Finite Group Databasebeta

← C101×#17598 #38799749

Subgroups — C101×#17598 #38799749

Order 25856.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3520C211yesmaximal, characteristic
2C101×#2974C211yesmaximal, characteristic, complemented
3C101×#2318C211yesmaximal, characteristic, complemented
4C101×#1521C211yesmaximal, characteristic, complemented
5C101×#1520C211yesmaximal, characteristic, complemented
6C101×#1518C211yesmaximal, characteristic, complemented
7C101×#1516C211yesmaximal, characteristic, complemented
8C101×#1515C211yesmaximal, characteristic, complemented
9C101×#1513C211yesmaximal, characteristic, complemented
10C101×#1512C211yesmaximal, characteristic, complemented
11C101×#1511C211yesmaximal, characteristic, complemented
12C101×#1508C211yesmaximal, characteristic, complemented
13C101×#1504C211yesmaximal, characteristic, complemented
14C101×#1501C211yesmaximal, characteristic, complemented
15C2×#328×C101C211yesmaximal, characteristic, complemented
16#556×C101C411yescharacteristic, complemented
17#554×C101—21no—
18#552×C101C411yescharacteristic, complemented
19#552×C101C411yescharacteristic, complemented
20#551×C101—21no—
21#551×C101—21no—
22D4×Q8×C101C411yescharacteristic, complemented
23#548×C101C411yescharacteristic, complemented
24#548×C101C411yescharacteristic, complemented
25#547×C101C411yescharacteristic, complemented
26#547×C101C411yescharacteristic, complemented
27#546×C101—21no—
28#542×C101—21no—
29#539×C101—21no—
30#539×C101—21no—
31#533×C101C2211yescharacteristic
32#529×C101C2211yescharacteristic
33#525×C101C2211yescharacteristic
34#525×C101C2211yescharacteristic
35C2×C22⋊Q8×C101C2211yescharacteristic
36C2×C22⋊Q8×C101C2211yescharacteristic
37#520×C101—21no—
38C2×C4×D4×C101C2211yescharacteristic
39#436×C101—21no—
40#435×C101—21no—
41#435×C101—21no—
42C8×D4×C101—21no—
43#432×C101C2211yescharacteristic
44#431×C101C2211yescharacteristic
45#407×C101C2211yescharacteristic
46#407×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48C2×C22⋊C8×C101C2211yescharacteristic
49#388×C101—21no—
50#387×C101—21no—
51#386×C101—21no—
52#385×C101—21no—
53#383×C101C2211yescharacteristic
54#382×C101C2211yescharacteristic
55#381×C101C2211yescharacteristic
56#380×C101C2211yescharacteristic
57C4×C22⋊C4×C101C2211yescharacteristic
58C2×#95×C101C2211yescharacteristic
59#328×C101C2211yescharacteristic
60#328×C101C2211yescharacteristic
61#328×C101C2211yescharacteristic
62#328×C101C2211yescharacteristic
63#328×C101C2211yescharacteristic
64#328×C101C2211yescharacteristic
65#328×C101C2211yescharacteristic
66#328×C101C2211yescharacteristic
67#328×C101C2211yescharacteristic
68#328×C101C2211yescharacteristic
69#328×C101C2211yescharacteristic
70#328×C101C2211yescharacteristic
71#327×C101C2211yescharacteristic
72#327×C101C2211yescharacteristic
73#327×C101C2211yescharacteristic
74#327×C101C2211yescharacteristic
75C2×#41×C101—21no—
76C2×#41×C101C2×C411yescharacteristic
77C2×#41×C101C2×C411yescharacteristic, complemented
78C22×Q8×C101C2×C411yescharacteristic
79C22×Q8×C101C2×C411yescharacteristic, complemented
80C22×D4×C101D411yescharacteristic
81C23×C4×C101—21no—
82C23×C4×C101C2311yescharacteristic
83C23×C4×C101C2311yescharacteristic
84C2×M16×C101—21no—
85C2×M16×C101—21no—
86C22×C8×C101—21no—
87C22×C8×C101—21no—
88C4⋊Q8×C101—21no—
89C4⋊Q8×C101C2×C411yescharacteristic, complemented
90C4⋊Q8×C101C2×C411yescharacteristic, complemented
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×C101C2×C411yescharacteristic, complemented
100#124×C101—21no—
101#124×C101—21no—
102#124×C101—21no—
103#124×C101C2×C411yescharacteristic, complemented
104#123×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—
113C22⋊Q8×C101—21no—
114C22⋊Q8×C101—21no—
115C22⋊Q8×C101—21no—
116C22⋊Q8×C101—21no—
117C22⋊Q8×C101—21no—
118C22⋊Q8×C101—21no—
119C22⋊Q8×C101—21no—
120C22⋊Q8×C101—21no—
121C22⋊Q8×C101—21no—
122C22⋊Q8×C101—21no—
123C22⋊Q8×C101C2×C411yescharacteristic
124C22⋊Q8×C101C2×C411yescharacteristic
125C22⋊Q8×C101C2×C411yescharacteristic
126C22⋊Q8×C101C2×C411yescharacteristic, complemented
127C22⋊Q8×C101C2×C411yescharacteristic, complemented
128C22⋊Q8×C101C2×C411yescharacteristic, complemented
129C22⋊Q8×C101C2311yescharacteristic
130C22⋊Q8×C101C2311yescharacteristic
131C22⋊Q8×C101C2311yescharacteristic
132#121×C101—21no—
133#121×C101—21no—
134#121×C101—21no—
135#121×C101C2×C411yescharacteristic
136#121×C101C2×C411yescharacteristic, complemented
137#121×C101C2311yescharacteristic
138#120×C101—21no—
139#120×C101—21no—
140C4×Q8×C101—21no—
141C4×Q8×C101—21no—
142C4×Q8×C101C2×C411yescharacteristic, complemented
143C4×Q8×C101C2×C411yescharacteristic, complemented
144C4×Q8×C101C2×C411yescharacteristic, complemented
145C4×D4×C101—21no—
146C4×D4×C101—21no—
147C4×D4×C101—21no—
148C4×D4×C101—21no—
149C4×D4×C101—21no—
150C4×D4×C101—21no—
151C4×D4×C101—21no—
152C4×D4×C101—21no—
153C4×D4×C101C2×C411yescharacteristic
154C4×D4×C101C2×C411yescharacteristic
155C4×D4×C101C2×C411yescharacteristic
156C4×D4×C101C2×C411yescharacteristic
157C4×D4×C101C2×C411yescharacteristic, complemented
158C4×D4×C101D411yescharacteristic
159C4×D4×C101D411yescharacteristic
160C4×D4×C101D411yescharacteristic
161C4×D4×C101D411yescharacteristic
162#117×C101—21no—
163#117×C101—21no—
164#117×C101—21no—
165#117×C101—21no—
166#117×C101C2×C411yescharacteristic
167#117×C101C2×C411yescharacteristic, complemented
168C2×C4⋊C4×C101—21no—
169C2×C4⋊C4×C101—21no—
170C2×C4⋊C4×C101—21no—
171C2×C4⋊C4×C101—21no—
172C2×C4⋊C4×C101—21no—
173C2×C4⋊C4×C101C2×C411yescharacteristic
174C2×C4⋊C4×C101C2×C411yescharacteristic, complemented
175C2×C4⋊C4×C101D411yescharacteristic
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×C42×C101—21no—
184C2×C42×C101C2311yescharacteristic
185C4⋊C8×C101—21no—
186C4⋊C8×C101—21no—
187C22⋊C8×C101—21no—
188C22⋊C8×C101—21no—
189C22⋊C8×C101—21no—
190C22⋊C8×C101—21no—
191C22⋊C8×C101C2311yescharacteristic
192C22⋊C8×C101C2311yescharacteristic
193C22⋊C8×C101C2311yescharacteristic
194C22⋊C8×C101C2311yescharacteristic
195#97×C101—21no—
196C4×C8×C101—21no—
197#95×C101—21no—
198#95×C101—21no—
199#95×C101—21no—
200#95×C101—21no—
201#95×C101—21no—
202#95×C101C2311yescharacteristic
203#95×C101C2311yescharacteristic
204#95×C101C2311yescharacteristic
205#95×C101C2311yescharacteristic
206C24×C101C2×D411yescharacteristic
207C24×C101C2×D411yescharacteristic
208#41×C101—44no—
209#41×C101—81no—
210#41×C101—81no—
211C2×Q8×C101—21no—
212C2×Q8×C101—21no—
213C2×Q8×C101—21no—
214C2×Q8×C101—81no—
215C2×Q8×C101—81no—
216C2×Q8×C101C22×C411yescharacteristic
217C2×Q8×C101C22×C411yescharacteristic
218C2×Q8×C101C22×C411yescharacteristic
219C2×D4×C101—21no—
220C2×D4×C101—21no—
221C2×D4×C101—21no—
222C2×D4×C101—21no—
223C2×D4×C101—21no—
224C2×D4×C101—42no—
225C2×D4×C101C22⋊C411yescharacteristic
226C2×D4×C101C22⋊C411yescharacteristic
227C2×D4×C101C22⋊C411yescharacteristic
228C2×D4×C101C22⋊C411yescharacteristic
229C2×D4×C101C22×C411yescharacteristic
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—21no—
241C22×C4×C101—42no—
242C22×C4×C101—81no—
243C22×C4×C101—81no—
244C22×C4×C101—81no—
245C22×C4×C101—81no—
246C22×C4×C101C22×C411yescharacteristic
247C22×C4×C101C22×C411yescharacteristic
248C22×C4×C101C22×C411yescharacteristic
249C22×C4×C101C22×C411yescharacteristic
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×C101C2×D411yescharacteristic
257C22×C4×C101C2×D411yescharacteristic
258C22×C4×C101C2411yescharacteristic
259M16×C101—81no—
260M16×C101—81no—
261C2×C8×C101—21no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—81no—
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—81no—
287C4⋊C4×C101—81no—
288C4⋊C4×C101C22⋊C411yescharacteristic
289C4⋊C4×C101C22⋊C411yescharacteristic
290C4⋊C4×C101C22⋊C411yescharacteristic
291C4⋊C4×C101C22⋊C411yescharacteristic
292C4⋊C4×C101C22×C411yescharacteristic
293C4⋊C4×C101C22×C411yescharacteristic
294C4⋊C4×C101C22×C411yescharacteristic
295C4⋊C4×C101C22×C411yescharacteristic
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—42no—
314C22⋊C4×C101—81no—
315C22⋊C4×C101—81no—
316C22⋊C4×C101C22⋊C411yescharacteristic
317C22⋊C4×C101C22⋊C411yescharacteristic
318C22⋊C4×C101C22⋊C411yescharacteristic
319C22⋊C4×C101C22⋊C411yescharacteristic
320C22⋊C4×C101C22⋊C411yescharacteristic
321C22⋊C4×C101C22⋊C411yescharacteristic
322C22⋊C4×C101C22⋊C411yescharacteristic
323C22⋊C4×C101C22⋊C411yescharacteristic
324C42×C101—21no—
325C42×C101—21no—
326C42×C101—21no—
327C42×C101—21no—
328C42×C101—21no—
329C42×C101—81no—
330C42×C101C22×C411yescharacteristic
331C42×C101C22×C411yescharacteristic
332C42×C101C2×D411yescharacteristic
333C42×C101C2×D411yescharacteristic
334C23×C101—21no—
335C23×C101—21no—
336C23×C101—22no—
337C23×C101—21no—
338C23×C101—21no—
339C23×C101—21no—
340C23×C101—41no—
341C23×C101—41no—
342C23×C101—41no—
343C23×C101C2×C22⋊C411yescharacteristic
344C23×C101C2×C22⋊C411yescharacteristic
345C23×C101C2×C22⋊C411yescharacteristic
346C23×C101C2×C22⋊C411yescharacteristic
347C23×C101C22×D411yescharacteristic
348Q8×C101—41no—
349Q8×C101—41no—
350Q8×C101—41no—
351Q8×C101—42no—
352Q8×C101—81no—
353Q8×C101—81no—
354D4×C101—22no—
355D4×C101—22no—
356D4×C101—41no—
357D4×C101—41no—
358D4×C101—41no—
359D4×C101—42no—
360D4×C101—41no—
361D4×C101—41no—
362D4×C101—42no—
363D4×C101—81no—
364D4×C101—81no—
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—21no—
372C2×C4×C101—21no—
373C2×C4×C101—21no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
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—42no—
387C2×C4×C101—42no—
388C2×C4×C101—42no—
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—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—41no—
400C2×C4×C101—41no—
401C2×C4×C101—81no—
402C2×C4×C101—81no—
403C2×C4×C101—81no—
404C2×C4×C101—81no—
405C2×C4×C101—84no—
406C2×C4×C101C2×C22⋊C411yescharacteristic
407C2×C4×C101C2×C22⋊C411yescharacteristic
408C2×C4×C101C2×C22⋊C411yescharacteristic
409C2×C4×C101C2×C22⋊C411yescharacteristic
410C2×C4×C101C2×C22⋊C411yescharacteristic
411C2×C4×C101C2×C22⋊C411yescharacteristic
412C2×C4×C101C2×C22⋊C411yescharacteristic
413C2×C4×C101C2×C22⋊C411yescharacteristic
414C2×C4×C101C23×C411yescharacteristic
415C2×C4×C101C22×D411yescharacteristic
416C8×C101—41no—
417C8×C101—41no—
418C8×C101—41no—
419C8×C101—41no—
420C22×C101—21no—
421C22×C101—21no—
422C22×C101—21no—
423C22×C101—21no—
424C22×C101—21no—
425C22×C101—21no—
426C22×C101—21no—
427C22×C101—21no—
428C22×C101—21no—
429C22×C101—21no—
430C22×C101—21no—
431C22×C101—21no—
432C22×C101—21no—
433C22×C101—42no—
434C22×C101—42no—
435C22×C101—41no—
436C22×C101—41no—
437C22×C101—41no—
438C22×C101—81no—
439C22×C101—81no—
440C22×C101#42112yes—
441C22×C101C22×C22⋊C411yescharacteristic
442C22×C101#57711yescharacteristic
443C22×C101#57811yescharacteristic
444C4×C101—21no—
445C4×C101—21no—
446C4×C101—21no—
447C4×C101—21no—
448C4×C101—21no—
449C4×C101—21no—
450C4×C101—21no—
451C4×C101—21no—
452C4×C101—21no—
453C4×C101—21no—
454C4×C101—41no—
455C4×C101—41no—
456C4×C101—41no—
457C4×C101—41no—
458C4×C101—41no—
459C4×C101—41no—
460C4×C101—41no—
461C4×C101—81no—
462C4×C101—81no—
463C4×C101—81no—
464C4×C101—81no—
465#17598C10111yesmaximal, characteristic, direct product factor, Sylow
466C2×C101—21no—
467C2×C101—21no—
468C2×C101—22no—
469C2×C101—41no—
470C2×C101—41no—
471C2×C101—41no—
472C2×C101—81no—
473C2×C101#288311yescharacteristic
474C2×C101#289811yescharacteristic
475C2×C101C2×#42111yescharacteristic
476#3520C2×C10111yescharacteristic
477#2974C2×C10111yescharacteristic, complemented
478#2318C2×C10111yescharacteristic, complemented
479#1521C2×C10111yescharacteristic, complemented
480#1520C2×C10111yescharacteristic, complemented
481#1518C2×C10111yescharacteristic, complemented
482#1516C2×C10111yescharacteristic, complemented
483#1515C2×C10111yescharacteristic, complemented
484#1513C2×C10111yescharacteristic, complemented
485#1512C2×C10111yescharacteristic, complemented
486#1511C2×C10111yescharacteristic, complemented
487#1508C2×C10111yescharacteristic, complemented
488#1504C2×C10111yescharacteristic, complemented
489#1501C2×C10111yescharacteristic, complemented
490C2×#328C2×C10111yescharacteristic, complemented
491C101#1759811yescharacteristic, direct product factor, Sylow
492#556C4×C10111yescharacteristic, complemented
493#554—21no—
494#552C4×C10111yescharacteristic, complemented
495#552C4×C10111yescharacteristic, complemented
496#551—21no—
497#551—21no—
498D4×Q8C4×C10111yescharacteristic, complemented
499#548C4×C10111yescharacteristic, complemented
500#548C4×C10111yescharacteristic, complemented
501#547C4×C10111yescharacteristic, complemented
502#547C4×C10111yescharacteristic, complemented
503#546—21no—
504#542—21no—
505#539—21no—
506#539—21no—
507#533C22×C10111yescharacteristic
508#529C22×C10111yescharacteristic
509#525C22×C10111yescharacteristic
510#525C22×C10111yescharacteristic
511C2×C22⋊Q8C22×C10111yescharacteristic
512C2×C22⋊Q8C22×C10111yescharacteristic
513#520—21no—
514C2×C4×D4C22×C10111yescharacteristic
515#436—21no—
516#435—21no—
517#435—21no—
518C8×D4—21no—
519#432C22×C10111yescharacteristic
520#431C22×C10111yescharacteristic
521#407C22×C10111yescharacteristic
522#407C22×C10111yescharacteristic
523C2×C22⋊C8C22×C10111yescharacteristic
524C2×C22⋊C8C22×C10111yescharacteristic
525#388—21no—
526#387—21no—
527#386—21no—
528#385—21no—
529#383C22×C10111yescharacteristic
530#382C22×C10111yescharacteristic
531#381C22×C10111yescharacteristic
532#380C22×C10111yescharacteristic
533C4×C22⋊C4C22×C10111yescharacteristic
534C2×#95C22×C10111yescharacteristic
535#328C22×C10111yescharacteristic
536#328C22×C10111yescharacteristic
537#328C22×C10111yescharacteristic
538#328C22×C10111yescharacteristic
539#328C22×C10111yescharacteristic
540#328C22×C10111yescharacteristic
541#328C22×C10111yescharacteristic
542#328C22×C10111yescharacteristic
543#328C22×C10111yescharacteristic
544#328C22×C10111yescharacteristic
545#328C22×C10111yescharacteristic
546#328C22×C10111yescharacteristic
547#327C22×C10111yescharacteristic
548#327C22×C10111yescharacteristic
549#327C22×C10111yescharacteristic
550#327C22×C10111yescharacteristic
551C2×#41—21no—
552C2×#41C2×C4×C10111yescharacteristic
553C2×#41C2×C4×C10111yescharacteristic, complemented
554C22×Q8C2×C4×C10111yescharacteristic
555C22×Q8C2×C4×C10111yescharacteristic, complemented
556C22×D4D4×C10111yescharacteristic
557C23×C4—21no—
558C23×C4C23×C10111yescharacteristic
559C23×C4C23×C10111yescharacteristic
560C2×M16—21no—
561C2×M16—21no—
562C22×C8—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8C2×C4×C10111yescharacteristic, complemented
566C4⋊Q8C2×C4×C10111yescharacteristic, complemented
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#125C2×C4×C10111yescharacteristic, complemented
576#124—21no—
577#124—21no—
578#124—21no—
579#124C2×C4×C10111yescharacteristic, complemented
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8C2×C4×C10111yescharacteristic
600C22⋊Q8C2×C4×C10111yescharacteristic
601C22⋊Q8C2×C4×C10111yescharacteristic
602C22⋊Q8C2×C4×C10111yescharacteristic, complemented
603C22⋊Q8C2×C4×C10111yescharacteristic, complemented
604C22⋊Q8C2×C4×C10111yescharacteristic, complemented
605C22⋊Q8C23×C10111yescharacteristic
606C22⋊Q8C23×C10111yescharacteristic
607C22⋊Q8C23×C10111yescharacteristic
608#121—21no—
609#121—21no—
610#121—21no—
611#121C2×C4×C10111yescharacteristic
612#121C2×C4×C10111yescharacteristic, complemented
613#121C23×C10111yescharacteristic
614#120—21no—
615#120—21no—
616C4×Q8—21no—
617C4×Q8—21no—
618C4×Q8C2×C4×C10111yescharacteristic, complemented
619C4×Q8C2×C4×C10111yescharacteristic, complemented
620C4×Q8C2×C4×C10111yescharacteristic, complemented
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4C2×C4×C10111yescharacteristic
630C4×D4C2×C4×C10111yescharacteristic
631C4×D4C2×C4×C10111yescharacteristic
632C4×D4C2×C4×C10111yescharacteristic
633C4×D4C2×C4×C10111yescharacteristic, complemented
634C4×D4D4×C10111yescharacteristic
635C4×D4D4×C10111yescharacteristic
636C4×D4D4×C10111yescharacteristic
637C4×D4D4×C10111yescharacteristic
638#117—21no—
639#117—21no—
640#117—21no—
641#117—21no—
642#117C2×C4×C10111yescharacteristic
643#117C2×C4×C10111yescharacteristic, complemented
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4C2×C4×C10111yescharacteristic
650C2×C4⋊C4C2×C4×C10111yescharacteristic, complemented
651C2×C4⋊C4D4×C10111yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4D4×C10111yescharacteristic
658C2×C22⋊C4D4×C10111yescharacteristic
659C2×C42—21no—
660C2×C42C23×C10111yescharacteristic
661C4⋊C8—21no—
662C4⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8C23×C10111yescharacteristic
668C22⋊C8C23×C10111yescharacteristic
669C22⋊C8C23×C10111yescharacteristic
670C22⋊C8C23×C10111yescharacteristic
671#97—21no—
672C4×C8—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95C23×C10111yescharacteristic
679#95C23×C10111yescharacteristic
680#95C23×C10111yescharacteristic
681#95C23×C10111yescharacteristic
682C24C2×D4×C10111yescharacteristic
683C24C2×D4×C10111yescharacteristic
684#41—44no—
685#41—81no—
686#41—81no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—81no—
691C2×Q8—81no—
692C2×Q8C22×C4×C10111yescharacteristic
693C2×Q8C22×C4×C10111yescharacteristic
694C2×Q8C22×C4×C10111yescharacteristic
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4C22⋊C4×C10111yescharacteristic
702C2×D4C22⋊C4×C10111yescharacteristic
703C2×D4C22⋊C4×C10111yescharacteristic
704C2×D4C22⋊C4×C10111yescharacteristic
705C2×D4C22×C4×C10111yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—42no—
718C22×C4—81no—
719C22×C4—81no—
720C22×C4—81no—
721C22×C4—81no—
722C22×C4C22×C4×C10111yescharacteristic
723C22×C4C22×C4×C10111yescharacteristic
724C22×C4C22×C4×C10111yescharacteristic
725C22×C4C22×C4×C10111yescharacteristic
726C22×C4C2×D4×C10111yescharacteristic
727C22×C4C2×D4×C10111yescharacteristic
728C22×C4C2×D4×C10111yescharacteristic
729C22×C4C2×D4×C10111yescharacteristic
730C22×C4C2×D4×C10111yescharacteristic
731C22×C4C2×D4×C10111yescharacteristic
732C22×C4C2×D4×C10111yescharacteristic
733C22×C4C2×D4×C10111yescharacteristic
734C22×C4C24×C10111yescharacteristic
735M16—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C2×C8—81no—
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—81no—
763C4⋊C4—81no—
764C4⋊C4C22⋊C4×C10111yescharacteristic
765C4⋊C4C22⋊C4×C10111yescharacteristic
766C4⋊C4C22⋊C4×C10111yescharacteristic
767C4⋊C4C22⋊C4×C10111yescharacteristic
768C4⋊C4C22×C4×C10111yescharacteristic
769C4⋊C4C22×C4×C10111yescharacteristic
770C4⋊C4C22×C4×C10111yescharacteristic
771C4⋊C4C22×C4×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—42no—
790C22⋊C4—81no—
791C22⋊C4—81no—
792C22⋊C4C22⋊C4×C10111yescharacteristic
793C22⋊C4C22⋊C4×C10111yescharacteristic
794C22⋊C4C22⋊C4×C10111yescharacteristic
795C22⋊C4C22⋊C4×C10111yescharacteristic
796C22⋊C4C22⋊C4×C10111yescharacteristic
797C22⋊C4C22⋊C4×C10111yescharacteristic
798C22⋊C4C22⋊C4×C10111yescharacteristic
799C22⋊C4C22⋊C4×C10111yescharacteristic
800C42—21no—
801C42—21no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—81no—
806C42C22×C4×C10111yescharacteristic
807C42C22×C4×C10111yescharacteristic
808C42C2×D4×C10111yescharacteristic
809C42C2×D4×C10111yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23C2×C22⋊C4×C10111yescharacteristic
820C23C2×C22⋊C4×C10111yescharacteristic
821C23C2×C22⋊C4×C10111yescharacteristic
822C23C2×C22⋊C4×C10111yescharacteristic
823C23C22×D4×C10111yescharacteristic
824Q8—41no—
825Q8—41no—
826Q8—41no—
827Q8—42no—
828Q8—81no—
829Q8—81no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—42no—
836D4—42no—
837D4—41no—
838D4—41no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—84no—
882C2×C4C2×C22⋊C4×C10111yescharacteristic
883C2×C4C2×C22⋊C4×C10111yescharacteristic
884C2×C4C2×C22⋊C4×C10111yescharacteristic
885C2×C4C2×C22⋊C4×C10111yescharacteristic
886C2×C4C2×C22⋊C4×C10111yescharacteristic
887C2×C4C2×C22⋊C4×C10111yescharacteristic
888C2×C4C2×C22⋊C4×C10111yescharacteristic
889C2×C4C2×C22⋊C4×C10111yescharacteristic
890C2×C4C23×C4×C10111yescharacteristic
891C2×C4C22×D4×C10111yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—81no—
915C22—81no—
916C22#421×C10112yes—
917C22C22×C22⋊C4×C10111yescharacteristic
918C22#577×C10111yescharacteristic
919C22#578×C10111yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C4—81no—
940C4—81no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—81no—
948C2C101×#288311yescharacteristic
949C2C101×#289811yescharacteristic
950C2C2×#421×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C22×C22⋊C4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3520C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2974C2semidirect
3. C101×#2318C2semidirect
4. C101×#1521C2semidirect
5. C101×#1520C2semidirect
6. C101×#1518C2semidirect
7. C101×#1516C2semidirect
8. C101×#1515C2semidirect
9. C101×#1513C2semidirect
10. C101×#1512C2semidirect
11. C101×#1511C2semidirect
12. C101×#1508C2semidirect
13. C101×#1504C2semidirect
14. C101×#1501C2semidirect
15. C2×#328×C101C2semidirect
16. #556×C101C4semidirect
18. #552×C101C4semidirect
19. #552×C101C4semidirect
22. D4×Q8×C101C4semidirect
23. #548×C101C4semidirect
24. #548×C101C4semidirect
25. #547×C101C4semidirect
26. #547×C101C4semidirect
77. C2×#41×C101C2×C4semidirect
79. C22×Q8×C101C2×C4semidirect
89. C4⋊Q8×C101C2×C4semidirect
90. C4⋊Q8×C101C2×C4semidirect
99. #125×C101C2×C4semidirect
103. #124×C101C2×C4semidirect
126. C22⋊Q8×C101C2×C4semidirect
127. C22⋊Q8×C101C2×C4semidirect
128. C22⋊Q8×C101C2×C4semidirect
136. #121×C101C2×C4semidirect
142. C4×Q8×C101C2×C4semidirect
143. C4×Q8×C101C2×C4semidirect
144. C4×Q8×C101C2×C4semidirect
157. C4×D4×C101C2×C4semidirect
167. #117×C101C2×C4semidirect
174. C2×C4⋊C4×C101C2×C4semidirect
465. #17598C101direct (N × H)
477. #2974C2×C101semidirect
478. #2318C2×C101semidirect
479. #1521C2×C101semidirect
480. #1520C2×C101semidirect
481. #1518C2×C101semidirect
482. #1516C2×C101semidirect
483. #1515C2×C101semidirect
484. #1513C2×C101semidirect
485. #1512C2×C101semidirect
486. #1511C2×C101semidirect
487. #1508C2×C101semidirect
488. #1504C2×C101semidirect
489. #1501C2×C101semidirect
490. C2×#328C2×C101semidirect
491. C101#17598direct (N × H)
492. #556C4×C101semidirect
494. #552C4×C101semidirect
495. #552C4×C101semidirect
498. D4×Q8C4×C101semidirect
499. #548C4×C101semidirect
500. #548C4×C101semidirect
501. #547C4×C101semidirect
502. #547C4×C101semidirect
553. C2×#41C2×C4×C101semidirect
555. C22×Q8C2×C4×C101semidirect
565. C4⋊Q8C2×C4×C101semidirect
566. C4⋊Q8C2×C4×C101semidirect
575. #125C2×C4×C101semidirect
579. #124C2×C4×C101semidirect
602. C22⋊Q8C2×C4×C101semidirect
603. C22⋊Q8C2×C4×C101semidirect
604. C22⋊Q8C2×C4×C101semidirect
612. #121C2×C4×C101semidirect
618. C4×Q8C2×C4×C101semidirect
619. C4×Q8C2×C4×C101semidirect
620. C4×Q8C2×C4×C101semidirect
633. C4×D4C2×C4×C101semidirect
643. #117C2×C4×C101semidirect
650. C2×C4⋊C4C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35202
C101×#29742
C101×#23182
C101×#15212
C101×#15202
C101×#15182
C101×#15162
C101×#15152
C101×#15132
C101×#15122
C101×#15112
C101×#15082
C101×#15042
C101×#15012
C2×#328×C1012
#17598101