21no—
158#100×C101—21no—
159#100×C101—22no—
160#100×C101—22no—
161#100×C101D412yescomplemented
162#99×C101—22no—
163#97×C101—21no—
164#97×C101—21no—
165C4×C8×C101—21no—
166C4×C8×C101—21no—
167C24×C101—21no—
168#41×C101—21no—
169#41×C101—21no—
170#41×C101—21no—
171#41×C101—21no—
172#41×C101—21no—
173#41×C101—21no—
174#41×C101—21no—
175#41×C101—21no—
176#41×C101—21no—
177#41×C101—21no—
178#41×C101—21no—
179#41×C101—21no—
180C2×Q8×C101—21no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101C2×D411yescharacteristic
187C2×Q8×C101C2×D411yescharacteristic
188C2×Q8×C101C2×D411yescharacteristic
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—42no—
199C2×D4×C101C2×D411yescharacteristic
200C2×D4×C101C2×D411yescharacteristic
201C2×D4×C101C2×D411yescharacteristic
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101C2411yescharacteristic
207Q16×C101—21no—
208Q16×C101—21no—
209Q16×C101—42no—
210Q16×C101—42no—
211Q16×C101—41no—
212Q16×C101—41no—
213SD16×C101—21no—
214SD16×C101—21no—
215SD16×C101—21no—
216SD16×C101—21no—
217SD16×C101—42no—
218SD16×C101—42no—
219SD16×C101—42no—
220SD16×C101—42no—
221SD16×C101—41no—
222SD16×C101—41no—
223SD16×C101—41no—
224SD16×C101—41no—
225SD16×C101—41no—
226SD16×C101—41no—
227SD16×C101—41no—
228SD16×C101—41no—
229D8×C101—21no—
230D8×C101—21no—
231D8×C101—42no—
232D8×C101—42no—
233D8×C101—41no—
234D8×C101—41no—
235M16×C101—21no—
236M16×C101—21no—
237M16×C101—21no—
238M16×C101—21no—
239M16×C101—21no—
240M16×C101—21no—
241M16×C101—21no—
242M16×C101—21no—
243M16×C101—21no—
244M16×C101—21no—
245M16×C101—42no—
246M16×C101—42no—
247M16×C101—41no—
248M16×C101—41no—
249M16×C101C2×D412yes—
250M16×C101C2×D412yes—
251M16×C101C2×D412yes—
252M16×C101C2×D412yes—
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×C101—42no—
261C2×C8×C101—42no—
262C2×C8×C101—41no—
263C2×C8×C101—41no—
264C2×C8×C101C2×D411yescharacteristic
265C2×C8×C101C2×D411yescharacteristic
266C2×C8×C101C2×D411yescharacteristic
267C2×C8×C101C2×D411yescharacteristic
268C2×C8×C101#4111yescharacteristic
269C2×C8×C101#4111yescharacteristic
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—42no—
273C22⋊C4×C101—21no—
274C22⋊C4×C101—42no—
275C22⋊C4×C101—42no—
276C22⋊C4×C101#4112yes—
277C42×C101—21no—
278C42×C101—21no—
279C23×C101—21no—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—41no—
285C23×C101—161no—
286C23×C101C2×#4111yescharacteristic
287Q8×C101—21no—
288Q8×C101—21no—
289Q8×C101—21no—
290Q8×C101—21no—
291Q8×C101—21no—
292Q8×C101—21no—
293Q8×C101—41no—
294Q8×C101—41no—
295Q8×C101—41no—
296Q8×C101—41no—
297D4×C101—21no—
298D4×C101—21no—
299D4×C101—21no—
300D4×C101—21no—
301D4×C101—21no—
302D4×C101—21no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—41no—
310D4×C101—41no—
311D4×C101—41no—
312D4×C101—41no—
313D4×C101—162no—
314C2×C4×C101—21no—
315C2×C4×C101—22no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
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×C101C22×D411yescharacteristic
329C2×C4×C101C22×D411yescharacteristic
330C2×C4×C101C22×D411yescharacteristic
331C2×C4×C101C2×#4111yescharacteristic
332C2×C4×C101H(5,𝔽2)11yescharacteristic
333C2×C4×C101H(5,𝔽2)11yescharacteristic
334C8×C101—22no—
335C8×C101—22no—
336C8×C101—22no—
337C8×C101—22no—
338C8×C101—41no—
339C8×C101—41no—
340C8×C101—41no—
341C8×C101#12111yescharacteristic
342C8×C101#12111yescharacteristic
343C8×C101#12111yescharacteristic
344C8×C101#12111yescharacteristic
345C22×C101—41no—
346C22×C101—41no—
347C22×C101—41no—
348C22×C101—41no—
349C22×C101—81no—
350C22×C101—81no—
351C22×C101—81no—
352C22×C101—82no—
353C22×C101—81no—
354C22×C101—161no—
355C22×C101—161no—
356C22×C101#53211yescharacteristic
357C22×C101#54611yescharacteristic
358C22×C101#55011yescharacteristic
359C4×C101—42no—
360C4×C101—41no—
361C4×C101—41no—
362C4×C101—41no—
363C4×C101—81no—
364C4×C101—81no—
365C4×C101C2×#12111yescharacteristic
366C4×C101#54011yescharacteristic
367C4×C101D4211yescharacteristic
368C4×C101D4211yescharacteristic
369#25446C10111yesmaximal, characteristic, direct product factor, Sylow
370C2×C101—21no—
371C2×C101—21no—
372C2×C101—21no—
373C2×C101—81no—
374C2×C101—81no—
375C2×C101—81no—
376C2×C101—161no—
377C2×C101#242811yescharacteristic
378#3154C2×C10111yescharacteristic, complemented
379#3069C2×C10111yescharacteristic, complemented
380#3068C2×C10111yescharacteristic, complemented
381#3067C2×C10111yescharacteristic, complemented
382C2×#471C2×C10111yescharacteristic, complemented
383#2957C2×C10111yescharacteristic, complemented
384#2049C2×C10111yescharacteristic, complemented
385#2048C2×C10111yescharacteristic, complemented
386#2009C2×C10111yescharacteristic, complemented
387#2008C2×C10111yescharacteristic, complemented
388#1977C2×C10111yescharacteristic, complemented
389#1953C2×C10111yescharacteristic, complemented
390#1915C2×C10111yescharacteristic, complemented
391#1914C2×C10111yescharacteristic, complemented
392#1757C2×C10111yescharacteristic, complemented
393C101#2544611yescharacteristic, direct product factor, Sylow
394#575C22×C10111yescharacteristic
395#575C22×C10111yescharacteristic
396C2×#137C22×C10111yescharacteristic
397C2×#137C22×C10111yescharacteristic
398C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
399C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
400C2×#135C22×C10111yescharacteristic
401C22×SD16C22×C10111yescharacteristic
402#568C22×C10111yescharacteristic
403#568C22×C10111yescharacteristic
404C2×#131C22×C10111yescharacteristic
405#536C22×C10111yescharacteristic
406#535C22×C10111yescharacteristic
407#497—21no—
408#496—21no—
409#495—21no—
410#492—21no—
411#473—21no—
412#473—22no—
413#472—21no—
414#472—22no—
415#471—21no—
416#471—21no—
417#471—22no—
418#471—22no—
419#471—22no—
420#471—22no—
421#444—22no—
422#443—22no—
423#430C22×C10111yescharacteristic
424#430C22×C10111yescharacteristic
425C2×#108C22×C10111yescharacteristic
426C2×#108C22×C10111yescharacteristic
427#421C22×C10111yescharacteristic
428#421C22×C10111yescharacteristic
429#419C22×C10111yescharacteristic
430#418C22×C10111yescharacteristic
431#413C22×C10111yescharacteristic
432#413C22×C10111yescharacteristic
433#413C22×C10111yescharacteristic
434C2×#101C22×C10111yescharacteristic
435C2×#101C22×C10111yescharacteristic
436C2×#100C22×C10111yescharacteristic
437C2×#100C22×C10111yescharacteristic
438#410C22×C10111yescharacteristic
439#405C22×C10111yescharacteristic
440#405C22×C10111yescharacteristic
441#344C22×C10111yescharacteristic
442#344C22×C10111yescharacteristic
443#344C22×C10111yescharacteristic
444#344C22×C10111yescharacteristic
445C2×#41C23×C10111yescharacteristic
446C2×#41C23×C10111yescharacteristic
447C2×#41C23×C10111yescharacteristic
448C22×Q8C23×C10111yescharacteristic
449C22×D4C23×C10111yescharacteristic
450#137—21no—
451#137—21no—
452#137—21no—
453#137—21no—
454#137—22no—
455#137—22no—
456#137—41no—
457#137—41no—
458AGL(1,ℤ/8)—21no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—21no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—22no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)—41no—
466#135—21no—
467#135—21no—
468#135—21no—
469#135—21no—
470#135—41no—
471#135—41no—
472C2×Q16—21no—
473C2×Q16—21no—
474C2×Q16D4×C10111yescharacteristic
475C2×SD16—21no—
476C2×SD16—21no—
477C2×SD16—21no—
478C2×SD16—21no—
479C2×SD16—21no—
480C2×SD16—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16D4×C10111yescharacteristic
486C2×SD16D4×C10111yescharacteristic
487C2×D8—21no—
488C2×D8—21no—
489C2×D8D4×C10111yescharacteristic
490#131—22no—
491#131—22no—
492#131—22no—
493#131—22no—
494#131—21no—
495#131—21no—
496#131—21no—
497#131—21no—
498C2×M16—21no—
499C2×M16—41no—
500C2×M16—41no—
501C2×M16C23×C10111yescharacteristic
502C2×M16C23×C10111yescharacteristic
503C2×M16C23×C10111yescharacteristic
504C2×M16C23×C10111yescharacteristic
505C2×M16C23×C10111yescharacteristic
506C2×M16C23×C10111yescharacteristic
507C2×M16C23×C10111yescharacteristic
508C22×C8—21no—
509C22×C8C23×C10111yescharacteristic
510C4⋊Q8—21no—
511#127—21no—
512#124—21no—
513#124—21no—
514#123—22no—
515C22⋊Q8—41no—
516#121—41no—
517#120—22no—
518#117C23×C10111yescharacteristic
519#117C23×C10111yescharacteristic
520#108—22no—
521#108—22no—
522#108—21no—
523#108—21no—
524#108D4×C10112yescomplemented
525#108D4×C10112yescomplemented
526#104—22no—
527#104—22no—
528#103—41no—
529#102—41no—
530#101—21no—
531#101—21no—
532#101—22no—
533#101—22no—
534#101D4×C10112yescomplemented
535#100—21no—
536#100—21no—
537#100—22no—
538#100—22no—
539#100D4×C10112yescomplemented
540#99—22no—
541#97—21no—
542#97—21no—
543C4×C8—21no—
544C4×C8—21no—
545C24—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×D4×C10111yescharacteristic
565C2×Q8C2×D4×C10111yescharacteristic
566C2×Q8C2×D4×C10111yescharacteristic
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4C2×D4×C10111yescharacteristic
578C2×D4C2×D4×C10111yescharacteristic
579C2×D4C2×D4×C10111yescharacteristic
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C10111yescharacteristic
585Q16—21no—
586Q16—21no—
587Q16—42no—
588Q16—42no—
589Q16—41no—
590Q16—41no—
591SD16—21no—
592SD16—21no—
593SD16—21no—
594SD16—21no—
595SD16—42no—
596SD16—42no—
597SD16—42no—
598SD16—42no—
599SD16—41no—
600SD16—41no—
601SD16—41no—
602SD16—41no—
603SD16—41no—
604SD16—41no—
605SD16—41no—
606SD16—41no—
607D8—21no—
608D8—21no—
609D8—42no—
610D8—42no—
611D8—41no—
612D8—41no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—42no—
624M16—42no—
625M16—41no—
626M16—41no—
627M16C2×D4×C10112yes—
628M16C2×D4×C10112yes—
629M16C2×D4×C10112yes—
630M16C2×D4×C10112yes—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8C2×D4×C10111yescharacteristic
643C2×C8C2×D4×C10111yescharacteristic
644C2×C8C2×D4×C10111yescharacteristic
645C2×C8C2×D4×C10111yescharacteristic
646C2×C8#41×C10111yescharacteristic
647C2×C8#41×C10111yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C22⋊C4—21no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4#41×C10112yes—
655C42—21no—
656C42—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—161no—
664C23C2×#41×C10111yescharacteristic
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675D4—21no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—162no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4C22×D4×C10111yescharacteristic
707C2×C4C22×D4×C10111yescharacteristic
708C2×C4C22×D4×C10111yescharacteristic
709C2×C4C2×#41×C10111yescharacteristic
710C2×C4H(5,𝔽2)×C10111yescharacteristic
711C2×C4H(5,𝔽2)×C10111yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C8#121×C10111yescharacteristic
720C8#121×C10111yescharacteristic
721C8#121×C10111yescharacteristic
722C8#121×C10111yescharacteristic
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—82no—
731C22—81no—
732C22—161no—
733C22—161no—
734C22#532×C10111yescharacteristic
735C22#546×C10111yescharacteristic
736C22#550×C10111yescharacteristic
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—81no—
742C4—81no—
743C4C2×#121×C10111yescharacteristic
744C4#540×C10111yescharacteristic
745C4D42×C10111yescharacteristic
746C4D42×C10111yescharacteristic
747C2—21no—
748C2—21no—
749C2—21no—
750C2—81no—
751C2—81no—
752C2—81no—
753C2—161no—
754C2C101×#242811yescharacteristic
subgroupG/H
center, socleC2×C101#2428
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3154C2semidirect
2. C101×#3069C2semidirect
3. C101×#3068C2semidirect
4. C101×#3067C2semidirect
5. C2×#471×C101C2semidirect
6. C101×#2957C2semidirect
7. C101×#2049C2semidirect
8. C101×#2048C2semidirect
9. C101×#2009C2semidirect
10. C101×#2008C2semidirect
11. C101×#1977C2semidirect
12. C101×#1953C2semidirect
13. C101×#1915C2semidirect
14. C101×#1914C2semidirect
15. C101×#1757C2semidirect
146. #108×C101D4semidirect
147. #108×C101D4semidirect
156. #101×C101D4semidirect
161. #100×C101D4semidirect
369. #25446C101direct (N × H)
378. #3154C2×C101semidirect
379. #3069C2×C101semidirect
380. #3068C2×C101semidirect
381. #3067C2×C101semidirect
382. C2×#471C2×C101semidirect
383. #2957C2×C101semidirect
384. #2049C2×C101semidirect
385. #2048C2×C101semidirect
386. #2009C2×C101semidirect
387. #2008C2×C101semidirect
388. #1977C2×C101semidirect
389. #1953C2×C101semidirect
390. #1915C2×C101semidirect
391. #1914C2×C101semidirect
392. #1757C2×C101semidirect
393. C101#25446direct (N × H)
524. #108D4×C101semidirect
525. #108D4×C101semidirect
534. #101D4×C101semidirect
539. #100D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31542
C101×#30692
C101×#30682
C101×#30672
C2×#471×C1012
C101×#29572
C101×#20492
C101×#20482
C101×#20092
C101×#20082
C101×#19772
C101×#19532
C101×#19152
C101×#19142
C101×#17572
#25446101