Finite Group Databasebeta

← #11811922

Subgroups — #11811922

Order 1152.

1791 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×#63888C211yesmaximal, characteristic, complemented
4C2×#63839C211yesmaximal, characteristic, complemented
5#10592658C211yesmaximal, characteristic, complemented
6C3×#4946C211yesmaximal, characteristic, complemented
7#10591712C211yesmaximal, characteristic, complemented
8#10591707C211yesmaximal, characteristic, complemented
9#10591693C211yesmaximal, characteristic, complemented
10#10591373C211yesmaximal, characteristic, complemented
11#10591372C211yesmaximal, characteristic, complemented
12#10591292C211yesmaximal, characteristic, complemented
13#10591291C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#82959—31nomaximal
17#74411—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3804—24no—
26C2×#3804—24no—
27C2×#3804—24no—
28C22×D3×Dic3C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#885—24no—
42C2×#3724C2211yescharacteristic
43C2×#3724C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51#63888—24no—
52#63839—24no—
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×#237—31no—
60C22×#235—31no—
61C2×C3×#124—31no—
62C2×#946—31no—
63C2×#944—31no—
64C2×#896—31no—
65C2×#888—31no—
66C2×#885D311yescharacteristic, complemented
67C3×#385—31no—
68#5221—31no—
69#5210—31no—
70#4991—31no—
71#4989—31no—
72#4961—31no—
73#4959—31no—
74#4959—31no—
75#4959—31no—
76#4959—31no—
77#4959—31no—
78#4959—61no—
79#4957—31no—
80#4946—31no—
81#4946—31no—
82#4946—31no—
83#4946D311yescharacteristic, complemented
84C4×(C2×D3)⋊C4—31no—
85#4929—31no—
86#4672—31no—
87#4668—31no—
88#4666—31no—
89#4646—31no—
90C24×C32C2311yescharacteristic
91C23×C3⋊D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—22no—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C2×C3×#67D414yes—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×Dic6—22no—
115C2×C3×Dic6—22no—
116C2×C3×Dic6—22no—
117C2×#627—22no—
118C2×#627—22no—
119C2×#627D414yes—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#624—22no—
124C2×#624—22no—
125C2×#624D414yes—
126#3804—232no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3—22no—
130C32×C22⋊C4—22no—
131#3757—22no—
132#3752—22no—
133#3752—22no—
134#3750—22no—
135C3×#217—22no—
136C3×#217—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—22no—
141C3×C4×Dic3—22no—
142#3724—22no—
143#3724—22no—
144Dic3⋊Dic3—22no—
145Dic3⋊Dic3—22no—
146#3722—22no—
147#3722—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—22no—
150Dic32—22no—
151#2432—91noSylow
152C22×C3×Q8—31no—
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—61no—
159C22×#67C2×D311yescharacteristic
160C23×Dic3—31no—
161C23×Dic3C2×D311yescharacteristic
162C2×#237—64no—
163C2×#237—64no—
164C2×#237—64no—
165C2×#235—64no—
166C2×#235—64no—
167C2×#235—64no—
168C22×D12—31no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×Dic6—31no—
173C22×Dic6—31no—
174C22×Dic6C2×D311yescharacteristic
175C3×#124—64no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4C2×D311yescharacteristic
184C2×C3×C22⋊C4C2×D311yescharacteristic
185C2×C3×C42—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—61no—
191C2×#217C2×D311yescharacteristic
192C2×#217C2×D311yescharacteristic
193#946—64no—
194#944—64no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4—61no—
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—61no—
220C2×Dic3⋊C4C2×D311yescharacteristic
221C2×Dic3⋊C4C2×D311yescharacteristic
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224C2×C4×Dic3C2×D311yescharacteristic
225#896—64no—
226#888—64no—
227#885—24no—
228C3×#95—31no—
229C3×#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—61no—
239C3⋊#95C2×D311yescharacteristic
240C3⋊#95C2×D311yescharacteristic
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32C2×D412yes—
248C23×C32C2411yescharacteristic
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D412yes—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3C2×D412yes—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269#638—28no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3C2×D412yes—
278C2×C3⋊Dic3#4112yescomplemented
279C3×#67—28no—
280C2×C3×Dic3—28no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3C2×D412yes—
297C2×C3×Dic3C2×D412yes—
298C2×C3×Dic3C2×D412yes—
299C2×C3×Dic3C2×D412yes—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3#4112yescomplemented
302C3×Dic6—44no—
303#627—28no—
304#626—28no—
305#624—28no—
306D3×Dic3—28no—
307C22×#41—91no—
308C2×C4⋊Q8—91no—
309C2×#124—31no—
310C2×C22⋊Q8—91no—
311#394—91no—
312#394—91no—
313#394—91no—
314#394—91no—
315#391—91no—
316#390—91no—
317#385—31no—
318#385—91no—
319#385—91no—
320#385—91no—
321C4×C22⋊C4—91no—
322C24×C3—21no—
323C24×C3—31no—
324C24×C3C22×D311yescharacteristic
325C24×C3C22×D311yescharacteristic
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—61no—
329C23×D3C22×D311yescharacteristic
330C2×C3×Q8—62no—
331C2×C3×Q8—62no—
332C2×C3×Q8—62no—
333C2×C3×D4—34no—
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—62no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—22no—
353C2×#67—22no—
354C2×#67—62no—
355C2×#67—62no—
356C2×#67—62no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—122no—
364C2×#67—122no—
365C2×#67—122no—
366C2×#67#6714yes—
367C22×Dic3—22no—
368C22×Dic3—22no—
369C22×Dic3—22no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—62no—
380C22×Dic3—62no—
381C22×Dic3—62no—
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389#237—632no—
390#235—632no—
391C2×D12—62no—
392C2×D12—62no—
393C2×D12—62no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—62no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C2×Dic6—22no—
404C2×Dic6—22no—
405C2×Dic6—22no—
406C2×Dic6—34no—
407C2×Dic6—34no—
408C2×Dic6—62no—
409C2×Dic6—62no—
410C2×Dic6—62no—
411C2×Dic6—62no—
412C3×C4⋊C4—62no—
413C3×C4⋊C4—62no—
414C3×C22⋊C4—22no—
415C3×C22⋊C4—22no—
416C3×C22⋊C4—42no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C42—62no—
422#217—22no—
423#217—22no—
424#217—62no—
425#217—62no—
426#217—62no—
427#217—62no—
428#217—122no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—22no—
431(C2×D3)⋊C4—62no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—122no—
442(C2×D3)⋊C4—122no—
443C4⋊Dic3—62no—
444C4⋊Dic3—62no—
445Dic3⋊C4—22no—
446Dic3⋊C4—22no—
447Dic3⋊C4—62no—
448Dic3⋊C4—62no—
449Dic3⋊C4—62no—
450Dic3⋊C4—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—62no—
455Dic3⋊C4—122no—
456C4×Dic3—22no—
457C4×Dic3—62no—
458C4×Dic3—62no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C22×C32C22×D411yescharacteristic
468C22×C32C22×D411yescharacteristic
469C22×C32C2×#4111yescharacteristic
470C22×C32C2×#4111yescharacteristic
471C22×C322−1+411yescharacteristic
472C22×C322−1+411yescharacteristic
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C32×C4—41no—
488C32×C4—41no—
489C3⋊Dic3—22no—
490C3⋊Dic3—22no—
491C3⋊Dic3—41no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3—41no—
498C3×Dic3#12014yes—
499C2×#41—184no—
500C2×#41—184no—
501C2×#41—184no—
502C22×Q8—31no—
503C22×Q8—91no—
504C22×D4—31no—
505C22×D4—91no—
506C22×D4—91no—
507C23×C4—31no—
508C23×C4—91no—
509C23×C4—91no—
510C4⋊Q8—184no—
511#124—64no—
512C22⋊Q8—184no—
513C2×C4⋊C4—31no—
514C2×C4⋊C4—31no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4—91no—
518C2×C4⋊C4—91no—
519C2×C4⋊C4—91no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—91no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4D3211yescharacteristic
532C2×C42—31no—
533C2×C42—91no—
534#95—31no—
535#95—31no—
536#95—91no—
537#95—91no—
538#95—91no—
539#95—91no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—22no—
554C23×C3—32no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3D3×D412yes—
568C23×C3C2×#6712yes—
569C23×C3C23×D311yescharacteristic
570C23×C3C23×D311yescharacteristic
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—32no—
578C22×D3—32no—
579C22×D3—62no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—121no—
593C22×D3—121no—
594C22×D3—121no—
595C22×D3—121no—
596C22×D3—121no—
597C22×D3—121no—
598C22×D3C2×#6712yes—
599C3×Q8—124no—
600C3×D4—68no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—32no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—68no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641#67—28no—
642#67—68no—
643#67—68no—
644#67—68no—
645#67—128no—
646C2×Dic3—28no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—68no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—121no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686C2×Dic3—121no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×Dic3#23512yescomplemented
691C2×Dic3D3×D412yes—
692C2×Dic3D3×D412yes—
693C2×Dic3D3×D412yes—
694C2×Dic3D3×D412yes—
695C2×Dic3C2×#6712yes—
696D12—68no—
697C4×D3—68no—
698C4×D3—68no—
699C4×D3—68no—
700Dic6—44no—
701Dic6—68no—
702Dic6—68no—
703C2×C32—42no—
704C2×C32C2×#12011yescharacteristic
705C2×C32#53211yescharacteristic
706C2×C32#53611yescharacteristic
707C2×C32#54711yescharacteristic
708C2×C32#54711yescharacteristic
709C2×C32#54811yescharacteristic
710C2×C32#54811yescharacteristic
711C3⋊D3—42no—
712C3×D3—42no—
713C24—31no—
714C24—91no—
715C24C2×D3211yescharacteristic
716#41—1832no—
717C2×Q8—62no—
718C2×Q8—62no—
719C2×Q8—62no—
720C2×Q8—94no—
721C2×Q8—182no—
722C2×Q8—182no—
723C2×D4—34no—
724C2×D4—62no—
725C2×D4—62no—
726C2×D4—182no—
727C2×D4—182no—
728C2×D4—182no—
729C2×D4—182no—
730C2×D4—182no—
731C2×D4—182no—
732C22×C4—31no—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—62no—
740C22×C4—62no—
741C22×C4—62no—
742C22×C4—94no—
743C22×C4—91no—
744C22×C4—91no—
745C22×C4—91no—
746C22×C4—182no—
747C22×C4—182no—
748C22×C4—182no—
749C22×C4—182no—
750C22×C4—182no—
751C22×C4C2×D3211yescharacteristic
752C22×C4C2×D3211yescharacteristic
753C4⋊C4—62no—
754C4⋊C4—62no—
755C4⋊C4—182no—
756C4⋊C4—182no—
757C4⋊C4—182no—
758C4⋊C4—182no—
759C4⋊C4—182no—
760C22⋊C4—22no—
761C22⋊C4—62no—
762C22⋊C4—62no—
763C22⋊C4—62no—
764C22⋊C4—62no—
765C22⋊C4—182no—
766C22⋊C4—182no—
767C22⋊C4—182no—
768C22⋊C4—182no—
769C22⋊C4—182no—
770C22⋊C4—182no—
771C22⋊C4—182no—
772C42—62no—
773C42—182no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—81no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3—81no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3C2×#23511yescharacteristic
810C22×C3C2×D3×D411yescharacteristic
811C22×C3C2×D3×D411yescharacteristic
812C22×C3C2×D3×D411yescharacteristic
813C22×C3C2×D3×D411yescharacteristic
814C22×C3C2×D3×D411yescharacteristic
815C22×C3#100711yescharacteristic
816C22×C3D3×#4111yescharacteristic
817C22×C3D3×#4111yescharacteristic
818C22×C3D3×#4111yescharacteristic
819C22×C3#101011yescharacteristic
820C22×C3#101011yescharacteristic
821C22×C3#101011yescharacteristic
822C22×C3C22×#6711yescharacteristic
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—41no—
827C2×D3—41no—
828C2×D3—41no—
829C2×D3—41no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—122no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—241no—
848C2×D3—241no—
849C2×D3—241no—
850C2×D3—241no—
851C3×C4—34no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—41no—
855C3×C4—41no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—62no—
859C3×C4—81no—
860C3×C4—81no—
861C3×C4—121no—
862C3×C4—121no—
863C3×C4—121no—
864Dic3—22no—
865Dic3—22no—
866Dic3—22no—
867Dic3—41no—
868Dic3—41no—
869Dic3—41no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—62no—
874Dic3—122no—
875Dic3—122no—
876Dic3—121no—
877Dic3—121no—
878Dic3—241no—
879Dic3#93714yes—
880C32#243211yescharacteristic, complemented, Sylow
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—32no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—92no—
895C23—181no—
896C23—181no—
897C23—181no—
898C23—181no—
899C23—181no—
900C23—181no—
901C23D3×#6712yes—
902C23C22×D3211yescharacteristic
903Q8—124no—
904Q8—188no—
905D4—68no—
906D4—188no—
907D4—188no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—32no—
920C2×C4—68no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—92no—
937C2×C4—92no—
938C2×C4—188no—
939C2×C4—188no—
940C2×C4—181no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—181no—
944C2×C4—181no—
945C2×C4—181no—
946C2×C4—181no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—42no—
955C2×C3—42no—
956C2×C3—82no—
957C2×C3—122no—
958C2×C3#550711yescharacteristic
959C2×C3#554811yescharacteristic
960C2×C3#555211yescharacteristic
961C2×C3D3×#12011yescharacteristic
962C2×C3#562811yescharacteristic
963C2×C3#563311yescharacteristic
964C2×C3#565511yescharacteristic
965C2×C3#566811yescharacteristic
966C2×C3#567511yescharacteristic
967C2×C3#567711yescharacteristic
968C2×C3#567711yescharacteristic
969C2×C3C2×#93711yescharacteristic
970C2×C3#582411yescharacteristic
971C2×C3#582411yescharacteristic
972D3—42no—
973D3—122no—
974D3—122no—
975D3—242no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—182no—
991C22—182no—
992C22—182no—
993C22—361no—
994C22—361no—
995C22—361no—
996C22—361no—
997C22#6429711yescharacteristic
998C22D3×#23511yescharacteristic
999C22#6430911yescharacteristic
1000C22D32×D411yescharacteristic
1001C22D32×D411yescharacteristic
1002C22#6431211yescharacteristic
1003C22C2×D3×#6711yescharacteristic
1004C4—34no—
1005C4—41no—
1006C4—41no—
1007C4—62no—
1008C4—62no—
1009C4—62no—
1010C4—121no—
1011C4—121no—
1012C4—121no—
1013C4—182no—
1014C4—182no—
1015C4—361no—
1016C3—21no—
1017C3#7441111yescharacteristic, complemented
1018C3#8295911yescharacteristic, complemented
1019C2—42no—
1020C2—122no—
1021C2—362no—
1022C2#1059406811yescharacteristic
1023C2#1059407011yescharacteristic
1024C2#1059407311yescharacteristic
1025C2#1059407511yescharacteristic
1026C2#1059488511yescharacteristic
1027C2#1059514911yescharacteristic
1028C2D3×#93711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×#3804C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#885C2semidirect
3. C2×#63888C2semidirect
4. C2×#63839C2semidirect
5. #10592658C2semidirect
6. C3×#4946C2semidirect
7. #10591712C2semidirect
8. #10591707C2semidirect
9. #10591693C2semidirect
10. #10591373C2semidirect
11. #10591372C2semidirect
12. #10591292C2semidirect
13. #10591291C2semidirect
14. #10591233C2semidirect
15. #10591191C2semidirect
66. C2×#885D3semidirect
83. #4946D3semidirect
278. C2×C3⋊Dic3#41semidirect
301. C2×C3×Dic3#41semidirect
690. C2×Dic3#235semidirect
880. C32#2432semidirect
1017. C3#74411semidirect
1018. C3#82959semidirect

Maximal subgroups

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

subgroupindex
C22×#38042
C2×C3×#8852
C2×#638882
C2×#638392
#105926582
C3×#49462
#105917122
#105917072
#105916932
#105913732
#105913722
#105912922
#105912912
#105912332
#105911912
#829593
#744113