Finite Group Databasebeta

← #11811920

Subgroups — #11811920

Order 1152.

1765 conjugacy classes of subgroups.

The subgroup lattice has 1005 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C2×#63915C211yesmaximal, characteristic, complemented
3C2×#63899C211yesmaximal, characteristic, complemented
4C2×#63840C211yesmaximal, characteristic, complemented
5#10592345C211yesmaximal, characteristic, complemented
6C3×#4672C211yesmaximal, characteristic, complemented
7C3×#4668C211yesmaximal, characteristic, complemented
8#10591390C211yesmaximal, characteristic, complemented
9#10591390C211yesmaximal, characteristic, complemented
10#10591386C211yesmaximal, characteristic, complemented
11#10591377C211yesmaximal, characteristic, complemented
12#10591373C211yesmaximal, characteristic, complemented
13#10591368C211yesmaximal, characteristic, complemented
14#10591300C211yesmaximal, characteristic, complemented
15#10591277C211yesmaximal, characteristic, complemented
16#76904—31nomaximal
17#74411—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C2×#3795—24no—
27C2×#3795—24no—
28C2×#3795—24no—
29C2×#3750C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50#63915—24no—
51#63899—24no—
52#63840—24no—
53C32×#95C2211yescharacteristic
54#63658C2211yescharacteristic
55#63658C2211yescharacteristic
56#63658C2211yescharacteristic
57C3×C3⋊#95C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×#237—31no—
60C22×#235—31no—
61C2×#896—31no—
62C2×#888—31no—
63C2×#888—31no—
64C2×#885—31no—
65C2×#885—31no—
66C2×#878—31no—
67C3×#394—31no—
68C3×#385—31no—
69#5222—31no—
70#5210—31no—
71#4991—31no—
72#4989—31no—
73#4989—31no—
74#4961—31no—
75#4961—31no—
76#4959—31no—
77#4959—31no—
78#4957—31no—
79#4957—31no—
80#4950—31no—
81#4946—31no—
82Dic3×C22⋊C4—31no—
83#4672D311yescharacteristic, complemented
84#4668—31no—
85#4668D311yescharacteristic, complemented
86#4666—31no—
87#4646—31no—
88#4646—31no—
89#4646—61no—
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C2×#634—22no—
101C2×#634—22no—
102C2×#634D414yes—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C2×C3×D12—22no—
109C2×C3×D12—22no—
110C2×C3×D12—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×#627—22no—
115C2×#627—22no—
116C2×#627—22no—
117C2×#625—22no—
118C2×#625—22no—
119C2×#625—22no—
120C2×#625—22no—
121C2×#625—22no—
122C2×#625D414yes—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3D414yes—
129#3795—232no—
130#3750—22no—
131C4×C3⋊Dic3—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×C4⋊Dic3—22no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—22no—
141#3724—22no—
142Dic3⋊Dic3—22no—
143Dic3⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—22no—
150Dic32—22no—
151#2432—91noSylow
152C22×C3×D4—31no—
153C23×C3×C4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C2×#237—64no—
161C2×#237—64no—
162C2×#237—64no—
163C2×#235—64no—
164C2×#235—64no—
165C2×#235—64no—
166C22×D12C2×D311yescharacteristic
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C22×C4×D3C2×D311yescharacteristic
170C22×Dic6—31no—
171C22×Dic6—31no—
172C22×Dic6—31no—
173C22×Dic6—31no—
174C22×Dic6—61no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4C2×D311yescharacteristic
197C2×(C2×D3)⋊C4C2×D311yescharacteristic
198C2×(C2×D3)⋊C4C2×D311yescharacteristic
199C2×(C2×D3)⋊C4C2×D311yescharacteristic
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×C4⋊Dic3—31no—
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3C2×D311yescharacteristic
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—61no—
212C2×Dic3⋊C4C2×D311yescharacteristic
213C2×Dic3⋊C4C2×D311yescharacteristic
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3—61no—
219#896—64no—
220#888—64no—
221#888—64no—
222#885—64no—
223#885—64no—
224#878—64no—
225C3×#95—21no—
226C3×#95—31no—
227C3×#95C2×D311yescharacteristic
228C3×#95C2×D311yescharacteristic
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—61no—
238C3⋊#95—61no—
239C3⋊#95—61no—
240C3⋊#95C2×D311yescharacteristic
241C23×C32C2411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
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×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D412yes—
261C22×C3×D3C2×D412yes—
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—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D412yes—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3C2×D412yes—
281C2×C3⋊Dic3C2×D412yes—
282C2×C3⋊Dic3C2×D412yes—
283C2×C3⋊Dic3C2×D412yes—
284#634—28no—
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×Dic3—21no—
297C2×C3×Dic3C2×D412yes—
298C2×C3×Dic3#4112yescomplemented
299C2×C3×Dic3#4112yescomplemented
300C3×D12—28no—
301C3×C4×D3—28no—
302#627—44no—
303#625—28no—
304#625—28no—
305D3×Dic3—28no—
306D3×Dic3—28no—
307C22×#41—91no—
308C2×C4⋊Q8—91no—
309C2×#124—91no—
310C2×C22⋊Q8—91no—
311#394—31no—
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—31no—
323C24×C3—31no—
324C24×C3—31no—
325C23×D3C22×D311yescharacteristic
326C23×D3C22×D311yescharacteristic
327C23×D3C22×D311yescharacteristic
328C2×C3×D4—62no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—62no—
340C22×C3×C4—62no—
341C22×C3×C4—62no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C2×#67—34no—
349C2×#67—34no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—62no—
355C2×#67—62no—
356C2×#67—62no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—34no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—62no—
376C22×Dic3—62no—
377C22×Dic3—62no—
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383#237—632no—
384#235—632no—
385C2×D12—22no—
386C2×D12—22no—
387C2×D12—22no—
388C2×C4×D3—22no—
389C2×C4×D3—22no—
390C2×C4×D3—22no—
391C2×C4×D3—34no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×Dic6—34no—
398C2×Dic6—34no—
399C2×Dic6—64no—
400C2×Dic6—62no—
401C2×Dic6—62no—
402C2×Dic6—62no—
403C2×Dic6—62no—
404C2×Dic6—62no—
405C2×Dic6—62no—
406C2×Dic6—62no—
407C2×Dic6—62no—
408C2×Dic6—62no—
409C2×Dic6—62no—
410C2×Dic6—122no—
411C2×Dic6—122no—
412C3×C4⋊C4—62no—
413C3×C4⋊C4—62no—
414C3×C4⋊C4—62no—
415C3×C22⋊C4—62no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421#217—62no—
422#217—62no—
423#217—62no—
424#217—62no—
425#217—62no—
426#217—62no—
427(C2×D3)⋊C4—22no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—22no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—22no—
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—
439C4⋊Dic3—22no—
440C4⋊Dic3—62no—
441C4⋊Dic3—62no—
442Dic3⋊C4—22no—
443Dic3⋊C4—22no—
444Dic3⋊C4—62no—
445Dic3⋊C4—62no—
446Dic3⋊C4—62no—
447Dic3⋊C4—62no—
448Dic3⋊C4—62no—
449Dic3⋊C4—62no—
450Dic3⋊C4—122no—
451C4×Dic3—62no—
452C4×Dic3—62no—
453C4×Dic3—62no—
454C4×Dic3—62no—
455C4×Dic3—122no—
456C22×C32C22×D411yescharacteristic
457C22×C32C22×D411yescharacteristic
458C22×C32C22×D411yescharacteristic
459C22×C32C2×#4111yescharacteristic
460C22×C32C2×#4111yescharacteristic
461C22×C322−1+411yescharacteristic
462C22×C322−1+411yescharacteristic
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C32×C4—22no—
485C32×C4—41no—
486C32×C4—41no—
487C3⋊Dic3—22no—
488C3⋊Dic3—41no—
489C3⋊Dic3—41no—
490C3⋊Dic3#12014yes—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—184no—
497C2×#41—184no—
498C2×#41—184no—
499C22×Q8—91no—
500C22×Q8—91no—
501C22×D4—31no—
502C22×D4—91no—
503C22×D4—91no—
504C23×C4—31no—
505C23×C4—91no—
506C23×C4—91no—
507C4⋊Q8—184no—
508#124—184no—
509C22⋊Q8—184no—
510C2×C4⋊C4—31no—
511C2×C4⋊C4—31no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4—91no—
514C2×C4⋊C4—91no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C22⋊C4—31no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—91no—
524C2×C22⋊C4—91no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C42—91no—
530C2×C42—91no—
531#95—31no—
532#95—91no—
533#95—91no—
534#95—91no—
535#95—91no—
536#95D3211yescharacteristic
537C23×C3—21no—
538C23×C3—32no—
539C23×C3—32no—
540C23×C3—32no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3C23×D311yescharacteristic
560C23×C3C23×D311yescharacteristic
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3D3×D412yes—
580C22×D3D3×D412yes—
581C22×D3D3×D412yes—
582C3×D4—68no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—22no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—22no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—68no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4D3×D412yes—
625C2×C3×C4D3×D412yes—
626#67—68no—
627#67—68no—
628#67—68no—
629#67—68no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—68no—
655C2×Dic3—68no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—62no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—121no—
674C2×Dic3—121no—
675C2×Dic3—121no—
676C2×Dic3—121no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3#23512yescomplemented
681C2×Dic3D3×D412yes—
682C2×Dic3#23712yescomplemented
683D12—28no—
684C4×D3—28no—
685C4×D3—68no—
686C4×D3—68no—
687Dic6—68no—
688Dic6—68no—
689Dic6—128no—
690Dic6—124no—
691Dic6—124no—
692C2×C32C2×#12011yescharacteristic
693C2×C32#53211yescharacteristic
694C2×C32#53611yescharacteristic
695C2×C32#54711yescharacteristic
696C2×C32#54711yescharacteristic
697C2×C32#54811yescharacteristic
698C2×C32#54811yescharacteristic
699C3×D3—42no—
700C3×D3—42no—
701C3×D3—42no—
702C24—31no—
703C24—31no—
704C24—31no—
705#41—1832no—
706C2×Q8—94no—
707C2×Q8—182no—
708C2×Q8—182no—
709C2×Q8—182no—
710C2×Q8—182no—
711C2×Q8—182no—
712C2×D4—62no—
713C2×D4—62no—
714C2×D4—62no—
715C2×D4—94no—
716C2×D4—182no—
717C2×D4—182no—
718C2×D4—182no—
719C2×D4—182no—
720C2×D4—182no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—62no—
727C22×C4—62no—
728C22×C4—62no—
729C22×C4—94no—
730C22×C4—91no—
731C22×C4—91no—
732C22×C4—91no—
733C22×C4—91no—
734C22×C4—182no—
735C22×C4—182no—
736C22×C4—182no—
737C22×C4—182no—
738C22×C4—182no—
739C22×C4C2×D3211yescharacteristic
740C22×C4C2×D3211yescharacteristic
741C22×C4C2×D3211yescharacteristic
742C4⋊C4—62no—
743C4⋊C4—62no—
744C4⋊C4—62no—
745C4⋊C4—182no—
746C4⋊C4—182no—
747C4⋊C4—182no—
748C4⋊C4—182no—
749C22⋊C4—62no—
750C22⋊C4—62no—
751C22⋊C4—62no—
752C22⋊C4—62no—
753C22⋊C4—62no—
754C22⋊C4—62no—
755C22⋊C4—182no—
756C22⋊C4—182no—
757C22⋊C4—182no—
758C22⋊C4—182no—
759C22⋊C4—182no—
760C22⋊C4—182no—
761C42—182no—
762C42—182no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3—121no—
791C22×C3C2×#23511yescharacteristic
792C22×C3C2×D3×D411yescharacteristic
793C22×C3C2×D3×D411yescharacteristic
794C22×C3C2×D3×D411yescharacteristic
795C22×C3C2×D3×D411yescharacteristic
796C22×C3C2×D3×D411yescharacteristic
797C22×C3C2×D3×D411yescharacteristic
798C22×C3C2×#23711yescharacteristic
799C22×C3#100711yescharacteristic
800C22×C3D3×#4111yescharacteristic
801C22×C3D3×#4111yescharacteristic
802C22×C3#101011yescharacteristic
803C22×C3#101011yescharacteristic
804C22×C3#101011yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—41no—
826C3×C4—22no—
827C3×C4—22no—
828C3×C4—42no—
829C3×C4—42no—
830C3×C4—41no—
831C3×C4—41no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—62no—
835C3×C4—62no—
836C3×C4—62no—
837C3×C4—81no—
838C3×C4—121no—
839C3×C4—121no—
840Dic3—22no—
841Dic3—22no—
842Dic3—22no—
843Dic3—34no—
844Dic3—34no—
845Dic3—41no—
846Dic3—41no—
847Dic3—64no—
848Dic3—62no—
849Dic3—62no—
850Dic3—122no—
851Dic3—122no—
852Dic3—121no—
853Dic3—121no—
854Dic3—121no—
855Dic3—121no—
856Dic3—241no—
857C32#243211yescharacteristic, complemented, Sylow
858C23—32no—
859C23—32no—
860C23—32no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—61no—
869C23—61no—
870C23—61no—
871C23—61no—
872C23—61no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23C22×D3211yescharacteristic
880Q8—188no—
881Q8—364no—
882D4—68no—
883D4—188no—
884D4—188no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—32no—
894C2×C4—32no—
895C2×C4—32no—
896C2×C4—68no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—92no—
910C2×C4—92no—
911C2×C4—92no—
912C2×C4—92no—
913C2×C4—188no—
914C2×C4—188no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—181no—
919C2×C4—181no—
920C2×C4—181no—
921C2×C4—181no—
922C2×C4—181no—
923C2×C4#380212yes—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—122no—
932C2×C3—122no—
933C2×C3—122no—
934C2×C3#550711yescharacteristic
935C2×C3#554811yescharacteristic
936C2×C3#555211yescharacteristic
937C2×C3D3×#12011yescharacteristic
938C2×C3D3×#12011yescharacteristic
939C2×C3#559611yescharacteristic
940C2×C3#559811yescharacteristic
941C2×C3#561111yescharacteristic
942C2×C3#562811yescharacteristic
943C2×C3#563311yescharacteristic
944C2×C3#564811yescharacteristic
945C2×C3#565511yescharacteristic
946C2×C3#565511yescharacteristic
947C2×C3#567711yescharacteristic
948D3—42no—
949D3—42no—
950D3—42no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—121no—
961C22—121no—
962C22—121no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—121no—
972C22#6429811yescharacteristic
973C22C2×#380211yescharacteristic
974C22D3×#23511yescharacteristic
975C22D32×D411yescharacteristic
976C22D32×D411yescharacteristic
977C22D3×#23711yescharacteristic
978C22#6431511yescharacteristic
979C4—22no—
980C4—41no—
981C4—41no—
982C4—62no—
983C4—62no—
984C4—62no—
985C4—94no—
986C4—121no—
987C4—121no—
988C4—182no—
989C4—361no—
990C4—361no—
991C3—21no—
992C3#7441111yescharacteristic, complemented
993C3#7690411yescharacteristic, complemented
994C2—122no—
995C2—122no—
996C2—122no—
997C2#1059390511yescharacteristic
998C2#1059405811yescharacteristic
999C2#1059406211yescharacteristic
1000C2#1059425811yescharacteristic
1001C2#1059436511yescharacteristic
1002C2#1059451311yescharacteristic
1003C2#1059452511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×#3795C2
hypercenter#95D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63915C2semidirect
3. C2×#63899C2semidirect
4. C2×#63840C2semidirect
5. #10592345C2semidirect
6. C3×#4672C2semidirect
7. C3×#4668C2semidirect
8. #10591390C2semidirect
9. #10591390C2semidirect
10. #10591386C2semidirect
11. #10591377C2semidirect
12. #10591373C2semidirect
13. #10591368C2semidirect
14. #10591300C2semidirect
15. #10591277C2semidirect
83. #4672D3semidirect
85. #4668D3semidirect
298. C2×C3×Dic3#41semidirect
299. C2×C3×Dic3#41semidirect
680. C2×Dic3#235semidirect
682. C2×Dic3#237semidirect
857. C32#2432semidirect
992. C3#74411semidirect
993. C3#76904semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
C2×#639152
C2×#638992
C2×#638402
#105923452
C3×#46722
C3×#46682
#105913902
#105913862
#105913772
#105913732
#105913682
#105913002
#105912772
#769043
#744113