Finite Group Databasebeta

← C101×#18434 #38800585

Subgroups — C101×#18434 #38800585

Order 25856.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3560C211yesmaximal, characteristic, complemented
2C101×#3213C211yesmaximal, characteristic, complemented
3C101×#3211C211yesmaximal, characteristic, complemented
4C101×#2662C211yesmaximal, characteristic, complemented
5C101×#1606C211yesmaximal, characteristic, complemented
6C101×#1604C211yesmaximal, characteristic, complemented
7C101×#1603C211yesmaximal, characteristic, complemented
8C101×#1601C211yesmaximal, characteristic, complemented
9C101×#1600C211yesmaximal, characteristic, complemented
10C101×#1598C211yesmaximal, characteristic, complemented
11C101×#1597C211yesmaximal, characteristic, complemented
12C101×#1595C211yesmaximal, characteristic, complemented
13C101×#1509C211yesmaximal, characteristic, complemented
14C101×#1502C211yesmaximal, characteristic, complemented
15C101×#1473C211yesmaximal, characteristic, complemented
16#563×C101—21no—
17#560×C101—21no—
18#553×C101—21no—
19#553×C101—21no—
20#551×C101—21no—
21#547×C101—21no—
22#546×C101—21no—
23#546×C101—21no—
24#542×C101—21no—
25#539×C101—21no—
26#539×C101C2211yescharacteristic
27#538×C101—21no—
28#538×C101—21no—
29#538×C101C2211yescharacteristic
30#537×C101C2211yescharacteristic
31#534×C101C2211yescharacteristic
32#532×C101C2211yescharacteristic
33#529×C101C2211yescharacteristic
34C2×#126×C101C2211yescharacteristic
35C2×#124×C101C2211yescharacteristic, complemented
36#496×C101—21no—
37#495×C101—21no—
38#489×C101—21no—
39#488×C101—21no—
40#464×C101—21no—
41#463×C101—21no—
42#463×C101—21no—
43#463×C101—21no—
44#451×C101C2211yescharacteristic, complemented
45#450×C101C2211yescharacteristic, complemented
46#448×C101C2211yescharacteristic
47#448×C101C2211yescharacteristic
48#448×C101C2211yescharacteristic, complemented
49#447×C101C2211yescharacteristic
50#447×C101C2211yescharacteristic
51#447×C101C2211yescharacteristic, complemented
52#432×C101C2211yescharacteristic, complemented
53#431×C101C2211yescharacteristic, complemented
54#396×C101—21no—
55#395×C101C2211yescharacteristic, complemented
56#394×C101—21no—
57#394×C101C2211yescharacteristic, complemented
58#393×C101C2211yescharacteristic
59#392×C101C2211yescharacteristic
60#390×C101—21no—
61#388×C101—21no—
62C4×C4⋊C4×C101C2211yescharacteristic, complemented
63#328×C101C2211yescharacteristic, complemented
64#328×C101C2211yescharacteristic, complemented
65#327×C101C2211yescharacteristic
66#327×C101C2211yescharacteristic
67#327×C101C2211yescharacteristic
68#327×C101C2211yescharacteristic
69#327×C101C2211yescharacteristic, complemented
70#327×C101C2211yescharacteristic, complemented
71#324×C101C2211yescharacteristic, complemented
72#324×C101C2211yescharacteristic, complemented
73#323×C101C2211yescharacteristic
74#323×C101C2211yescharacteristic
75C2×#41×C101—21no—
76C2×#41×C101—21no—
77C22×Q8×C101C2311yescharacteristic
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101C2311yescharacteristic
81C2×Q16×C101—21no—
82C2×SD16×C101—21no—
83C2×SD16×C101—21no—
84C2×SD16×C101—21no—
85C2×SD16×C101—21no—
86C2×D8×C101—21no—
87C2×D8×C101—21no—
88C2×D8×C101—21no—
89C4⋊Q8×C101—21no—
90C4⋊Q8×C101D411yescharacteristic, complemented
91#127×C101D411yescharacteristic, complemented
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#126×C101—21no—
99#126×C101—21no—
100#126×C101—21no—
101#125×C101—21no—
102#125×C101—21no—
103#125×C101D411yescharacteristic, complemented
104#124×C101—21no—
105#124×C101—21no—
106#124×C101—21no—
107#124×C101—21no—
108#124×C101—21no—
109#124×C101—21no—
110#124×C101—21no—
111#124×C101—21no—
112#124×C101D411yescharacteristic, complemented
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—
121#123×C101—21no—
122#123×C101—21no—
123#123×C101—21no—
124#123×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×C101C2311yescharacteristic
133#121×C101—21no—
134#121×C101—21no—
135#121×C101—21no—
136#121×C101—21no—
137#121×C101—21no—
138#121×C101—21no—
139#121×C101—21no—
140#121×C101—21no—
141#121×C101—21no—
142#121×C101—21no—
143#121×C101—21no—
144#121×C101—21no—
145#121×C101C2311yescharacteristic
146#121×C101C2311yescharacteristic
147#121×C101C2311yescharacteristic
148#120×C101—21no—
149#120×C101—21no—
150#120×C101—21no—
151#120×C101—21no—
152#120×C101—21no—
153C4×Q8×C101D411yescharacteristic, complemented
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—
161C4×D4×C101—21no—
162C4×D4×C101D411yescharacteristic, complemented
163C4×D4×C101D411yescharacteristic, complemented
164C4×D4×C101D411yescharacteristic, complemented
165#117×C101—21no—
166#117×C101—21no—
167C2×C4⋊C4×C101—21no—
168C2×C4⋊C4×C101—21no—
169C2×C4⋊C4×C101—21no—
170C2×C4⋊C4×C101D411yescharacteristic
171C2×C4⋊C4×C101D411yescharacteristic
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×C101—21no—
180C2×C22⋊C4×C101—21no—
181C2×C22⋊C4×C101D411yescharacteristic
182C2×C22⋊C4×C101D411yescharacteristic
183C2×C22⋊C4×C101C2311yescharacteristic
184C2×C42×C101—21no—
185C2×C42×C101C2311yescharacteristic
186C4⋊C8×C101—21no—
187C4⋊C8×C101—21no—
188#103×C101—21no—
189#103×C101—21no—
190#103×C101—21no—
191#103×C101—21no—
192#102×C101—21no—
193#102×C101—21no—
194#102×C101—21no—
195#102×C101—21no—
196C22⋊C8×C101C2311yescharacteristic
197C22⋊C8×C101C2311yescharacteristic
198C22⋊C8×C101C2311yescharacteristic
199C22⋊C8×C101C2311yescharacteristic
200#97×C101—21no—
201C4×C8×C101—21no—
202#95×C101—21no—
203#95×C101—21no—
204#95×C101C2311yescharacteristic
205#95×C101C2311yescharacteristic
206C24×C101—21no—
207C24×C101—21no—
208C24×C101C2×D411yescharacteristic
209#41×C101—81no—
210#41×C101—81no—
211#41×C101—81no—
212#41×C101—81no—
213C2×Q8×C101—21no—
214C2×Q8×C101—21no—
215C2×Q8×C101—21no—
216C2×Q8×C101—21no—
217C2×Q8×C101—81no—
218C2×Q8×C101C2×D411yescharacteristic
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—21no—
228C2×D4×C101—21no—
229C2×D4×C101—21no—
230C2×D4×C101—21no—
231C2×D4×C101—21no—
232C2×D4×C101—21no—
233C2×D4×C101—42no—
234C2×D4×C101—81no—
235C2×D4×C101—81no—
236C2×D4×C101—81no—
237C2×D4×C101—81no—
238C2×D4×C101—81no—
239C2×D4×C101C2×D411yescharacteristic
240C2×D4×C101C2×D411yescharacteristic
241C2×D4×C101C2×D411yescharacteristic
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—21no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—21no—
248C22×C4×C101—21no—
249C22×C4×C101—21no—
250C22×C4×C101—21no—
251C22×C4×C101—21no—
252C22×C4×C101—21no—
253C22×C4×C101C2×D411yescharacteristic
254C22×C4×C101C2×D411yescharacteristic
255C22×C4×C101C2×D411yescharacteristic
256C22×C4×C101C2×D411yescharacteristic
257C22×C4×C101C2×D411yescharacteristic
258C22×C4×C101C2411yescharacteristic
259Q16×C101—81no—
260SD16×C101—81no—
261SD16×C101—81no—
262SD16×C101—81no—
263SD16×C101—81no—
264D8×C101—81no—
265D8×C101—81no—
266D8×C101—81no—
267C2×C8×C101—21no—
268C2×C8×C101—21no—
269C2×C8×C101—21no—
270C2×C8×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—42no—
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—21no—
318C22⋊C4×C101—21no—
319C22⋊C4×C101—42no—
320C22⋊C4×C101—41no—
321C22⋊C4×C101—41no—
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—81no—
331C42×C101C2×D411yescharacteristic
332C42×C101C2×D411yescharacteristic
333C42×C101C2×D411yescharacteristic
334C42×C101C2×D411yescharacteristic
335C23×C101—21no—
336C23×C101—21no—
337C23×C101—21no—
338C23×C101—21no—
339C23×C101—21no—
340C23×C101—21no—
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—81no—
351C23×C101—81no—
352C23×C101—81no—
353C23×C101C22×D411yescharacteristic
354Q8×C101—41no—
355Q8×C101—41no—
356Q8×C101—41no—
357Q8×C101—41no—
358Q8×C101—41no—
359Q8×C101—81no—
360Q8×C101—81no—
361D4×C101—41no—
362D4×C101—41no—
363D4×C101—41no—
364D4×C101—41no—
365D4×C101—41no—
366D4×C101—41no—
367D4×C101—41no—
368D4×C101—41no—
369D4×C101—41no—
370D4×C101—41no—
371D4×C101—41no—
372D4×C101—41no—
373D4×C101—41no—
374D4×C101—81no—
375D4×C101—81no—
376D4×C101—81no—
377D4×C101—81no—
378D4×C101—81no—
379D4×C101—81no—
380D4×C101—81no—
381D4×C101—81no—
382D4×C101—81no—
383D4×C101—84no—
384C2×C4×C101—21no—
385C2×C4×C101—21no—
386C2×C4×C101—22no—
387C2×C4×C101—21no—
388C2×C4×C101—21no—
389C2×C4×C101—21no—
390C2×C4×C101—21no—
391C2×C4×C101—21no—
392C2×C4×C101—21no—
393C2×C4×C101—21no—
394C2×C4×C101—21no—
395C2×C4×C101—21no—
396C2×C4×C101—21no—
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—41no—
406C2×C4×C101—41no—
407C2×C4×C101—41no—
408C2×C4×C101—41no—
409C2×C4×C101—81no—
410C2×C4×C101—81no—
411C2×C4×C101—81no—
412C2×C4×C101—81no—
413C2×C4×C101—81no—
414C2×C4×C101—81no—
415C2×C4×C101—81no—
416C2×C4×C101—81no—
417C2×C4×C101#12011yescharacteristic
418C2×C4×C101#12011yescharacteristic
419C2×C4×C101#12011yescharacteristic
420C2×C4×C101#12011yescharacteristic
421C2×C4×C101C22×D411yescharacteristic
422C2×C4×C101C22×D411yescharacteristic
423C8×C101—41no—
424C8×C101—41no—
425C8×C101—41no—
426C8×C101—41no—
427C22×C101—21no—
428C22×C101—21no—
429C22×C101—41no—
430C22×C101—41no—
431C22×C101—41no—
432C22×C101—41no—
433C22×C101—41no—
434C22×C101—41no—
435C22×C101—41no—
436C22×C101—41no—
437C22×C101—41no—
438C22×C101—41no—
439C22×C101—41no—
440C22×C101—41no—
441C22×C101—81no—
442C22×C101—81no—
443C22×C101—81no—
444C22×C101—81no—
445C22×C101—81no—
446C22×C101—81no—
447C22×C101—81no—
448C22×C101—81no—
449C22×C101—81no—
450C22×C101—162no—
451C22×C101C2×#12011yescharacteristic
452C22×C101#57611yescharacteristic
453C22×C101#57711yescharacteristic
454C4×C101—21no—
455C4×C101—21no—
456C4×C101—21no—
457C4×C101—21no—
458C4×C101—21no—
459C4×C101—21no—
460C4×C101—42no—
461C4×C101—41no—
462C4×C101—41no—
463C4×C101—41no—
464C4×C101—41no—
465C4×C101—41no—
466C4×C101—41no—
467C4×C101—41no—
468C4×C101—41no—
469C4×C101—81no—
470C4×C101—81no—
471#18434C10111yesmaximal, characteristic, direct product factor, Sylow
472C2×C101—21no—
473C2×C101—21no—
474C2×C101—81no—
475C2×C101—81no—
476C2×C101—81no—
477C2×C101—81no—
478C2×C101—161no—
479C2×C101#301211yescharacteristic
480C2×C101#301811yescharacteristic
481C2×C101#302711yescharacteristic
482#3560C2×C10111yescharacteristic, complemented
483#3213C2×C10111yescharacteristic, complemented
484#3211C2×C10111yescharacteristic, complemented
485#2662C2×C10111yescharacteristic, complemented
486#1606C2×C10111yescharacteristic, complemented
487#1604C2×C10111yescharacteristic, complemented
488#1603C2×C10111yescharacteristic, complemented
489#1601C2×C10111yescharacteristic, complemented
490#1600C2×C10111yescharacteristic, complemented
491#1598C2×C10111yescharacteristic, complemented
492#1597C2×C10111yescharacteristic, complemented
493#1595C2×C10111yescharacteristic, complemented
494#1509C2×C10111yescharacteristic, complemented
495#1502C2×C10111yescharacteristic, complemented
496#1473C2×C10111yescharacteristic, complemented
497C101#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C10111yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C10111yescharacteristic
512#537C22×C10111yescharacteristic
513#534C22×C10111yescharacteristic
514#532C22×C10111yescharacteristic
515#529C22×C10111yescharacteristic
516C2×#126C22×C10111yescharacteristic
517C2×#124C22×C10111yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C10111yescharacteristic, complemented
527#450C22×C10111yescharacteristic, complemented
528#448C22×C10111yescharacteristic
529#448C22×C10111yescharacteristic
530#448C22×C10111yescharacteristic, complemented
531#447C22×C10111yescharacteristic
532#447C22×C10111yescharacteristic
533#447C22×C10111yescharacteristic, complemented
534#432C22×C10111yescharacteristic, complemented
535#431C22×C10111yescharacteristic, complemented
536#396—21no—
537#395C22×C10111yescharacteristic, complemented
538#394—21no—
539#394C22×C10111yescharacteristic, complemented
540#393C22×C10111yescharacteristic
541#392C22×C10111yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C10111yescharacteristic, complemented
545#328C22×C10111yescharacteristic, complemented
546#328C22×C10111yescharacteristic, complemented
547#327C22×C10111yescharacteristic
548#327C22×C10111yescharacteristic
549#327C22×C10111yescharacteristic
550#327C22×C10111yescharacteristic
551#327C22×C10111yescharacteristic, complemented
552#327C22×C10111yescharacteristic, complemented
553#324C22×C10111yescharacteristic, complemented
554#324C22×C10111yescharacteristic, complemented
555#323C22×C10111yescharacteristic
556#323C22×C10111yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C10111yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C10111yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C10111yescharacteristic, complemented
573#127D4×C10111yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C10111yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C10111yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C10111yescharacteristic
615#121—21no—
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#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C10111yescharacteristic
628#121C23×C10111yescharacteristic
629#121C23×C10111yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C10111yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C10111yescharacteristic, complemented
645C4×D4D4×C10111yescharacteristic, complemented
646C4×D4D4×C10111yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C10111yescharacteristic
653C2×C4⋊C4D4×C10111yescharacteristic
654C2×C4⋊C4C23×C10111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C10111yescharacteristic
664C2×C22⋊C4D4×C10111yescharacteristic
665C2×C22⋊C4C23×C10111yescharacteristic
666C2×C42—21no—
667C2×C42C23×C10111yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C10111yescharacteristic
679C22⋊C8C23×C10111yescharacteristic
680C22⋊C8C23×C10111yescharacteristic
681C22⋊C8C23×C10111yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C10111yescharacteristic
687#95C23×C10111yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C10111yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C10111yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C10111yescharacteristic
722C2×D4C2×D4×C10111yescharacteristic
723C2×D4C2×D4×C10111yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C10111yescharacteristic
736C22×C4C2×D4×C10111yescharacteristic
737C22×C4C2×D4×C10111yescharacteristic
738C22×C4C2×D4×C10111yescharacteristic
739C22×C4C2×D4×C10111yescharacteristic
740C22×C4C24×C10111yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C10111yescharacteristic
773C4⋊C4C2×D4×C10111yescharacteristic
774C4⋊C4C2×D4×C10111yescharacteristic
775C4⋊C4C2×D4×C10111yescharacteristic
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—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C10111yescharacteristic
814C42C2×D4×C10111yescharacteristic
815C42C2×D4×C10111yescharacteristic
816C42C2×D4×C10111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C10111yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C10111yescharacteristic
900C2×C4#120×C10111yescharacteristic
901C2×C4#120×C10111yescharacteristic
902C2×C4#120×C10111yescharacteristic
903C2×C4C22×D4×C10111yescharacteristic
904C2×C4C22×D4×C10111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C10111yescharacteristic
934C22#576×C10111yescharacteristic
935C22#577×C10111yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C101×#301211yescharacteristic
961C2C101×#301811yescharacteristic
962C2C101×#302711yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3560C2semidirect
2. C101×#3213C2semidirect
3. C101×#3211C2semidirect
4. C101×#2662C2semidirect
5. C101×#1606C2semidirect
6. C101×#1604C2semidirect
7. C101×#1603C2semidirect
8. C101×#1601C2semidirect
9. C101×#1600C2semidirect
10. C101×#1598C2semidirect
11. C101×#1597C2semidirect
12. C101×#1595C2semidirect
13. C101×#1509C2semidirect
14. C101×#1502C2semidirect
15. C101×#1473C2semidirect
35. C2×#124×C101C22semidirect
44. #451×C101C22semidirect
45. #450×C101C22semidirect
48. #448×C101C22semidirect
51. #447×C101C22semidirect
52. #432×C101C22semidirect
53. #431×C101C22semidirect
55. #395×C101C22semidirect
57. #394×C101C22semidirect
62. C4×C4⋊C4×C101C22semidirect
63. #328×C101C22semidirect
64. #328×C101C22semidirect
69. #327×C101C22semidirect
70. #327×C101C22semidirect
71. #324×C101C22semidirect
72. #324×C101C22semidirect
90. C4⋊Q8×C101D4semidirect
91. #127×C101D4semidirect
103. #125×C101D4semidirect
112. #124×C101D4semidirect
153. C4×Q8×C101D4semidirect
162. C4×D4×C101D4semidirect
163. C4×D4×C101D4semidirect
164. C4×D4×C101D4semidirect
471. #18434C101direct (N × H)
482. #3560C2×C101semidirect
483. #3213C2×C101semidirect
484. #3211C2×C101semidirect
485. #2662C2×C101semidirect
486. #1606C2×C101semidirect
487. #1604C2×C101semidirect
488. #1603C2×C101semidirect
489. #1601C2×C101semidirect
490. #1600C2×C101semidirect
491. #1598C2×C101semidirect
492. #1597C2×C101semidirect
493. #1595C2×C101semidirect
494. #1509C2×C101semidirect
495. #1502C2×C101semidirect
496. #1473C2×C101semidirect
497. C101#18434direct (N × H)
517. C2×#124C22×C101semidirect
526. #451C22×C101semidirect
527. #450C22×C101semidirect
530. #448C22×C101semidirect
533. #447C22×C101semidirect
534. #432C22×C101semidirect
535. #431C22×C101semidirect
537. #395C22×C101semidirect
539. #394C22×C101semidirect
544. C4×C4⋊C4C22×C101semidirect
545. #328C22×C101semidirect
546. #328C22×C101semidirect
551. #327C22×C101semidirect
552. #327C22×C101semidirect
553. #324C22×C101semidirect
554. #324C22×C101semidirect
572. C4⋊Q8D4×C101semidirect
573. #127D4×C101semidirect
585. #125D4×C101semidirect
594. #124D4×C101semidirect
635. C4×Q8D4×C101semidirect
644. C4×D4D4×C101semidirect
645. C4×D4D4×C101semidirect
646. C4×D4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35602
C101×#32132
C101×#32112
C101×#26622
C101×#16062
C101×#16042
C101×#16032
C101×#16012
C101×#16002
C101×#15982
C101×#15972
C101×#15952
C101×#15092
C101×#15022
C101×#14732
#18434101