Finite Group Databasebeta

← #21459879

Subgroups — #21459879

Order 7808.

1042 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840479C211yesmaximal, characteristic, complemented
2#16840479C211yesmaximal, characteristic, complemented
3#16840467C211yesmaximal, characteristic, complemented
4#16840463C211yesmaximal, characteristic, complemented
5#16840463C211yesmaximal, characteristic, complemented
6#16840460C211yesmaximal, characteristic, complemented
7#16840448C211yesmaximal, characteristic, complemented
8#16840448C211yesmaximal, characteristic, complemented
9#16840447C211yesmaximal, characteristic, complemented
10#16840438C211yesmaximal, characteristic, complemented
11#16840438C211yesmaximal, characteristic, complemented
12#16840437C211yesmaximal, characteristic, complemented
13#16840437C211yesmaximal, characteristic, complemented
14#16840413C211yesmaximal, characteristic, complemented
15#16840402C211yesmaximal, characteristic, complemented
16#16840402C211yesmaximal, characteristic, complemented
17#16840378C211yesmaximal, characteristic, complemented
18#16840369C211yesmaximal, characteristic, complemented
19#16840359C211yesmaximal, characteristic, complemented
20#16840353C211yesmaximal, characteristic, complemented
21#16840351C211yesmaximal, characteristic, complemented
22#16840350C211yesmaximal, characteristic, complemented
23#16840296C211yesmaximal, characteristic, complemented
24#16840295C211yesmaximal, characteristic, complemented
25#16840295C211yesmaximal, characteristic, complemented
26#16840295C211yesmaximal, characteristic, complemented
27#126×D61C211yesmaximal, characteristic, complemented
28#16840243C211yesmaximal, characteristic, complemented
29#16840235C211yesmaximal, characteristic, complemented
30C4×#11758222C211yesmaximal, characteristic, complemented
31C2×#126×C61C211yesmaximal, characteristic, complemented
32C2×#11758222C2211yescharacteristic
33C2×#11758222C2211yescharacteristic
34C22×C22⋊D61C2211yescharacteristic
35#14519776C2211yescharacteristic, complemented
36#14519776C2211yescharacteristic, complemented
37#14519772C2211yescharacteristic, complemented
38#14519772C2211yescharacteristic, complemented
39#14519772C2211yescharacteristic, complemented
40#14519772C2211yescharacteristic, complemented
41#14519772C2211yescharacteristic, complemented
42#14519772C2211yescharacteristic, complemented
43#14519771C2211yescharacteristic, complemented
44#14519771C2211yescharacteristic, complemented
45#14519770C2211yescharacteristic
46#14519770C2211yescharacteristic
47#14519770C2211yescharacteristic
48#14519770C2211yescharacteristic
49#14519770C2211yescharacteristic
50#14519770C2211yescharacteristic, complemented
51#14519769C2211yescharacteristic, complemented
52#14519768C2211yescharacteristic, complemented
53#14519768C2211yescharacteristic, complemented
54#14519767C2211yescharacteristic, complemented
55#14519767C2211yescharacteristic, complemented
56#14519767C2211yescharacteristic, complemented
57#14519767C2211yescharacteristic, complemented
58#14519767C2211yescharacteristic, complemented
59#14519767C2211yescharacteristic, complemented
60#14519765C2211yescharacteristic, complemented
61#14519763C2211yescharacteristic
62#14519763C2211yescharacteristic
63#14519763C2211yescharacteristic
64#14519763C2211yescharacteristic
65#14519763C2211yescharacteristic
66#14519763C2211yescharacteristic, complemented
67#14519762C2211yescharacteristic, complemented
68#14519762C2211yescharacteristic, complemented
69#14519762C2211yescharacteristic, complemented
70#14519762C2211yescharacteristic, complemented
71#14519762C2211yescharacteristic, complemented
72#14519762C2211yescharacteristic, complemented
73#14519761C2211yescharacteristic, complemented
74#14519761C2211yescharacteristic, complemented
75#14519760C2211yescharacteristic
76#14519760C2211yescharacteristic
77#14519760C2211yescharacteristic, complemented
78#14519760C2211yescharacteristic, complemented
79#14519759C2211yescharacteristic
80#14519759C2211yescharacteristic
81#14519759C2211yescharacteristic
82#14519759C2211yescharacteristic
83#14519759C2211yescharacteristic
84#14519759C2211yescharacteristic, complemented
85#14519757C2211yescharacteristic, complemented
86#14519757C2211yescharacteristic, complemented
87#14519756C2211yescharacteristic, complemented
88#14519756C2211yescharacteristic, complemented
89#14519756C2211yescharacteristic, complemented
90#14519755C2211yescharacteristic, complemented
91#14519755C2211yescharacteristic, complemented
92#14519755C2211yescharacteristic, complemented
93#14519755C2211yescharacteristic, complemented
94#14519755C2211yescharacteristic, complemented
95#14519755C2211yescharacteristic, complemented
96#14519754C2211yescharacteristic
97#14519754C2211yescharacteristic
98#14519754C2211yescharacteristic, complemented
99#14519754C2211yescharacteristic, complemented
100#14519752C2211yescharacteristic, complemented
101#14519752C2211yescharacteristic, complemented
102#14519751C2211yescharacteristic
103#14519751C2211yescharacteristic
104#14519751C2211yescharacteristic, complemented
105#14519750C2211yescharacteristic
106#14519750C2211yescharacteristic
107#14519750C2211yescharacteristic
108#14519750C2211yescharacteristic
109#14519750C2211yescharacteristic
110#14519750C2211yescharacteristic, complemented
111#14519747C2211yescharacteristic
112#14519747C2211yescharacteristic
113#14519746C2211yescharacteristic
114#14519746C2211yescharacteristic
115C4×Dic122C2211yescharacteristic, complemented
116C4×Dic122C2211yescharacteristic, complemented
117C4×Dic122C2211yescharacteristic, complemented
118#14519742C2211yescharacteristic, complemented
119#14519742C2211yescharacteristic, complemented
120#14519742C2211yescharacteristic, complemented
121#14519742C2211yescharacteristic, complemented
122C4×D244C2211yescharacteristic, complemented
123C4×D244C2211yescharacteristic, complemented
124C4×D244C2211yescharacteristic, complemented
125#14519739C2211yescharacteristic, complemented
126#14519739C2211yescharacteristic, complemented
127#14519739C2211yescharacteristic, complemented
128#14519739C2211yescharacteristic, complemented
129C4×C22⋊D61C2211yescharacteristic
130C4×C22⋊D61C2211yescharacteristic
131C4×C22⋊D61C2211yescharacteristic
132C4×C22⋊D61C2211yescharacteristic
133C4×C22⋊D61C2211yescharacteristic
134C4×C22⋊D61C2211yescharacteristic
135C4×C22⋊D61C2211yescharacteristic, complemented
136C4×C22⋊D61C2211yescharacteristic, complemented
137C4×C22⋊D61C2211yescharacteristic, complemented
138C4×C22⋊D61C2211yescharacteristic, complemented
139#14519737C2211yescharacteristic
140#14519737C2211yescharacteristic
141#14519737C2211yescharacteristic
142#14519737C2211yescharacteristic
143#14519737C2211yescharacteristic
144#14519737C2211yescharacteristic
145#14519737C2211yescharacteristic, complemented
146#14519737C2211yescharacteristic, complemented
147#14519736C2211yescharacteristic, complemented
148#14519736C2211yescharacteristic, complemented
149#14519735C2211yescharacteristic, complemented
150#14519735C2211yescharacteristic, complemented
151#14519735C2211yescharacteristic, complemented
152#14519735C2211yescharacteristic, complemented
153#14519734C2211yescharacteristic, complemented
154#14519734C2211yescharacteristic, complemented
155#14519734C2211yescharacteristic, complemented
156#14519734C2211yescharacteristic, complemented
157#14519733C2211yescharacteristic
158#14519733C2211yescharacteristic
159#14519733C2211yescharacteristic, complemented
160#14519733C2211yescharacteristic, complemented
161C4⋊C4×D61C2211yescharacteristic, complemented
162C4⋊C4×D61C2211yescharacteristic, complemented
163C4⋊C4×D61C2211yescharacteristic, complemented
164C4⋊C4×D61C2211yescharacteristic, complemented
165C2×C22⋊Dic61C2211yescharacteristic
166C22⋊C4×D61C2211yescharacteristic
167C22⋊C4×D61C2211yescharacteristic
168C22⋊C4×D61C2211yescharacteristic
169C22⋊C4×D61C2211yescharacteristic
170C42×D61C2211yescharacteristic, complemented
171C42×D61C2211yescharacteristic, complemented
172#126×C61C2211yescharacteristic
173#126×C61C2211yescharacteristic
174#126×C61C2211yescharacteristic
175#126×C61C2211yescharacteristic
176#126×C61C2211yescharacteristic, complemented
177#126×C61C2211yescharacteristic, complemented
178#126×C61C2211yescharacteristic, complemented
179#126×C61C2211yescharacteristic, complemented
180C2×C4⋊C4×C61C2211yescharacteristic, complemented
181C2×C4⋊C4×C61C2211yescharacteristic, complemented
182C2×C4⋊C4×C61C2211yescharacteristic, complemented
183C2×C22⋊C4×C61C2211yescharacteristic
184C2×C22⋊C4×C61C2211yescharacteristic
185C2×C22⋊C4×C61C2211yescharacteristic
186C2×C42×C61C2211yescharacteristic, complemented
187C24×C61C2311yescharacteristic
188C23×D61C2311yescharacteristic
189C22×C4×C61C2311yescharacteristic
190C22×C4×C61C2311yescharacteristic
191C22×C4×C61C2311yescharacteristic
192C22×C4×C61C2311yescharacteristic
193C22×C4×C61C2311yescharacteristic
194C22×C4×C61C2311yescharacteristic
195C2×C22⋊D61—24no—
196C2×C22⋊D61C2311yescharacteristic
197C2×C22⋊D61C2311yescharacteristic
198C2×C22⋊D61C2311yescharacteristic
199C2×C22⋊D61C2311yescharacteristic
200C2×C22⋊D61C2311yescharacteristic
201C2×C22⋊D61C2311yescharacteristic
202C2×C22⋊D61C2311yescharacteristic
203C2×C22⋊D61C2311yescharacteristic
204C2×C22⋊D61C2311yescharacteristic
205C2×C22⋊D61C2311yescharacteristic
206C22×Dic61C2311yescharacteristic
207C22×Dic61C2311yescharacteristic
208C22×Dic61C2311yescharacteristic
209#11758222—24no—
210#11758222—24no—
211C2×D244C2311yescharacteristic
212C2×D244C2311yescharacteristic
213C2×D244C2311yescharacteristic
214C2×D244C2311yescharacteristic
215C2×D244C2311yescharacteristic
216C2×C4×D61C2311yescharacteristic
217C2×C4×D61C2311yescharacteristic
218C2×C4×D61C2311yescharacteristic
219C2×C4×D61C2311yescharacteristic
220C2×C4×D61C2311yescharacteristic
221C2×C4×D61C2311yescharacteristic
222C2×C4×D61C2311yescharacteristic
223C2×C4×D61C2311yescharacteristic
224C2×C4×D61C2311yescharacteristic
225C2×C4×D61C2311yescharacteristic
226C2×C4×D61C2311yescharacteristic
227C2×C4×D61C2311yescharacteristic
228C2×C4×D61C2311yescharacteristic
229C2×C4×D61C2311yescharacteristic
230C2×Dic122C2311yescharacteristic
231C2×Dic122C2311yescharacteristic
232C2×Dic122C2311yescharacteristic
233C2×Dic122C2311yescharacteristic
234C2×Dic122C2311yescharacteristic
235C4⋊C4×C61C2311yescharacteristic
236C4⋊C4×C61C2311yescharacteristic
237C4⋊C4×C61C2311yescharacteristic
238C4⋊C4×C61C2311yescharacteristic
239C4⋊C4×C61C2311yescharacteristic
240C4⋊C4×C61C2311yescharacteristic
241C4⋊C4×C61C2311yescharacteristic
242C4⋊C4×C61C2311yescharacteristic
243C4⋊C4×C61C2311yescharacteristic
244C4⋊C4×C61C2311yescharacteristic
245C4⋊C4×C61C2311yescharacteristic
246C4⋊C4×C61C2311yescharacteristic
247C22⋊C4×C61C2311yescharacteristic
248C22⋊C4×C61C2311yescharacteristic
249C22⋊C4×C61C2311yescharacteristic
250C22⋊C4×C61C2311yescharacteristic
251C22⋊C4×C61C2311yescharacteristic
252C22⋊C4×C61C2311yescharacteristic
253C22⋊C4×C61C2311yescharacteristic
254C22⋊C4×C61C2311yescharacteristic
255C22⋊C4×C61C2311yescharacteristic
256C22⋊C4×C61C2311yescharacteristic
257C22⋊C4×C61C2311yescharacteristic
258C22⋊C4×C61C2311yescharacteristic
259C42×C61C2311yescharacteristic
260C42×C61C2311yescharacteristic
261C42×C61C2311yescharacteristic
262C42×C61C2311yescharacteristic
263C22⋊Dic61C2311yescharacteristic
264C22⋊Dic61C2311yescharacteristic
265C22⋊Dic61C2311yescharacteristic
266C22⋊Dic61C2311yescharacteristic
267C22⋊Dic61C2311yescharacteristic
268C22⋊Dic61C2311yescharacteristic
269C22⋊Dic61C2311yescharacteristic
270C22⋊Dic61C2311yescharacteristic
271C22⋊Dic61C2311yescharacteristic
272C22⋊Dic61C2311yescharacteristic
273#11758198C2311yescharacteristic
274#11758198C2311yescharacteristic
275#11758198C2311yescharacteristic
276#11758198C2311yescharacteristic
277#11758198C2311yescharacteristic
278#11758198C2311yescharacteristic
279#11758198C2311yescharacteristic
280#11758198C2311yescharacteristic
281#11758198C2311yescharacteristic
282#11758198C2311yescharacteristic
283#11758198C2311yescharacteristic
284#11758198C2311yescharacteristic
285#11758198C2311yescharacteristic
286#11758198C2311yescharacteristic
287#11758198C2311yescharacteristic
288#11758198C2311yescharacteristic
289#11758198C2311yescharacteristic
290#11758198C2311yescharacteristic
291#11758198C2311yescharacteristic
292#11758198C2311yescharacteristic
293#11758198C2311yescharacteristic
294#11758198C2311yescharacteristic
295#11758198C2311yescharacteristic
296#11758198C2311yescharacteristic
297C4⋊Dic61C2311yescharacteristic
298C4⋊Dic61C2311yescharacteristic
299C4⋊Dic61C2311yescharacteristic
300C4⋊Dic61C2311yescharacteristic
301C4⋊Dic61C2311yescharacteristic
302C4⋊Dic61C2311yescharacteristic
303C4⋊Dic61C2311yescharacteristic
304C4⋊Dic61C2311yescharacteristic
305C4⋊Dic61C2311yescharacteristic
306C4⋊Dic61C2311yescharacteristic
307#11758196C2311yescharacteristic
308#11758196C2311yescharacteristic
309#11758196C2311yescharacteristic
310#11758196C2311yescharacteristic
311#11758196C2311yescharacteristic
312#11758196C2311yescharacteristic
313#11758196C2311yescharacteristic
314#11758196C2311yescharacteristic
315#11758196C2311yescharacteristic
316#11758196C2311yescharacteristic
317#11758196C2311yescharacteristic
318#11758196C2311yescharacteristic
319#11758196C2311yescharacteristic
320#11758196C2311yescharacteristic
321#11758196C2311yescharacteristic
322#11758196C2311yescharacteristic
323#11758196C2311yescharacteristic
324#11758196C2311yescharacteristic
325#11758196C2311yescharacteristic
326#11758196C2311yescharacteristic
327#11758196C2311yescharacteristic
328#11758196C2311yescharacteristic
329#11758196C2311yescharacteristic
330#11758196C2311yescharacteristic
331C4×Dic61C2311yescharacteristic
332C4×Dic61C2311yescharacteristic
333C4×Dic61C2311yescharacteristic
334C4×Dic61C2311yescharacteristic
335C4×Dic61C2311yescharacteristic
336C4×Dic61C2311yescharacteristic
337C4×Dic61C2311yescharacteristic
338C4×Dic61C2311yescharacteristic
339C4×Dic61C2311yescharacteristic
340C4×Dic61C2311yescharacteristic
341C4×Dic61C2311yescharacteristic
342C4×Dic61C2311yescharacteristic
343C4×Dic61C2311yescharacteristic
344C4×Dic61C2311yescharacteristic
345C23×C61—22no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61C2411yescharacteristic
349C23×C61C2411yescharacteristic
350C23×C61C2411yescharacteristic
351C22×D61—22no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61C2411yescharacteristic
355C22×D61C2411yescharacteristic
356C22×D61C2411yescharacteristic
357C22×D61C2411yescharacteristic
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61C2411yescharacteristic
365C2×C4×C61C2411yescharacteristic
366C2×C4×C61C2411yescharacteristic
367C2×C4×C61C2411yescharacteristic
368C2×C4×C61C2411yescharacteristic
369C2×C4×C61C2411yescharacteristic
370C2×C4×C61C2411yescharacteristic
371C2×C4×C61C2411yescharacteristic
372C2×C4×C61C2411yescharacteristic
373C2×C4×C61C2411yescharacteristic
374C2×C4×C61C2411yescharacteristic
375C2×C4×C61C2411yescharacteristic
376C22⋊D61—22no—
377C22⋊D61—22no—
378C22⋊D61—22no—
379C22⋊D61—22no—
380C22⋊D61—22no—
381C22⋊D61—41no—
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61#4114yes—
386C2×Dic61—22no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61C2411yescharacteristic
390C2×Dic61C2411yescharacteristic
391C2×Dic61C2411yescharacteristic
392C2×Dic61C2411yescharacteristic
393C2×Dic61C2411yescharacteristic
394C2×Dic61C2411yescharacteristic
395C2×Dic61C2411yescharacteristic
396C2×Dic61C2411yescharacteristic
397C2×Dic61C2411yescharacteristic
398C2×Dic61C2411yescharacteristic
399C2×Dic61C2411yescharacteristic
400C2×Dic61C2411yescharacteristic
401D244—22no—
402D244—22no—
403D244—41no—
404D244—41no—
405D244—41no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420Dic122—22no—
421Dic122—22no—
422Dic122—41no—
423Dic122—41no—
424Dic122—41no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—82no—
434C22×C61C2×#4112yes—
435C22×C61C2511yescharacteristic
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—82no—
448C2×D61C2×#4112yes—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—21no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61C2×#4112yes—
473#3521—611nomaximal, Sylow
474C2×C61—22no—
475C2×C61—41no—
476C2×C61—41no—
477C2×C61C22×#4111yescharacteristic
478C2×C61#58511yescharacteristic
479C2×C61#58511yescharacteristic
480D61—22no—
481D61—41no—
482D61—41no—
483D61—41no—
484#556—611no—
485#556—611no—
486#554—611no—
487#553—611no—
488#553—611no—
489#553—611no—
490#552—611no—
491#552—611no—
492#552—611no—
493#551—611no—
494#551—611no—
495#551—611no—
496#551—611no—
497#547—611no—
498#546—611no—
499#546—611no—
500#542—611no—
501#541—611no—
502#539—611no—
503#539—611no—
504#538—611no—
505#538—611no—
506#529—611no—
507#529—611no—
508#529—611no—
509#529—611no—
510C2×#126—611no—
511C2×#126D6111yescharacteristic, complemented
512#520—611no—
513#518—611no—
514C4×#41—611no—
515C61#352111yescharacteristic, complemented, Sylow
516C2×#41—611no—
517C2×#41—611no—
518C22×D4—611no—
519C4⋊Q8—611no—
520C4⋊Q8—611no—
521#126—611no—
522#126—611no—
523#126—611no—
524#126—611no—
525#126—611no—
526#126—611no—
527#126—611no—
528#126—611no—
529#126—611no—
530#126—611no—
531#126—611no—
532#126—611no—
533#126—611no—
534#126—611no—
535#126C2×D6111yescharacteristic
536#126C2×D6111yescharacteristic
537#126C2×D6111yescharacteristic
538#126C2×D6111yescharacteristic
539#126C2×D6111yescharacteristic, complemented
540#126C2×D6111yescharacteristic, complemented
541#126C2×D6111yescharacteristic, complemented
542#126C2×D6111yescharacteristic, complemented
543#125—611no—
544#125—611no—
545#125—611no—
546#125—611no—
547#125—611no—
548#125—611no—
549#125—611no—
550#125—611no—
551#125—611no—
552#124—611no—
553#124—611no—
554#124—611no—
555#124—611no—
556#124—611no—
557#124—611no—
558#124—611no—
559#123—611no—
560#123—611no—
561#123—611no—
562#123—611no—
563#123—611no—
564#123—611no—
565#123—611no—
566#123—611no—
567#123—611no—
568#123—611no—
569#123—611no—
570#123—611no—
571#123—611no—
572#123—611no—
573#123—611no—
574#123—611no—
575#123—611no—
576#123—611no—
577C22⋊Q8—611no—
578C22⋊Q8—611no—
579C22⋊Q8—611no—
580C22⋊Q8—611no—
581C22⋊Q8—611no—
582C22⋊Q8—611no—
583C22⋊Q8—611no—
584C22⋊Q8—611no—
585C22⋊Q8—611no—
586C22⋊Q8—611no—
587C22⋊Q8—611no—
588C22⋊Q8—611no—
589C22⋊Q8—611no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592#121—611no—
593#121—611no—
594#121—611no—
595#121—611no—
596#121—611no—
597#121—611no—
598#121—611no—
599#121—611no—
600#121—611no—
601#121—611no—
602#121—611no—
603#120—611no—
604#120—611no—
605#120—611no—
606#120—611no—
607C4×Q8—611no—
608C4×Q8—611no—
609C4×Q8—611no—
610C4×Q8—611no—
611C4×Q8—611no—
612C4×Q8—611no—
613C4×Q8—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—611no—
628C4×D4—611no—
629C4×D4—611no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
639#117—611no—
640#117—611no—
641#117—611no—
642#117—611no—
643#117—611no—
644#117—611no—
645#117—611no—
646#117—611no—
647#117—611no—
648#117—611no—
649#117—611no—
650#117—611no—
651#117—611no—
652#117—611no—
653C2×C4⋊C4—611no—
654C2×C4⋊C4—611no—
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4C2×D6111yescharacteristic, complemented
658C2×C4⋊C4C2×D6111yescharacteristic, complemented
659C2×C4⋊C4C2×D6111yescharacteristic, complemented
660C2×C22⋊C4—611no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4—611no—
663C2×C22⋊C4—611no—
664C2×C22⋊C4—611no—
665C2×C22⋊C4C2×D6111yescharacteristic
666C2×C22⋊C4C2×D6111yescharacteristic
667C2×C22⋊C4C2×D6111yescharacteristic
668C2×C42—611no—
669C2×C42—611no—
670C2×C42C2×D6111yescharacteristic, complemented
671C24—611no—
672C24C22×D6111yescharacteristic
673#41—1224no—
674#41—1224no—
675C2×Q8—611no—
676C2×Q8—611no—
677C2×Q8—611no—
678C2×Q8—611no—
679C2×Q8—611no—
680C2×D4—611no—
681C2×D4—611no—
682C2×D4—611no—
683C2×D4—611no—
684C2×D4—611no—
685C2×D4—611no—
686C2×D4—611no—
687C2×D4—611no—
688C2×D4—611no—
689C2×D4—611no—
690C2×D4—611no—
691C2×D4—611no—
692C2×D4—611no—
693C2×D4—611no—
694C2×D4—611no—
695C2×D4—1224no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4C22×D6111yescharacteristic
714C22×C4C22×D6111yescharacteristic
715C22×C4C22×D6111yescharacteristic
716C22×C4C22×D6111yescharacteristic
717C22×C4C22×D6111yescharacteristic
718C22×C4C22×D6111yescharacteristic
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—611no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—611no—
737C4⋊C4—611no—
738C4⋊C4—611no—
739C4⋊C4—611no—
740C4⋊C4—611no—
741C4⋊C4—611no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4C22×D6111yescharacteristic
754C4⋊C4C22×D6111yescharacteristic
755C4⋊C4C22×D6111yescharacteristic
756C4⋊C4C22×D6111yescharacteristic
757C4⋊C4C22×D6111yescharacteristic
758C4⋊C4C22×D6111yescharacteristic
759C4⋊C4C22×D6111yescharacteristic
760C4⋊C4C22×D6111yescharacteristic
761C4⋊C4C22×D6111yescharacteristic
762C4⋊C4C22×D6111yescharacteristic
763C4⋊C4C22×D6111yescharacteristic
764C4⋊C4C22×D6111yescharacteristic
765C22⋊C4—611no—
766C22⋊C4—611no—
767C22⋊C4—611no—
768C22⋊C4—611no—
769C22⋊C4—611no—
770C22⋊C4—611no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—611no—
774C22⋊C4—611no—
775C22⋊C4—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—611no—
798C22⋊C4—611no—
799C22⋊C4C22×D6111yescharacteristic
800C22⋊C4C22×D6111yescharacteristic
801C22⋊C4C22×D6111yescharacteristic
802C22⋊C4C22×D6111yescharacteristic
803C22⋊C4C22×D6111yescharacteristic
804C22⋊C4C22×D6111yescharacteristic
805C22⋊C4C22×D6111yescharacteristic
806C22⋊C4C22×D6111yescharacteristic
807C22⋊C4C22×D6111yescharacteristic
808C22⋊C4C22×D6111yescharacteristic
809C22⋊C4C22×D6111yescharacteristic
810C22⋊C4C22×D6111yescharacteristic
811C42—611no—
812C42—611no—
813C42—611no—
814C42—611no—
815C42—611no—
816C42—611no—
817C42—611no—
818C42—611no—
819C42—611no—
820C42—611no—
821C42—611no—
822C42—611no—
823C42—611no—
824C42—611no—
825C42C22×D6111yescharacteristic
826C42C22×D6111yescharacteristic
827C42C22×D6111yescharacteristic
828C42C22×D6111yescharacteristic
829C23—22no—
830C23—41no—
831C23—41no—
832C23—611no—
833C23—611no—
834C23—611no—
835C23—611no—
836C23—1222no—
837C23—2441no—
838C23—2441no—
839C23C23×D6111yescharacteristic
840C23C23×D6111yescharacteristic
841C23C23×D6111yescharacteristic
842Q8—1222no—
843Q8—1222no—
844Q8—2441no—
845Q8—2441no—
846Q8—2441no—
847D4—614no—
848D4—1222no—
849D4—1222no—
850D4—1222no—
851D4—1222no—
852D4—1222no—
853D4—1222no—
854D4—1222no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2441no—
861D4—2441no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—611no—
876C2×C4—611no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4C23×D6111yescharacteristic
898C2×C4C23×D6111yescharacteristic
899C2×C4C23×D6111yescharacteristic
900C2×C4C23×D6111yescharacteristic
901C2×C4C23×D6111yescharacteristic
902C2×C4C23×D6111yescharacteristic
903C2×C4C23×D6111yescharacteristic
904C2×C4C23×D6111yescharacteristic
905C2×C4C23×D6111yescharacteristic
906C2×C4C23×D6111yescharacteristic
907C2×C4C23×D6111yescharacteristic
908C2×C4C23×D6111yescharacteristic
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—82no—
918C22—612no—
919C22—1221no—
920C22—1221no—
921C22—1221no—
922C22—1221no—
923C22—1221no—
924C22—1221no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—4882no—
931C22#41×D6112yes—
932C22C24×D6111yescharacteristic
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—21no—
943C4—21no—
944C4—21no—
945C4—612no—
946C4—1221no—
947C4—1221no—
948C4—1221no—
949C4—1221no—
950C4—1221no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C2—22no—
958C2—41no—
959C2—41no—
960C2—1222no—
961C2—2441no—
962C2—2441no—
963C2—2441no—
964C2C2×#41×D6111yescharacteristic
965C2#1684059811yescharacteristic
966C2#1684059811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC2×#126×C61C2
hypercenterC2×#126D61
hypocenterC61#3521
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #16840479C2semidirect
2. #16840479C2semidirect
3. #16840467C2semidirect
4. #16840463C2semidirect
5. #16840463C2semidirect
6. #16840460C2semidirect
7. #16840448C2semidirect
8. #16840448C2semidirect
9. #16840447C2semidirect
10. #16840438C2semidirect
11. #16840438C2semidirect
12. #16840437C2semidirect
13. #16840437C2semidirect
14. #16840413C2semidirect
15. #16840402C2semidirect
16. #16840402C2semidirect
17. #16840378C2semidirect
18. #16840369C2semidirect
19. #16840359C2semidirect
20. #16840353C2semidirect
21. #16840351C2semidirect
22. #16840350C2semidirect
23. #16840296C2semidirect
24. #16840295C2semidirect
25. #16840295C2semidirect
26. #16840295C2semidirect
27. #126×D61C2semidirect
28. #16840243C2semidirect
29. #16840235C2semidirect
30. C4×#11758222C2semidirect
31. C2×#126×C61C2semidirect
35. #14519776C22semidirect
36. #14519776C22semidirect
37. #14519772C22semidirect
38. #14519772C22semidirect
39. #14519772C22semidirect
40. #14519772C22semidirect
41. #14519772C22semidirect
42. #14519772C22semidirect
43. #14519771C22semidirect
44. #14519771C22semidirect
50. #14519770C22semidirect
51. #14519769C22semidirect
52. #14519768C22semidirect
53. #14519768C22semidirect
54. #14519767C22semidirect
55. #14519767C22semidirect
56. #14519767C22semidirect
57. #14519767C22semidirect
58. #14519767C22semidirect
59. #14519767C22semidirect
60. #14519765C22semidirect
66. #14519763C22semidirect
67. #14519762C22semidirect
68. #14519762C22semidirect
69. #14519762C22semidirect
70. #14519762C22semidirect
71. #14519762C22semidirect
72. #14519762C22semidirect
73. #14519761C22semidirect
74. #14519761C22semidirect
77. #14519760C22semidirect
78. #14519760C22semidirect
84. #14519759C22semidirect
85. #14519757C22semidirect
86. #14519757C22semidirect
87. #14519756C22semidirect
88. #14519756C22semidirect
89. #14519756C22semidirect
90. #14519755C22semidirect
91. #14519755C22semidirect
92. #14519755C22semidirect
93. #14519755C22semidirect
94. #14519755C22semidirect
95. #14519755C22semidirect
98. #14519754C22semidirect
99. #14519754C22semidirect
100. #14519752C22semidirect
101. #14519752C22semidirect
104. #14519751C22semidirect
110. #14519750C22semidirect
115. C4×Dic122C22semidirect
116. C4×Dic122C22semidirect
117. C4×Dic122C22semidirect
118. #14519742C22semidirect
119. #14519742C22semidirect
120. #14519742C22semidirect
121. #14519742C22semidirect
122. C4×D244C22semidirect
123. C4×D244C22semidirect
124. C4×D244C22semidirect
125. #14519739C22semidirect
126. #14519739C22semidirect
127. #14519739C22semidirect
128. #14519739C22semidirect
135. C4×C22⋊D61C22semidirect
136. C4×C22⋊D61C22semidirect
137. C4×C22⋊D61C22semidirect
138. C4×C22⋊D61C22semidirect
145. #14519737C22semidirect
146. #14519737C22semidirect
147. #14519736C22semidirect
148. #14519736C22semidirect
149. #14519735C22semidirect
150. #14519735C22semidirect
151. #14519735C22semidirect
152. #14519735C22semidirect
153. #14519734C22semidirect
154. #14519734C22semidirect
155. #14519734C22semidirect
156. #14519734C22semidirect
159. #14519733C22semidirect
160. #14519733C22semidirect
161. C4⋊C4×D61C22semidirect
162. C4⋊C4×D61C22semidirect
163. C4⋊C4×D61C22semidirect
164. C4⋊C4×D61C22semidirect
170. C42×D61C22semidirect
171. C42×D61C22semidirect
176. #126×C61C22semidirect
177. #126×C61C22semidirect
178. #126×C61C22semidirect
179. #126×C61C22semidirect
180. C2×C4⋊C4×C61C22semidirect
181. C2×C4⋊C4×C61C22semidirect
182. C2×C4⋊C4×C61C22semidirect
186. C2×C42×C61C22semidirect
511. C2×#126D61semidirect
515. C61#3521semidirect
539. #126C2×D61semidirect
540. #126C2×D61semidirect
541. #126C2×D61semidirect
542. #126C2×D61semidirect
657. C2×C4⋊C4C2×D61semidirect
658. C2×C4⋊C4C2×D61semidirect
659. C2×C4⋊C4C2×D61semidirect
670. C2×C42C2×D61semidirect