Finite Group Databasebeta

← #11808723

Subgroups — #11808723

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63841C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic, complemented
3#10592359C211yesmaximal, characteristic, complemented
4C3×#4666C211yesmaximal, characteristic
5C3×#4657C211yesmaximal, characteristic, complemented
6#10591397C211yesmaximal, characteristic, complemented
7#10591348C211yesmaximal, characteristic, complemented
8#10591306C211yesmaximal, characteristic
9#10591306C211yesmaximal, characteristic
10#10591303C211yesmaximal, characteristic
11#10591293C211yesmaximal, characteristic
12#10591242C211yesmaximal, characteristic, complemented
13Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic
16#77739—31nomaximal
17#73480—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
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#63841—24no—
44#63837—24no—
45C32×#95C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
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#4661—31no—
79#4660—31no—
80#4660—31no—
81#4660—61no—
82#4657D311yescharacteristic, complemented
83#4656—31no—
84#4656—31no—
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
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3Q814yescomplemented
104C2×#627—22no—
105C2×#627—22no—
106C2×#627—22no—
107C4⋊(C3⋊Dic3)—22no—
108#3750—22no—
109C3×(C2×D3)⋊C4—22no—
110C3×(C2×D3)⋊C4—22no—
111C3×C4⋊Dic3—22no—
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4—22no—
115C3×C4×Dic3—22no—
116C3×C4×Dic3—22no—
117Dic3⋊Dic3—22no—
118Dic3⋊Dic3—22no—
119Dic3⋊Dic3—22no—
120Dic3⋊Dic3—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—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×#217—31no—
146C2×#217—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4C2×D311yescharacteristic
152C2×(C2×D3)⋊C4C2×D311yescharacteristic
153#926—64no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—61no—
162C2×C4⋊Dic3C2×D311yescharacteristic
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—61no—
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×Dic3⋊C4C2×D311yescharacteristic
173C2×Dic3⋊C4C2×D311yescharacteristic
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
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×Dic3C2×D311yescharacteristic
183C2×C4×Dic3C2×D311yescharacteristic
184#892—64no—
185#887—64no—
186C4×Dic6—64no—
187C3×#95—21no—
188C3×#95—31no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95C2×D311yescharacteristic
192C3×#95C2×D311yescharacteristic
193C3⋊#95—31no—
194C3⋊#95—31no—
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—61no—
206C3⋊#95—61no—
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×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4C2×Q812yes—
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⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D412yes—
241C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
255C2×C3×Dic3C2×D412yes—
256C2×C3×Dic3C2×Q812yes—
257C2×C3×Dic3#4112yes—
258C2×C3×Dic3#4112yes—
259C2×C3×Dic3#4112yes—
260C2×C3×Dic3#4112yes—
261C2×C3×Dic3#4112yes—
262C3×C4×D3—28no—
263#627—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—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—34no—
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—
328C3×C4⋊C4—62no—
329C3×C4⋊C4—62no—
330C3×C4⋊C4—62no—
331C3×C4⋊C4—62no—
332C3×C22⋊C4—62no—
333C3×C22⋊C4—62no—
334C3×C42—62no—
335C3×C42—62no—
336#217—62no—
337#217—62no—
338#217—62no—
339#217—62no—
340(C2×D3)⋊C4—22no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344(C2×D3)⋊C4—62no—
345(C2×D3)⋊C4—62no—
346C4⋊Dic3—22no—
347C4⋊Dic3—62no—
348C4⋊Dic3—62no—
349C4⋊Dic3—62no—
350C4⋊Dic3—62no—
351C4⋊Dic3—62no—
352C4⋊Dic3—62no—
353C4⋊Dic3—62no—
354C4⋊Dic3—122no—
355Dic3⋊C4—22no—
356Dic3⋊C4—22no—
357Dic3⋊C4—22no—
358Dic3⋊C4—62no—
359Dic3⋊C4—62no—
360Dic3⋊C4—62no—
361Dic3⋊C4—62no—
362Dic3⋊C4—62no—
363Dic3⋊C4—62no—
364Dic3⋊C4—62no—
365Dic3⋊C4—122no—
366C4×Dic3—22no—
367C4×Dic3—22no—
368C4×Dic3—34no—
369C4×Dic3—34no—
370C4×Dic3—62no—
371C4×Dic3—62no—
372C4×Dic3—62no—
373C4×Dic3—62no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C22×C32C22×D411yescharacteristic
377C22×C32C22×Q811yescharacteristic
378C22×C32C2×#4111yescharacteristic
379C22×C32C2×#4111yescharacteristic
380C22×C32C2×#4111yescharacteristic
381C22×C32C2×#4111yescharacteristic
382C22×C32C2×#4111yescharacteristic
383C2×C3×D3—22no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—22no—
391C32×C4—41no—
392C32×C4—41no—
393C3⋊Dic3—22no—
394C3⋊Dic3—41no—
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—22no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—41no—
403C3×Dic3C22⋊Q814yes—
404C22×Q8—91no—
405C23×C4—31no—
406C4×Q8—184no—
407#117—184no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—91no—
413C2×C4⋊C4—91no—
414C2×C4⋊C4—91no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C22⋊C4—31no—
420C2×C22⋊C4—31no—
421C2×C22⋊C4—91no—
422C2×C22⋊C4—91no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C42—31no—
426C2×C42—31no—
427C2×C42—91no—
428C2×C42—91no—
429C2×C42—91no—
430C2×C42—91no—
431#95—31no—
432#95—31no—
433#95—31no—
434#95—91no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95D3211yescharacteristic
441C23×C3—21no—
442C23×C3—32no—
443C23×C3—61no—
444C23×C3—61no—
445C23×C3—61no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3C23×D311yescharacteristic
450C23×C3C23×D311yescharacteristic
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3C2×Dic612yes—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
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—32no—
476C2×C3×C4—32no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—68no—
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×C4D3×Q812yes—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
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—32no—
521C2×Dic3—32no—
522C2×Dic3—62no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
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—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3C2×Dic612yes—
557C2×Dic3#23512yes—
558C2×Dic3#23512yes—
559C2×Dic3D3×D412yes—
560C2×Dic3D3×D412yes—
561C2×Dic3#23712yes—
562C2×Dic3#23712yes—
563C2×Dic3#23912yes—
564C4×D3—28no—
565Dic6—68no—
566Dic6—68no—
567C2×C32C2×C22⋊Q811yescharacteristic
568C2×C32#52511yescharacteristic
569C2×C32#52911yescharacteristic
570C2×C32#52911yescharacteristic
571C2×C32#53211yescharacteristic
572C2×C32#53311yescharacteristic
573C2×C32#53311yescharacteristic
574C3×D3—42no—
575C24—31no—
576C2×Q8—182no—
577C2×Q8—182no—
578C2×Q8—182no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—34no—
586C22×C4—31no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—91no—
590C22×C4—91no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4C2×D3211yescharacteristic
594C22×C4C2×D3211yescharacteristic
595C22×C4C2×D3211yescharacteristic
596C4⋊C4—62no—
597C4⋊C4—62no—
598C4⋊C4—62no—
599C4⋊C4—62no—
600C4⋊C4—182no—
601C4⋊C4—182no—
602C4⋊C4—182no—
603C4⋊C4—182no—
604C4⋊C4—182no—
605C4⋊C4—182no—
606C4⋊C4—182no—
607C22⋊C4—62no—
608C22⋊C4—62no—
609C22⋊C4—182no—
610C22⋊C4—182no—
611C22⋊C4—182no—
612C22⋊C4—182no—
613C42—62no—
614C42—62no—
615C42—94no—
616C42—182no—
617C42—182no—
618C42—182no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—62no—
627C22×C3—62no—
628C22×C3—62no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3C22×Dic611yescharacteristic
634C22×C3C2×#23511yescharacteristic
635C22×C3C2×#23511yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C2×#23711yescharacteristic
639C22×C3C2×#23711yescharacteristic
640C22×C3C2×D3×Q811yescharacteristic
641C22×C3C2×#23911yescharacteristic
642C22×C3D3×#4111yescharacteristic
643C22×C3D3×#4111yescharacteristic
644C22×C3D3×#4111yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3D3×#4111yescharacteristic
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—34no—
657C3×C4—42no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—121no—
670Dic3—22no—
671Dic3—22no—
672Dic3—22no—
673Dic3—22no—
674Dic3—22no—
675Dic3—41no—
676Dic3—62no—
677Dic3—62no—
678Dic3—122no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—241no—
686Dic3—241no—
687Dic3—241no—
688Dic3#87814yes—
689C32#239611yescharacteristic, complemented, Sylow
690C23—32no—
691C23—61no—
692C23—61no—
693C23—61no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23C22×D3211yescharacteristic
698Q8—188no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—68no—
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—92no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4D3×Dic612yes—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—122no—
750C2×C3#547011yescharacteristic
751C2×C3C2×#87811yescharacteristic
752C2×C3#551711yescharacteristic
753C2×C3#553811yescharacteristic
754C2×C3#554711yescharacteristic
755C2×C3#554811yescharacteristic
756C2×C3#555711yescharacteristic
757C2×C3#559611yescharacteristic
758C2×C3D3×C22⋊Q811yescharacteristic
759C2×C3#562711yescharacteristic
760C2×C3#564911yescharacteristic
761C2×C3#568811yescharacteristic
762C2×C3#569111yescharacteristic
763C2×C3#572811yescharacteristic
764D3—42no—
765C22—62no—
766C22—62no—
767C22—62no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22C2×D3×Dic611yescharacteristic
773C22D3×#23511yescharacteristic
774C22D3×#23511yescharacteristic
775C22D32×D411yescharacteristic
776C22D3×#23711yescharacteristic
777C22D3×#23711yescharacteristic
778C22D3×#23911yescharacteristic
779C4—22no—
780C4—34no—
781C4—41no—
782C4—41no—
783C4—62no—
784C4—62no—
785C4—62no—
786C4—62no—
787C4—62no—
788C4—121no—
789C4—182no—
790C4—361no—
791C4—361no—
792C4—361no—
793C3—21no—
794C3#7348011yescharacteristic, complemented
795C3#7773911yescharacteristic, complemented
796C2—122no—
797C2#1059387411yescharacteristic
798C2D3×#87811yescharacteristic
799C2#1059405811yescharacteristic
800C2#1059409811yescharacteristic
801C2#1059440311yescharacteristic
802C2#1059444511yescharacteristic
803C2#1059462311yescharacteristic
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
2. C2×#63837C2semidirect
3. #10592359C2semidirect
5. C3×#4657C2semidirect
6. #10591397C2semidirect
7. #10591348C2semidirect
12. #10591242C2semidirect
13. Dic3×Dic3⋊C4C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
82. #4657D3semidirect
103. C2×C3×C4×D3Q8semidirect
321. C2×C4×D3Dic6semidirect
689. C32#2396semidirect
794. C3#73480semidirect
795. C3#77739semidirect

Maximal subgroups

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

subgroupindex
C2×#638412
C2×#638372
#105923592
C3×#46662
C3×#46572
#105913972
#105913482
#105913062
#105913032
#105912932
#105912422
Dic3×Dic3⋊C42
#105912372
#777393
#734803