Finite Group Databasebeta

← #11859484

Subgroups — #11859484

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic, complemented
2#10595003C211yesmaximal, characteristic
3C2×#63803C211yesmaximal, characteristic, complemented
4C8×#638C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591156C211yesmaximal, characteristic, complemented
7#10591145C211yesmaximal, characteristic, complemented
8#10591051C211yesmaximal, characteristic, complemented
9#10590955C211yesmaximal, characteristic, complemented
10#10590735C211yesmaximal, characteristic, complemented
11#10590731C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13C8×#625C211yesmaximal, characteristic, complemented
14#10590663C211yesmaximal, characteristic, complemented
15D3×C8×Dic3C211yesmaximal, characteristic, complemented
16#83786—31nomaximal
17#79422—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C4×#638C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C3×#901—24no—
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31#63979C411yescharacteristic
32#63971C411yescharacteristic
33#63970C411yescharacteristic
34#63959C411yescharacteristic
35#63907C411yescharacteristic
36C4×#626C2211yescharacteristic
37C4×#625C2211yescharacteristic
38#63886C411yescharacteristic
39#63885C411yescharacteristic
40C4×D3×Dic3C2211yescharacteristic
41#63839C411yescharacteristic
42C2×#3712C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63803—24no—
47#63657C2211yescharacteristic
48#63647C2211yescharacteristic
49#63641C2211yescharacteristic
50C8×C3⋊Dic3C2211yescharacteristic
51C3×#830C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63572C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63557C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#63553C2211yescharacteristic
62Dic3×C3⋊C8C2211yescharacteristic
63C2×C3×#131—31no—
64#5832—31no—
65C2×#901—31no—
66C2×#901—31no—
67C2×#901D311yescharacteristic, complemented
68#5548—31no—
69C3×C8×D4—31no—
70#5234—31no—
71#5129—31no—
72#5128—31no—
73#5128—31no—
74#5128—31no—
75#5128—31no—
76#5118—31no—
77C8×#67—31no—
78C8×#67—31no—
79C8×#67—31no—
80C8×#67—31no—
81C8×#67—31no—
82C8×#67—61no—
83C8×#67D311yescharacteristic, complemented
84C2×C8×Dic3—31no—
85#5012—31no—
86#4838—31no—
87#4837—31no—
88#4729—31no—
89#4729—31no—
90#4727—31no—
91#4727—31no—
92C8×D12—31no—
93C4×D3×C8—31no—
94C22×C32×C4C2311yescharacteristic
95C2×#638C2×C411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67C2×C411yescharacteristic
98C2×C3×#67C2×C411yescharacteristic
99C2×C3×#67C2×C411yescharacteristic
100C3×#235—22no—
101C3×#235—22no—
102C2×C3×D12C2×C411yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2×C411yescharacteristic
107C2×#627C2×C411yescharacteristic
108C2×#626C2×C411yescharacteristic
109C2×#626C2×C411yescharacteristic
110C2×#626C2×C411yescharacteristic
111C2×#625C2×C411yescharacteristic
112C2×#625C2×C411yescharacteristic
113C2×D3×Dic3C2×C411yescharacteristic
114C2×D3×Dic3C2×C411yescharacteristic
115#3798—22no—
116#3798—22no—
117C2×C32×C8—22no—
118C2×C32×C8C2311yescharacteristic
119C2×C32×C8C2311yescharacteristic
120#3757C2×C411yescharacteristic
121#3752C2×C411yescharacteristic
122#3750C2×C411yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—22no—
127C3×#217C2×C411yescharacteristic
128C3×(C2×D3)⋊C4C2×C411yescharacteristic
129C3×Dic3⋊C4C2×C411yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C3×#208—22no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×ΓL(1,𝔽25)—22no—
137C3×ΓL(1,𝔽25)—22no—
138C3×D3×C8—22no—
139C3×D3×C8—22no—
140C3×D3×C8D414yescomplemented
141#3724C2×C411yescharacteristic
142Dic3⋊Dic3C2×C411yescharacteristic
143#3722C2×C411yescharacteristic
144(C2×D3)⋊Dic3C2×C411yescharacteristic
145(C2×D3)⋊Dic3C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147Dic32C2×C411yescharacteristic
148Dic32C2×C411yescharacteristic
149#3712—22no—
150#3711—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#2931—91noSylow
154C2×C3×#41—31no—
155C2×#235—31no—
156C2×#235—31no—
157C2×#235C2×D311yescharacteristic
158C3×#131—64no—
159C2×C3×M16—31no—
160C2×C3×M16—31no—
161C2×C3×M16—31no—
162C22×C3×C8—21no—
163C22×C3×C8—31no—
164C22×C3×C8—31no—
165C22×C3×C8—31no—
166C22×C3×C8C2×D311yescharacteristic
167C22×C3×C8C2×D311yescharacteristic
168C3×C4×D4—31no—
169#947—31no—
170#944—31no—
171#940—31no—
172#940—31no—
173#939—31no—
174#939—31no—
175#939—31no—
176#939—31no—
177#938—31no—
178#936—31no—
179C4×#67—31no—
180C4×#67—31no—
181C4×#67—31no—
182C4×#67—31no—
183C4×#67—31no—
184C4×#67—61no—
185C4×#67C2×D311yescharacteristic
186C2×C4×Dic3—31no—
187C2×#208—31no—
188C2×#208—31no—
189C2×#208C2×D311yescharacteristic
190C22×C3⋊C8—31no—
191#901—24no—
192#901—64no—
193#901—64no—
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)C2×D311yescharacteristic
199C2×ΓL(1,𝔽25)C2×D311yescharacteristic
200C2×D3×C8—31no—
201C2×D3×C8—31no—
202C2×D3×C8—31no—
203C2×D3×C8—61no—
204C2×D3×C8C2×D311yescharacteristic
205C2×D3×C8C2×D311yescharacteristic
206C2×D3×C8C2×D311yescharacteristic
207#895—31no—
208#888—31no—
209#885—31no—
210#885—31no—
211#884—31no—
212#884—31no—
213C4×D12—31no—
214C42×D3—31no—
215C3×C4⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C4×C8—31no—
219#830—31no—
220#830—31no—
221#830—31no—
222#830—31no—
223#830—31no—
224#830—61no—
225#830C2×D311yescharacteristic
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—61no—
234(C2×D3)⋊C8C2×D311yescharacteristic
235Dic3⋊C8—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—61no—
241Dic3⋊C8C2×D311yescharacteristic
242C8×Dic3—31no—
243C8×Dic3—31no—
244C8×Dic3—31no—
245C8×Dic3—31no—
246C8×Dic3—31no—
247C8×Dic3—61no—
248C8×Dic3C2×D311yescharacteristic
249C4⋊(C3⋊C8)—31no—
250C4×C3⋊C8—31no—
251C23×C32C22×C411yescharacteristic
252C22×C3⋊D3C22×C411yescharacteristic
253C22×C3×D3C22×C411yescharacteristic
254C22×C3×D3C22×C411yescharacteristic
255C22×C3×D3C22×C411yescharacteristic
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C22×C411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260#638—22no—
261C2×C3⋊Dic3C22×C411yescharacteristic
262C2×C3⋊Dic3C22×C411yescharacteristic
263C2×C3⋊Dic3C22×C411yescharacteristic
264C4×C3⋊D3—21no—
265C4×C3⋊D3—21no—
266C3×#67—22no—
267C3×#67—22no—
268C3×#67—22no—
269C2×C3×Dic3C22×C411yescharacteristic
270C2×C3×Dic3C22×C411yescharacteristic
271C2×C3×Dic3C22×C411yescharacteristic
272C2×C3×Dic3C22×C411yescharacteristic
273C2×C3×Dic3C22×C411yescharacteristic
274C3×D12—22no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—22no—
282#627—22no—
283#626—22no—
284#626—22no—
285#626—22no—
286#625—22no—
287#625—22no—
288D3×Dic3—22no—
289D3×Dic3—22no—
290C32×C8—21no—
291C32×C8C2×D412yes—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C3×C3⋊C8C2×D412yes—
298C2×#131—31no—
299C2×#131—91no—
300#532—91no—
301#436—91no—
302#436—91no—
303#436—91no—
304#436—91no—
305C8×D4—31no—
306C8×D4—91no—
307C8×D4—91no—
308C8×D4—91no—
309#423—91no—
310#408—91no—
311#408—91no—
312C2×C4×C8—91no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C2×#67—31no—
327C2×#67—31no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—31no—
331C2×#67—31no—
332C2×#67—31no—
333C2×#67—31no—
334C2×#67—31no—
335C2×#67—61no—
336C2×#67C4×D311yescharacteristic
337C2×#67C4×D311yescharacteristic
338C2×#67C4×D311yescharacteristic
339C22×Dic3—31no—
340C22×Dic3—31no—
341#235—22no—
342#235—22no—
343#235—62no—
344#235—62no—
345#235—62no—
346#235—62no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12C4×D311yescharacteristic
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—31no—
355C2×C4×D3—61no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6C4×D311yescharacteristic
362C3×M16—62no—
363C3×M16—62no—
364C3×M16—62no—
365C2×C3×C8—22no—
366C2×C3×C8—22no—
367C2×C3×C8—21no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—34no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—42no—
375C2×C3×C8—62no—
376C2×C3×C8—62no—
377C2×C3×C8C22×D311yescharacteristic
378C2×C3×C8C22×D311yescharacteristic
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C3×C4⋊C4—31no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C42—31no—
385#217—31no—
386#217—31no—
387#217—31no—
388#217—31no—
389#217—31no—
390#217—61no—
391#217C4×D311yescharacteristic
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4C4×D311yescharacteristic
401C4⋊Dic3—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—61no—
408Dic3⋊C4C4×D311yescharacteristic
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—61no—
416C4×Dic3C22×D311yescharacteristic
417#208—22no—
418#208—62no—
419#208—62no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—31no—
422C2×C3⋊C8—31no—
423C2×C3⋊C8—31no—
424C2×C3⋊C8—61no—
425C2×C3⋊C8—61no—
426C2×C3⋊C8—62no—
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431ΓL(1,𝔽25)—22no—
432ΓL(1,𝔽25)—22no—
433ΓL(1,𝔽25)—62no—
434ΓL(1,𝔽25)—62no—
435ΓL(1,𝔽25)—62no—
436ΓL(1,𝔽25)—62no—
437D3×C8—22no—
438D3×C8—22no—
439D3×C8—62no—
440D3×C8—62no—
441D3×C8—62no—
442D3×C8—122no—
443D3×C8#6714yescomplemented
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32C23×C411yescharacteristic
448C2×C3⋊D3—21no—
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3C4×D412yes—
460C32×C4—21no—
461C32×C4C22×D411yescharacteristic
462C32×C4C2×#4111yescharacteristic
463C3⋊Dic3—21no—
464C3⋊Dic3—21no—
465C3⋊Dic3#13112yescomplemented
466C3×Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3C4×D412yes—
470C3×Dic3#13112yescomplemented
471C2×#41—31no—
472C2×#41—91no—
473#131—64no—
474#131—184no—
475C2×M16—31no—
476C2×M16—31no—
477C2×M16—31no—
478C2×M16—91no—
479C2×M16—91no—
480C2×M16—91no—
481C22×C8—31no—
482C22×C8—31no—
483C22×C8—31no—
484C22×C8—91no—
485C22×C8—91no—
486C22×C8D3211yescharacteristic
487C4⋊Q8—91no—
488#127—91no—
489#124—91no—
490#124—91no—
491#121—91no—
492#121—91no—
493#121—91no—
494#121—91no—
495C4×D4—31no—
496C4×D4—91no—
497C4×D4—91no—
498C4×D4—91no—
499C2×C42—91no—
500C4⋊C8—31no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C22⋊C8—31no—
505C22⋊C8—31no—
506C22⋊C8—91no—
507C22⋊C8—91no—
508C22⋊C8—91no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512C4×C8—31no—
513C4×C8—91no—
514C4×C8—91no—
515C4×C8—91no—
516C23×C3—21no—
517C23×C3—31no—
518C23×C3—31no—
519C23×C3—31no—
520C23×C3C2×C4×D311yescharacteristic
521C23×C3C2×C4×D311yescharacteristic
522C22×D3—31no—
523C22×D3—31no—
524C22×D3—61no—
525C22×D3C2×C4×D311yescharacteristic
526C22×D3C2×C4×D311yescharacteristic
527C22×D3C2×C4×D311yescharacteristic
528C3×Q8—62no—
529C3×D4—62no—
530C3×D4—62no—
531C3×D4—62no—
532C3×D4—62no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4C2×C4×D311yescharacteristic
553C2×C3×C4C2×C4×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—22no—
557#67—22no—
558#67—22no—
559#67—62no—
560#67—62no—
561#67—62no—
562#67—62no—
563#67—62no—
564#67—62no—
565#67—64no—
566#67—62no—
567#67—62no—
568#67—62no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—62no—
579C2×Dic3—62no—
580C2×Dic3C2×C4×D311yescharacteristic
581C2×Dic3C2×C4×D311yescharacteristic
582C2×Dic3C2×C4×D311yescharacteristic
583C2×Dic3C2×C4×D311yescharacteristic
584C2×Dic3C2×C4×D311yescharacteristic
585D12—22no—
586D12—62no—
587D12—62no—
588D12—62no—
589C4×D3—21no—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—62no—
594C4×D3—62no—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—121no—
600C4×D3—121no—
601C4×D3#23512yes—
602C4×D3C2×#6712yes—
603Dic6—22no—
604Dic6—62no—
605Dic6—62no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—22no—
609C3×C8—32no—
610C3×C8—41no—
611C3×C8—61no—
612C3×C8—61no—
613C3×C8—61no—
614C3×C8D3×D412yes—
615C3×C8C2×#6712yes—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C3⋊C8—61no—
620C3⋊C8—61no—
621C3⋊C8—61no—
622C3⋊C8—61no—
623C3⋊C8—121no—
624C3⋊C8—121no—
625C3⋊C8C2×#6712yes—
626C2×C32—41no—
627C2×C32C2×C4×D411yescharacteristic
628C2×C32C2×#13111yescharacteristic
629C2×C32C2×#13111yescharacteristic
630C3⋊D3—41no—
631C3×D3—22no—
632C3×D3—41no—
633C3×D3—41no—
634#41—62no—
635#41—62no—
636#41—182no—
637#41—182no—
638C2×Q8—31no—
639C2×Q8—91no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—31no—
643C2×D4—31no—
644C2×D4—91no—
645C2×D4—91no—
646C2×D4—91no—
647C2×D4—91no—
648C2×D4—91no—
649C2×D4—91no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—91no—
654C22×C4—91no—
655C22×C4—91no—
656C22×C4C2×D3211yescharacteristic
657M16—62no—
658M16—62no—
659M16—62no—
660M16—182no—
661M16—182no—
662M16—182no—
663C2×C8—22no—
664C2×C8—31no—
665C2×C8—34no—
666C2×C8—31no—
667C2×C8—31no—
668C2×C8—31no—
669C2×C8—62no—
670C2×C8—62no—
671C2×C8—91no—
672C2×C8—91no—
673C2×C8—182no—
674C2×C8—182no—
675C2×C8C2×D3211yescharacteristic
676C2×C8C2×D3211yescharacteristic
677C4⋊C4—31no—
678C4⋊C4—91no—
679C4⋊C4—91no—
680C4⋊C4—91no—
681C22⋊C4—31no—
682C22⋊C4—31no—
683C22⋊C4—91no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C42—31no—
690C42—91no—
691C42—91no—
692C42—91no—
693C22×C3—22no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—32no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3C22×C4×D311yescharacteristic
713C22×C3C22×C4×D311yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—62no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3C4×#6712yes—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—32no—
737C3×C4—32no—
738C3×C4—41no—
739C3×C4—61no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4C2×#23511yescharacteristic
743C3×C4C2×D3×D411yescharacteristic
744C3×C4D3×#4111yescharacteristic
745C3×C4C22×#6711yescharacteristic
746Dic3—21no—
747Dic3—21no—
748Dic3—21no—
749Dic3—32no—
750Dic3—32no—
751Dic3—62no—
752Dic3—61no—
753Dic3—61no—
754Dic3—61no—
755Dic3—61no—
756Dic3—121no—
757Dic3—121no—
758Dic3#90112yescomplemented
759Dic3C4×#6712yes—
760C32#293111yescharacteristic, complemented, Sylow
761C23—31no—
762C23—31no—
763C23—31no—
764C23—91no—
765C23C4×D3211yescharacteristic
766Q8—62no—
767Q8—182no—
768D4—62no—
769D4—62no—
770D4—62no—
771D4—62no—
772D4—182no—
773D4—182no—
774D4—182no—
775D4—182no—
776D4—182no—
777D4—182no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—31no—
781C2×C4—31no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—91no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—182no—
795C2×C4—182no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4C4×D3211yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—21no—
801C8—32no—
802C8—61no—
803C8—61no—
804C8—61no—
805C8—181no—
806C8—181no—
807C8D3×#6712yes—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—42no—
812C2×C3—41no—
813C2×C3—41no—
814C2×C3—62no—
815C2×C3—121no—
816C2×C3—121no—
817C2×C3C4×D3×D411yescharacteristic
818C2×C3C2×#90111yescharacteristic
819C2×C3D3×#13111yescharacteristic
820C2×C3D3×#13111yescharacteristic
821C2×C3D3×#13111yescharacteristic
822C2×C3C2×C4×#6711yescharacteristic
823D3—22no—
824D3—41no—
825D3—41no—
826D3—122no—
827D3—121no—
828D3—121no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—32no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—181no—
842C22—181no—
843C22—181no—
844C22C2×C4×D3211yescharacteristic
845C4—21no—
846C4—32no—
847C4—32no—
848C4—61no—
849C4—61no—
850C4—61no—
851C4—92no—
852C4—181no—
853C4—181no—
854C4D3×#23511yescharacteristic
855C4C2×D3×#6711yescharacteristic
856C3—21no—
857C3#7942211yescharacteristic, complemented
858C3#8378611yescharacteristic, complemented
859C2—41no—
860C2—62no—
861C2—121no—
862C2—121no—
863C2—361no—
864C2D3×#90111yescharacteristic
865C2#1059466911yescharacteristic
866C2C4×D3×#6711yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
prime radical#10595003C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#901C2semidirect
3. C2×#63803C2semidirect
4. C8×#638C2semidirect
5. C3×C8×#67C2semidirect
6. #10591156C2semidirect
7. #10591145C2semidirect
8. #10591051C2semidirect
9. #10590955C2semidirect
10. #10590735C2semidirect
11. #10590731C2semidirect
12. C8×#626C2semidirect
13. C8×#625C2semidirect
14. #10590663C2semidirect
15. D3×C8×Dic3C2semidirect
67. C2×#901D3semidirect
83. C8×#67D3semidirect
140. C3×D3×C8D4semidirect
443. D3×C8#67semidirect
465. C3⋊Dic3#131semidirect
470. C3×Dic3#131semidirect
758. Dic3#901semidirect
760. C32#2931semidirect
857. C3#79422semidirect
858. C3#83786semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
#105950032
C2×#638032
C8×#6382
C3×C8×#672
#105911562
#105911452
#105910512
#105909552
#105907352
#105907312
C8×#6262
C8×#6252
#105906632
D3×C8×Dic32
#837863
#794223