Finite Group Databasebeta

← #11808688

Subgroups — #11808688

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63844C211yesmaximal, characteristic, complemented
2C2×#63841C211yesmaximal, characteristic
3#10592355C211yesmaximal, characteristic, complemented
4C3×#4666C211yesmaximal, characteristic
5C3×#4661C211yesmaximal, characteristic, complemented
6#10591345C211yesmaximal, characteristic, complemented
7#10591324C211yesmaximal, characteristic
8#10591322C211yesmaximal, characteristic
9#10591319C211yesmaximal, characteristic
10#10591308C211yesmaximal, characteristic
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#10591243C211yesmaximal, characteristic, complemented
13Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#10591237C211yesmaximal, characteristic
15#10591218C211yesmaximal, characteristic, complemented
16#77739—31nomaximal
17#73480—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63844—24no—
44#63841—24no—
45C32×#95C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#926—31no—
56C2×#892—31no—
57C2×#887—31no—
58C2×C4×Dic6—31no—
59C3×#398—31no—
60C3×C4×C22⋊C4—31no—
61C4×#217—31no—
62#4994—31no—
63#4994—31no—
64#4993—31no—
65#4982—31no—
66Dic3×C4⋊C4—31no—
67Dic3×C4⋊C4—31no—
68#4949—31no—
69#4948—31no—
70#4948—31no—
71#4947—31no—
72C4×C4⋊Dic3—31no—
73C4×Dic3⋊C4—31no—
74C4×Dic3⋊C4—31no—
75#4673—31no—
76#4666—31no—
77#4666D311yescharacteristic
78#4661D311yescharacteristic, complemented
79#4660—31no—
80#4660—31no—
81#4657—31no—
82#4656—31no—
83#4656—31no—
84#4656—61no—
85#4649—31no—
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×#634—22no—
95C2×#634—22no—
96C2×#634—22no—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3Q814yescomplemented
107C4⋊(C3⋊Dic3)—22no—
108C4⋊(C3⋊Dic3)—22no—
109#3750—22no—
110C3×(C2×D3)⋊C4—22no—
111C3×(C2×D3)⋊C4—22no—
112C3×C4⋊Dic3—22no—
113C3×C4⋊Dic3—22no—
114C3×C4⋊Dic3—22no—
115C3×Dic3⋊C4—22no—
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118#3724—22no—
119#3724—22no—
120#3724—22no—
121Dic3⋊Dic3—22no—
122(C2×D3)⋊Dic3—22no—
123(C2×D3)⋊Dic3—22no—
124(C2×D3)⋊Dic3—22no—
125(C2×D3)⋊Dic3—22no—
126Dic32—22no—
127Dic32—22no—
128Dic32—22no—
129Dic32D414yes—
130#2396—91noSylow
131C23×C3×C4—31no—
132C22×C4×D3C2×D311yescharacteristic
133C22×Dic6—31no—
134C22×Dic6—31no—
135C22×Dic6—61no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×#217—31no—
145C2×#217—31no—
146C2×#217—31no—
147C2×#217—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4C2×D311yescharacteristic
153C2×(C2×D3)⋊C4C2×D311yescharacteristic
154#926—64no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—61no—
161C2×C4⋊Dic3—61no—
162C2×C4⋊Dic3C2×D311yescharacteristic
163C2×C4⋊Dic3C2×D311yescharacteristic
164C2×C4⋊Dic3C2×D311yescharacteristic
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—61no—
175C2×Dic3⋊C4C2×D311yescharacteristic
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3C2×D311yescharacteristic
185C2×C4×Dic3C2×D311yescharacteristic
186#892—64no—
187#887—64no—
188C4×Dic6—64no—
189C3×#95—21no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95C2×D311yescharacteristic
194C3×#95C2×D311yescharacteristic
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—61no—
208C3⋊#95—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C23×C32C2411yescharacteristic
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3C2×Q812yes—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4C2×Q812yes—
227C2×C32×C4#4112yes—
228C2×C32×C4#4112yes—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×D412yes—
239C2×C3⋊Dic3#4112yes—
240C2×C3⋊Dic3#4112yes—
241#634—28no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D412yes—
260C2×C3×Dic3C2×D412yes—
261C2×C3×Dic3C2×Q812yes—
262C2×C3×Dic3#4112yes—
263C3×C4×D3—28no—
264C2×C4×Q8—91no—
265C2×#117—91no—
266#400—91no—
267#399—91no—
268#398—31no—
269#398—91no—
270#396—91no—
271#396—91no—
272#395—91no—
273#393—91no—
274C4×C4⋊C4—91no—
275C4×C4⋊C4—91no—
276C4×C4⋊C4—91no—
277C4×C22⋊C4—31no—
278C4×C22⋊C4—91no—
279C24×C3—31no—
280C23×D3C22×D311yescharacteristic
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—34no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—62no—
293C22×C3×C4—62no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C2×C4×D3—22no—
320C2×C4×D3—22no—
321C2×C4×D3Dic614yescomplemented
322C2×Dic6—62no—
323C2×Dic6—62no—
324C2×Dic6—62no—
325C2×Dic6—62no—
326C2×Dic6—62no—
327C2×Dic6—62no—
328C2×Dic6—122no—
329C2×Dic6—122no—
330C2×Dic6—122no—
331C3×C4⋊C4—62no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—62no—
334C3×C4⋊C4—62no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—62no—
337C3×C42—62no—
338C3×C42—62no—
339#217—62no—
340#217—62no—
341#217—62no—
342#217—62no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—22no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—62no—
349C4⋊Dic3—22no—
350C4⋊Dic3—22no—
351C4⋊Dic3—22no—
352C4⋊Dic3—62no—
353C4⋊Dic3—62no—
354C4⋊Dic3—62no—
355C4⋊Dic3—62no—
356C4⋊Dic3—62no—
357C4⋊Dic3—122no—
358C4⋊Dic3—122no—
359Dic3⋊C4—22no—
360Dic3⋊C4—62no—
361Dic3⋊C4—62no—
362Dic3⋊C4—62no—
363Dic3⋊C4—62no—
364Dic3⋊C4—62no—
365Dic3⋊C4—62no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—122no—
370C4×Dic3—22no—
371C4×Dic3—22no—
372C4×Dic3—34no—
373C4×Dic3—34no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—62no—
377C4×Dic3—62no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C22×C32C22×D411yescharacteristic
381C22×C32C22×Q811yescharacteristic
382C22×C32C2×#4111yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32C2×#4111yescharacteristic
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C32×C4—22no—
395C32×C4—22no—
396C32×C4—22no—
397C3⋊Dic3—22no—
398C3⋊Dic3—22no—
399C3⋊Dic3—22no—
400C3⋊Dic3—41no—
401C3×Dic3—22no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3C22⋊Q814yes—
408C22×Q8—91no—
409C23×C4—31no—
410C4×Q8—184no—
411#117—184no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C22⋊C4—91no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—91no—
432C2×C42—91no—
433C2×C42—91no—
434C2×C42—91no—
435#95—31no—
436#95—31no—
437#95—31no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95D3211yescharacteristic
445C23×C3—21no—
446C23×C3—32no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3—61no—
452C23×C3—61no—
453C23×C3C23×D311yescharacteristic
454C23×C3C23×D311yescharacteristic
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3C2×Dic612yes—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—68no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4C2×Dic612yes—
506C2×C3×C4#23512yes—
507C2×C3×C4#23512yes—
508C2×C3×C4#23712yes—
509C2×C3×C4D3×Q812yes—
510C2×C3×C4#23912yes—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—32no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3C2×Dic612yes—
565C2×Dic3D3×D412yes—
566C2×Dic3D3×D412yes—
567C2×Dic3#23712yes—
568C4×D3—28no—
569Dic6—68no—
570Dic6—68no—
571Dic6—128no—
572C2×C32C2×C22⋊Q811yescharacteristic
573C2×C32#52511yescharacteristic
574C2×C32#52911yescharacteristic
575C2×C32#52911yescharacteristic
576C2×C32#53211yescharacteristic
577C2×C32#53311yescharacteristic
578C2×C32#53311yescharacteristic
579C3×D3—42no—
580C24—31no—
581C2×Q8—182no—
582C2×Q8—182no—
583C2×Q8—182no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—34no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4C2×D3211yescharacteristic
599C22×C4C2×D3211yescharacteristic
600C22×C4C2×D3211yescharacteristic
601C4⋊C4—62no—
602C4⋊C4—62no—
603C4⋊C4—62no—
604C4⋊C4—62no—
605C4⋊C4—182no—
606C4⋊C4—182no—
607C4⋊C4—182no—
608C4⋊C4—182no—
609C4⋊C4—182no—
610C4⋊C4—182no—
611C4⋊C4—182no—
612C22⋊C4—62no—
613C22⋊C4—62no—
614C22⋊C4—182no—
615C22⋊C4—182no—
616C22⋊C4—182no—
617C22⋊C4—182no—
618C42—62no—
619C42—62no—
620C42—94no—
621C42—182no—
622C42—182no—
623C42—182no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C22×Dic611yescharacteristic
639C22×C3C2×#23511yescharacteristic
640C22×C3C2×#23511yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×#23711yescharacteristic
644C22×C3C2×#23711yescharacteristic
645C22×C3C2×D3×Q811yescharacteristic
646C22×C3C2×#23911yescharacteristic
647C22×C3D3×#4111yescharacteristic
648C22×C3D3×#4111yescharacteristic
649C22×C3D3×#4111yescharacteristic
650C22×C3D3×#4111yescharacteristic
651C22×C3D3×#4111yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—34no—
666C3×C4—42no—
667C3×C4—42no—
668C3×C4—42no—
669C3×C4—62no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675Dic3—22no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—62no—
682Dic3—62no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—62no—
687Dic3—122no—
688Dic3—122no—
689Dic3—122no—
690Dic3—121no—
691Dic3—121no—
692Dic3—241no—
693Dic3#87814yes—
694C32#239611yescharacteristic, complemented, Sylow
695C23—32no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23C22×D3211yescharacteristic
703Q8—188no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—68no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—92no—
733C2×C4—92no—
734C2×C4—92no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4D3×Dic612yes—
745C2×C4#379512yes—
746C2×C4#379912yes—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—122no—
755C2×C3#547011yescharacteristic
756C2×C3C2×#87811yescharacteristic
757C2×C3#551711yescharacteristic
758C2×C3#553811yescharacteristic
759C2×C3#554711yescharacteristic
760C2×C3#554811yescharacteristic
761C2×C3#555711yescharacteristic
762C2×C3#559611yescharacteristic
763C2×C3D3×C22⋊Q811yescharacteristic
764C2×C3#562711yescharacteristic
765C2×C3#564911yescharacteristic
766C2×C3#568811yescharacteristic
767C2×C3#569111yescharacteristic
768C2×C3#572811yescharacteristic
769D3—42no—
770C22—62no—
771C22—62no—
772C22—62no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22C2×D3×Dic611yescharacteristic
778C22C2×#379511yescharacteristic
779C22C2×#379911yescharacteristic
780C22D32×D411yescharacteristic
781C22D3×#23711yescharacteristic
782C22#6431211yescharacteristic
783C22#6431911yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—34no—
788C4—62no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—121no—
794C4—182no—
795C4—182no—
796C4—182no—
797C4—361no—
798C3—21no—
799C3#7348011yescharacteristic, complemented
800C3#7773911yescharacteristic, complemented
801C2—122no—
802C2#1059385911yescharacteristic
803C2D3×#87811yescharacteristic
804C2#1059406611yescharacteristic
805C2#1059413111yescharacteristic
806C2#1059436711yescharacteristic
807C2#1059444711yescharacteristic
808C2#1059447711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63844C2semidirect
3. #10592355C2semidirect
5. C3×#4661C2semidirect
6. #10591345C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
12. #10591243C2semidirect
13. Dic3×Dic3⋊C4C2semidirect
15. #10591218C2semidirect
78. #4661D3semidirect
106. C2×C3×C4×D3Q8semidirect
321. C2×C4×D3Dic6semidirect
694. C32#2396semidirect
799. C3#73480semidirect
800. C3#77739semidirect

Maximal subgroups

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

subgroupindex
C2×#638442
C2×#638412
#105923552
C3×#46662
C3×#46612
#105913452
#105913242
#105913222
#105913192
#105913082
Dic3×C4⋊Dic32
#105912432
Dic3×Dic3⋊C42
#105912372
#105912182
#777393
#734803