Finite Group Databasebeta

← #11808823

Subgroups — #11808823

Order 1152.

1203 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63879C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic, complemented
3#10592357C211yesmaximal, characteristic, complemented
4C3×#4675C211yesmaximal, characteristic, complemented
5C3×#4666C211yesmaximal, characteristic, complemented
6#10591390C211yesmaximal, characteristic
7#10591388C211yesmaximal, characteristic
8Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
9Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#10591301C211yesmaximal, characteristic, complemented
11#10591293C211yesmaximal, characteristic, complemented
12#10591293C211yesmaximal, characteristic, complemented
13#10591239C211yesmaximal, characteristic, complemented
14#10591237C211yesmaximal, characteristic, complemented
15#10591210C211yesmaximal, characteristic, complemented
16#77460—31nomaximal
17#73481—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63879—24no—
42#63837—24no—
43C32×#95C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C4×#67—31no—
56C2×#887—31no—
57C2×#67⋊C4—31no—
58C2×C4×Dic6—31no—
59C3×#397—31no—
60C3×C4×C22⋊C4—31no—
61C4×#217—31no—
62#4992—31no—
63#4961—31no—
64#4959—31no—
65#4959—31no—
66#4959—31no—
67#4952—31no—
68#4947—31no—
69#4947—31no—
70Dic3×C22⋊C4—31no—
71Dic3×C22⋊C4—31no—
72C4×(C2×D3)⋊C4—31no—
73C4×(C2×D3)⋊C4—31no—
74#4932—31no—
75#4675D311yescharacteristic, complemented
76#4673—31no—
77#4673—31no—
78#4666—31no—
79#4666D311yescharacteristic, complemented
80#4660—31no—
81#4658—31no—
82#4658—31no—
83#4658—31no—
84#4658—61no—
85#4648—31no—
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
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×D3—22no—
104C2×#627—22no—
105C2×#627—22no—
106C2×#627—22no—
107C2×#625—22no—
108C2×#625—22no—
109C2×#625—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113#3750—22no—
114#3750—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—22no—
123Dic3⋊Dic3—22no—
124(C2×D3)⋊Dic3—22no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129Dic32—22no—
130Dic32—22no—
131Dic32D414yes—
132#2398—91noSylow
133C23×C3×C4—31no—
134C22×#67—31no—
135C22×#67—31no—
136C23×Dic3—31no—
137C22×C4×D3—31no—
138C22×C4×D3C2×D311yescharacteristic
139C22×Dic6—31no—
140C22×Dic6—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C4×#67—64no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4C2×D311yescharacteristic
161C2×(C2×D3)⋊C4C2×D311yescharacteristic
162C2×(C2×D3)⋊C4C2×D311yescharacteristic
163C2×(C2×D3)⋊C4C2×D311yescharacteristic
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165C2×C4⋊Dic3—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—61no—
172C2×Dic3⋊C4—61no—
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×Dic3C2×D311yescharacteristic
181C2×C4×Dic3C2×D311yescharacteristic
182#887—64no—
183#67⋊C4—64no—
184C4×Dic6—64no—
185C3×#95—21no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95C2×D311yescharacteristic
190C3×#95C2×D311yescharacteristic
191C3⋊#95—31no—
192C3⋊#95—31no—
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—31no—
206C3⋊#95—31no—
207C3⋊#95—61no—
208C3⋊#95—61no—
209C3⋊#95—61no—
210C3⋊#95—61no—
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32C2411yescharacteristic
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3#4112yes—
228C22×C3×D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
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⋊Dic3C2×D412yes—
249C2×C3⋊Dic3#4112yes—
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×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D412yes—
264C2×C3×Dic3C2×D412yes—
265C2×C3×Dic3#4112yes—
266C2×C3×Dic3#4112yes—
267C2×C3×Dic3#4112yes—
268C3×C4×D3—44no—
269#627—28no—
270#625—28no—
271D3×Dic3—44no—
272C2×C4×Q8—91no—
273C2×C4×D4—91no—
274#400—91no—
275#400—91no—
276#397—31no—
277#397—91no—
278#394—91no—
279#394—91no—
280#393—91no—
281#393—91no—
282C4×C22⋊C4—31no—
283C4×C22⋊C4—91no—
284C4×C22⋊C4—91no—
285C4×C22⋊C4—91no—
286#376—91no—
287C24×C3—31no—
288C24×C3—31no—
289C23×D3C22×D311yescharacteristic
290C23×D3C22×D311yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—62no—
301C22×C3×C4—62no—
302C22×C3×C4—62no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—62no—
310C2×#67—62no—
311C2×#67—62no—
312C2×#67—62no—
313C2×#67—62no—
314C2×#67—62no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—62no—
328C22×Dic3—62no—
329C22×Dic3—62no—
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C2×C4×D3—22no—
337C2×C4×D3—22no—
338C2×C4×D3—22no—
339C2×C4×D3—62no—
340C2×C4×D3—62no—
341C2×C4×D3—62no—
342C2×Dic6—62no—
343C2×Dic6—62no—
344C2×Dic6—62no—
345C2×Dic6—62no—
346C2×Dic6—62no—
347C2×Dic6—62no—
348C3×C4⋊C4—62no—
349C3×C22⋊C4—62no—
350C3×C22⋊C4—62no—
351C3×C22⋊C4—62no—
352C3×C22⋊C4—62no—
353C3×C22⋊C4—62no—
354C3×C42—62no—
355C3×C42—62no—
356#217—62no—
357#217—62no—
358#217—62no—
359#217—62no—
360#217—62no—
361(C2×D3)⋊C4—22no—
362(C2×D3)⋊C4—22no—
363(C2×D3)⋊C4—22no—
364(C2×D3)⋊C4—22no—
365(C2×D3)⋊C4—22no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—62no—
369(C2×D3)⋊C4—62no—
370(C2×D3)⋊C4—62no—
371C4⋊Dic3—62no—
372Dic3⋊C4—22no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—122no—
379Dic3⋊C4—122no—
380C4×Dic3—22no—
381C4×Dic3—22no—
382C4×Dic3—34no—
383C4×Dic3—34no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C22×C32C22×D411yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C22×C32C2×#4111yescharacteristic
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4—41no—
412C3⋊Dic3—22no—
413C3⋊Dic3—22no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3#12414yes—
422C22×Q8—91no—
423C22×D4—91no—
424C23×C4—31no—
425C23×C4—91no—
426C4×Q8—184no—
427C4×D4—184no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—91no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4—91no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—91no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C42—31no—
443C2×C42—31no—
444C2×C42—91no—
445C2×C42—91no—
446C2×C42—91no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—91no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95D3211yescharacteristic
459C23×C3—21no—
460C23×C3—32no—
461C23×C3—32no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3C23×D311yescharacteristic
475C23×C3C23×D311yescharacteristic
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3#23512yes—
489C22×D3#23712yes—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—124no—
536#67—68no—
537#67—68no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—32no—
552C2×Dic3—32no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—62no—
556C2×Dic3—62no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3—121no—
580C2×Dic3—121no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—124no—
588C2×Dic3#23512yes—
589C2×Dic3#23512yes—
590C2×Dic3D3×D412yes—
591C2×Dic3D3×D412yes—
592C2×Dic3#23712yes—
593C4×D3—44no—
594C4×D3—124no—
595Dic6—68no—
596Dic6—68no—
597C2×C32#52511yescharacteristic
598C2×C32#52511yescharacteristic
599C2×C32C2×#12411yescharacteristic
600C2×C32#52911yescharacteristic
601C2×C32#52911yescharacteristic
602C2×C32#52911yescharacteristic
603C2×C32#52911yescharacteristic
604C3×D3—42no—
605C3×D3—42no—
606C24—31no—
607C24—31no—
608C2×Q8—182no—
609C2×Q8—182no—
610C2×Q8—182no—
611C2×D4—182no—
612C2×D4—182no—
613C2×D4—182no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—91no—
624C22×C4—91no—
625C22×C4—91no—
626C22×C4—91no—
627C22×C4—182no—
628C22×C4—182no—
629C22×C4—182no—
630C22×C4C2×D3211yescharacteristic
631C22×C4C2×D3211yescharacteristic
632C22×C4C2×D3211yescharacteristic
633C4⋊C4—62no—
634C4⋊C4—182no—
635C4⋊C4—182no—
636C4⋊C4—182no—
637C22⋊C4—62no—
638C22⋊C4—62no—
639C22⋊C4—62no—
640C22⋊C4—62no—
641C22⋊C4—62no—
642C22⋊C4—182no—
643C22⋊C4—182no—
644C22⋊C4—182no—
645C22⋊C4—182no—
646C22⋊C4—182no—
647C42—62no—
648C42—62no—
649C42—94no—
650C42—182no—
651C42—182no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—62no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3C2×#23511yescharacteristic
674C22×C3C2×#23511yescharacteristic
675C22×C3C2×#23511yescharacteristic
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C22×C3C2×#23711yescharacteristic
679C22×C3C2×#23711yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3D3×#4111yescharacteristic
682C22×C3D3×#4111yescharacteristic
683C22×C3D3×#4111yescharacteristic
684C22×C3D3×#4111yescharacteristic
685C22×C3D3×#4111yescharacteristic
686C22×C3D3×#4111yescharacteristic
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C3×C4—34no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—62no—
709C3×C4—62no—
710C3×C4—81no—
711C3×C4—81no—
712C3×C4—81no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716Dic3—22no—
717Dic3—22no—
718Dic3—41no—
719Dic3—41no—
720Dic3—41no—
721Dic3—62no—
722Dic3—62no—
723Dic3—62no—
724Dic3—62no—
725Dic3—122no—
726Dic3—122no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—241no—
732Dic3—241no—
733Dic3#88514yes—
734C32#239811yescharacteristic, complemented, Sylow
735C23—32no—
736C23—32no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23C22×D3211yescharacteristic
750Q8—188no—
751D4—188no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—92no—
780C2×C4—92no—
781C2×C4—124no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—364no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—122no—
801C2×C3—122no—
802C2×C3#547911yescharacteristic
803C2×C3C2×#88511yescharacteristic
804C2×C3#552811yescharacteristic
805C2×C3#553811yescharacteristic
806C2×C3#554711yescharacteristic
807C2×C3#554711yescharacteristic
808C2×C3#555711yescharacteristic
809C2×C3#560611yescharacteristic
810C2×C3#564911yescharacteristic
811C2×C3#564911yescharacteristic
812C2×C3#565611yescharacteristic
813C2×C3D3×#12411yescharacteristic
814C2×C3#570611yescharacteristic
815C2×C3#570611yescharacteristic
816D3—42no—
817D3—42no—
818C22—62no—
819C22—62no—
820C22—62no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22D3×#23511yescharacteristic
833C22D3×#23511yescharacteristic
834C22D3×#23511yescharacteristic
835C22D32×D411yescharacteristic
836C22D3×#23711yescharacteristic
837C22D3×#23711yescharacteristic
838C22#6431911yescharacteristic
839C4—34no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—62no—
844C4—62no—
845C4—121no—
846C4—121no—
847C4—121no—
848C4—182no—
849C4—182no—
850C4—361no—
851C4—361no—
852C3—21no—
853C3#7348111yescharacteristic, complemented
854C3#7746011yescharacteristic, complemented
855C2—122no—
856C2—122no—
857C2#1059397511yescharacteristic
858C2#1059409811yescharacteristic
859C2D3×#88511yescharacteristic
860C2#1059428611yescharacteristic
861C2#1059440411yescharacteristic
862C2#1059440511yescharacteristic
863C2#1059461411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2398
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. #10592357C2semidirect
4. C3×#4675C2semidirect
5. C3×#4666C2semidirect
8. Dic3×(C2×D3)⋊C4C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. #10591301C2semidirect
11. #10591293C2semidirect
12. #10591293C2semidirect
13. #10591239C2semidirect
14. #10591237C2semidirect
15. #10591210C2semidirect
75. #4675D3semidirect
79. #4666D3semidirect
734. C32#2398semidirect
853. C3#73481semidirect
854. C3#77460semidirect

Maximal subgroups

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

subgroupindex
C2×#638792
C2×#638372
#105923572
C3×#46752
C3×#46662
#105913902
#105913882
Dic3×(C2×D3)⋊C42
#105913012
#105912932
#105912392
#105912372
#105912102
#774603
#734813