Finite Group Databasebeta

← #11810263

Subgroups — #11810263

Order 1152.

1413 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63964C211yesmaximal, characteristic, complemented
4C2×#63851C211yesmaximal, characteristic, complemented
5#10592641C211yesmaximal, characteristic, complemented
6C3×#4942C211yesmaximal, characteristic, complemented
7#10591713C211yesmaximal, characteristic
8#10591710C211yesmaximal, characteristic
9#10591340C211yesmaximal, characteristic, complemented
10#10591330C211yesmaximal, characteristic, complemented
11#10591309C211yesmaximal, characteristic, complemented
12#10591306C211yesmaximal, characteristic, complemented
13#10591295C211yesmaximal, characteristic, complemented
14#10591200C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#82353—31nomaximal
17#73889—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#67⋊C4—24no—
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3—24no—
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43#63964—24no—
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48#63851—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×C4×D4—31no—
58C22×C4⋊Dic3—31no—
59C2×#924—31no—
60C2×#924—31no—
61C22×Dic3⋊C4—31no—
62C2×#896—31no—
63C2×#67⋊C4D311yescharacteristic
64C2×#878—31no—
65C3×#380—31no—
66#5220—31no—
67#5220—31no—
68#5213—31no—
69#5212—31no—
70#4994—31no—
71#4983—31no—
72#4982—31no—
73#4982—31no—
74#4976—31no—
75#4958—31no—
76#4948—31no—
77#4948—31no—
78#4942—31no—
79#4942—31no—
80#4942—61no—
81#4942D311yescharacteristic, complemented
82#4929—31no—
83#4928—31no—
84#4676—31no—
85#4667—31no—
86#4657—31no—
87#4646—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3—22no—
93C22×C3⋊Dic3—22no—
94C22×C3⋊Dic3—41no—
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67Q814yescomplemented
102C22×C3×Dic3—22no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—41no—
107C22×C3×Dic3D414yes—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×#627—22no—
119C2×#627—22no—
120C2×#627—22no—
121C32×C22⋊C4—22no—
122#3757—22no—
123#3750—22no—
124#3750—41no—
125C3×#217—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—41no—
130C3×C4×Dic3—22no—
131#3724—22no—
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3D414yescomplemented
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—41no—
141(C2×D3)⋊Dic3—41no—
142#2417—91noSylow
143C22×C3×D4—31no—
144C23×C3×C4—31no—
145C23×C3×C4—31no—
146C23×C3×C4—31no—
147C22×#67C2×D311yescharacteristic
148C23×Dic3—31no—
149C23×Dic3—31no—
150C23×Dic3—61no—
151C23×Dic3C2×D311yescharacteristic
152C23×Dic3C2×D311yescharacteristic
153C22×C4×D3C2×D311yescharacteristic
154C22×Dic6—31no—
155C22×Dic6—31no—
156C3×C4×D4—64no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4C2×D311yescharacteristic
164C2×C3×C22⋊C4C2×D311yescharacteristic
165C2×C3×C42—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—61no—
173C2×#217C2×D311yescharacteristic
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4C2×D311yescharacteristic
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—64no—
186#924—64no—
187#924—64no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—61no—
201C2×Dic3⋊C4—61no—
202C2×Dic3⋊C4—64no—
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×Dic3⋊C4C2×D311yescharacteristic
206C2×C4×Dic3C2×D311yescharacteristic
207#896—64no—
208#67⋊C4—24no—
209#878—64no—
210C3×#95—31no—
211C3×#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—61no—
225C3⋊#95—61no—
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32C2×D412yes—
233C23×C32C2×Q812yes—
234C23×C32#4112yes—
235C23×C32C2411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×Q812yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—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⋊Dic3—21no—
260C2×C3⋊Dic3—44no—
261C2×C3⋊Dic3C2×D412yes—
262C3×#67—28no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—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×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—44no—
280C2×C3×Dic3C2×D412yes—
281C2×C3×Dic3C2×D412yes—
282C2×C3×Dic3C2×D412yes—
283C2×C3×Dic3C2×D412yes—
284C2×C3×Dic3C2×Q812yes—
285C2×C3×Dic3#4112yes—
286C3×C4×D3—44no—
287#627—44no—
288C2×C22⋊Q8—91no—
289C2×C22⋊Q8—91no—
290C2×C4×D4—31no—
291C22×C4⋊C4—91no—
292#398—91no—
293#398—91no—
294#396—91no—
295#396—91no—
296#391—91no—
297#389—91no—
298#386—91no—
299#386—91no—
300#380—31no—
301#380—91no—
302#380—91no—
303C24×C3—21no—
304C24×C3—31no—
305C24×C3C22×D311yescharacteristic
306C24×C3C22×D311yescharacteristic
307C23×D3C22×D311yescharacteristic
308C2×C3×D4—34no—
309C2×C3×D4—62no—
310C2×C3×D4—62no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—34no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—62no—
322C22×C3×C4—62no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4—62no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4—121no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—22no—
334C2×#67—22no—
335C2×#67Dic614yescomplemented
336C22×Dic3—22no—
337C22×Dic3—22no—
338C22×Dic3—22no—
339C22×Dic3—22no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—41no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—62no—
354C22×Dic3—62no—
355C22×Dic3—64no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3—122no—
359C22×Dic3—121no—
360C22×Dic3—121no—
361C22×Dic3—122no—
362C22×Dic3#6714yes—
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C2×C4×D3—22no—
371C2×C4×D3—22no—
372C2×C4×D3—22no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—62no—
377C2×Dic6—62no—
378C2×Dic6—62no—
379C3×C4⋊C4—62no—
380C3×C4⋊C4—62no—
381C3×C4⋊C4—121no—
382C3×C22⋊C4—22no—
383C3×C22⋊C4—22no—
384C3×C22⋊C4—42no—
385C3×C22⋊C4—62no—
386C3×C22⋊C4—62no—
387C3×C42—62no—
388#217—22no—
389#217—62no—
390#217—62no—
391#217—62no—
392#217—62no—
393#217—122no—
394#217—121no—
395#217—121no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—121no—
400(C2×D3)⋊C4—121no—
401C4⋊Dic3—34no—
402C4⋊Dic3—62no—
403C4⋊Dic3—62no—
404C4⋊Dic3—62no—
405C4⋊Dic3—62no—
406C4⋊Dic3—62no—
407Dic3⋊C4—22no—
408Dic3⋊C4—22no—
409Dic3⋊C4—34no—
410Dic3⋊C4—41no—
411Dic3⋊C4—62no—
412Dic3⋊C4—62no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420Dic3⋊C4—122no—
421Dic3⋊C4—121no—
422Dic3⋊C4—121no—
423Dic3⋊C4—122no—
424C4×Dic3—22no—
425C22×C32—22no—
426C22×C32—22no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32C22⋊Q814yescomplemented
432C22×C32C22×D411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32C22×Q811yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32H(5,𝔽2)11yescharacteristic
438C22×C322−1+411yescharacteristic
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C32×C4—41no—
447C32×C4—41no—
448C3⋊Dic3—22no—
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3#12114yes—
459C22×Q8—91no—
460C22×D4—31no—
461C23×C4—31no—
462C23×C4—31no—
463C23×C4—31no—
464C23×C4—91no—
465C22⋊Q8—184no—
466C22⋊Q8—184no—
467C4×D4—64no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—91no—
472C2×C4⋊C4—91no—
473C2×C4⋊C4—91no—
474C2×C4⋊C4—91no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4—91no—
480C2×C4⋊C4—184no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—91no—
484C2×C22⋊C4—91no—
485C2×C22⋊C4—91no—
486C2×C22⋊C4—91no—
487C2×C22⋊C4—91no—
488C2×C22⋊C4D3211yescharacteristic
489C2×C42—31no—
490#95—31no—
491#95—31no—
492#95—91no—
493#95—91no—
494#95—91no—
495#95—91no—
496#95—91no—
497#95—91no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—32no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3C2×Dic612yes—
522C23×C3#23512yes—
523C23×C3#23512yes—
524C23×C3D3×D412yes—
525C23×C3D3×Q812yes—
526C23×C3C2×#6712yes—
527C23×C3C23×D311yescharacteristic
528C23×C3C23×D311yescharacteristic
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3C2×Dic612yes—
536C3×D4—68no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—68no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—124no—
578C2×C3×C4—124no—
579#67—28no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—28no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—44no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—62no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—121no—
626C2×Dic3—121no—
627C2×Dic3—121no—
628C2×Dic3—121no—
629C2×Dic3—121no—
630C2×Dic3—121no—
631C2×Dic3—121no—
632C2×Dic3—121no—
633C2×Dic3—124no—
634C2×Dic3—124no—
635C2×Dic3—128no—
636C2×Dic3C2×Dic612yes—
637C2×Dic3D3×D412yes—
638C2×Dic3D3×D412yes—
639C2×Dic3#23712yes—
640C2×Dic3C2×#6712yes—
641C2×Dic3C2×#6712yes—
642C4×D3—44no—
643Dic6—124no—
644Dic6—124no—
645C2×C32—24no—
646C2×C32C2×#12111yescharacteristic
647C2×C32C2×C22⋊Q811yescharacteristic
648C2×C32#53711yescharacteristic
649C2×C32#54611yescharacteristic
650C2×C32D4×Q811yescharacteristic
651C2×C32#55211yescharacteristic
652C2×C32#55411yescharacteristic
653C3×D3—42no—
654C24—31no—
655C24C2×D3211yescharacteristic
656C2×Q8—182no—
657C2×Q8—182no—
658C2×Q8—182no—
659C2×D4—34no—
660C2×D4—62no—
661C2×D4—62no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—34no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—62no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—62no—
677C22×C4—91no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—121no—
682C22×C4—182no—
683C22×C4—182no—
684C22×C4—361no—
685C22×C4C2×D3211yescharacteristic
686C22×C4C2×D3211yescharacteristic
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—94no—
690C4⋊C4—121no—
691C4⋊C4—182no—
692C4⋊C4—182no—
693C4⋊C4—182no—
694C4⋊C4—182no—
695C4⋊C4—182no—
696C4⋊C4—182no—
697C4⋊C4—182no—
698C4⋊C4—361no—
699C22⋊C4—22no—
700C22⋊C4—62no—
701C22⋊C4—62no—
702C22⋊C4—182no—
703C22⋊C4—182no—
704C22⋊C4—182no—
705C22⋊C4—361no—
706C22⋊C4—361no—
707C42—62no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—24no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3#89614yescomplemented
742C22×C3#92414yescomplemented
743C22×C3C22×Dic611yescharacteristic
744C22×C3C2×#23511yescharacteristic
745C22×C3C2×#23511yescharacteristic
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×#23711yescharacteristic
750C22×C3#100411yescharacteristic
751C22×C3C2×D3×Q811yescharacteristic
752C22×C3D3×#4111yescharacteristic
753C22×C3#100911yescharacteristic
754C22×C3#101011yescharacteristic
755C22×C3#101011yescharacteristic
756C22×C3C22×#6711yescharacteristic
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C3×C4—34no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—81no—
773C3×C4—81no—
774C3×C4—121no—
775C3×C4—121no—
776C3×C4—121no—
777Dic3—22no—
778Dic3—22no—
779Dic3—22no—
780Dic3—41no—
781Dic3—41no—
782Dic3—41no—
783Dic3—64no—
784Dic3—62no—
785Dic3—62no—
786Dic3—122no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—121no—
793Dic3—241no—
794Dic3—241no—
795Dic3#93914yes—
796C32#241711yescharacteristic, complemented, Sylow
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—32no—
802C23—61no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—61no—
808C23D3×Dic612yes—
809C23#379812yes—
810C23D3×#6712yes—
811C23C22×D3211yescharacteristic
812Q8—364no—
813D4—68no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—68no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—92no—
843C2×C4—124no—
844C2×C4—124no—
845C2×C4—181no—
846C2×C4—181no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—181no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—364no—
857C2×C3—24no—
858C2×C3—24no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—44no—
867C2×C3—122no—
868C2×C3#549011yescharacteristic
869C2×C3C2×#89611yescharacteristic
870C2×C3#553111yescharacteristic
871C2×C3D4×Dic611yescharacteristic
872C2×C3#554111yescharacteristic
873C2×C3#554311yescharacteristic
874C2×C3#555011yescharacteristic
875C2×C3#559711yescharacteristic
876C2×C3D3×#12111yescharacteristic
877C2×C3#563211yescharacteristic
878C2×C3#563611yescharacteristic
879C2×C3C2×#92411yescharacteristic
880C2×C3C2×#93911yescharacteristic
881C2×C3#583311yescharacteristic
882D3—42no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22#6385114yescomplemented
897C22C2×D3×Dic611yescharacteristic
898C22C2×#379811yescharacteristic
899C22#6430911yescharacteristic
900C22D32×D411yescharacteristic
901C22D3×#23711yescharacteristic
902C22#6431411yescharacteristic
903C22C2×D3×#6711yescharacteristic
904C4—34no—
905C4—41no—
906C4—41no—
907C4—62no—
908C4—62no—
909C4—62no—
910C4—121no—
911C4—121no—
912C4—121no—
913C4—182no—
914C4—361no—
915C4—361no—
916C4—361no—
917C3—21no—
918C3#7388911yescharacteristic, complemented
919C3#8235311yescharacteristic, complemented
920C2—24no—
921C2—122no—
922C2#1059403911yescharacteristic
923C2#1059407111yescharacteristic
924C2#1059414611yescharacteristic
925C2#1059418611yescharacteristic
926C2C2×#6385111yescharacteristic
927C2#1059515611yescharacteristic
928C2D3×#93911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2417
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3⋊Dic3C2semidirect
3. C2×#63964C2semidirect
4. C2×#63851C2semidirect
5. #10592641C2semidirect
6. C3×#4942C2semidirect
9. #10591340C2semidirect
10. #10591330C2semidirect
11. #10591309C2semidirect
12. #10591306C2semidirect
13. #10591295C2semidirect
14. #10591200C2semidirect
15. #10591191C2semidirect
81. #4942D3semidirect
101. C2×C3×#67Q8semidirect
137. Dic3⋊Dic3D4semidirect
335. C2×#67Dic6semidirect
431. C22×C32C22⋊Q8semidirect
741. C22×C3#896semidirect
742. C22×C3#924semidirect
796. C32#2417semidirect
896. C22#63851semidirect
918. C3#73889semidirect
919. C3#82353semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C22×Dic3⋊Dic32
C2×#639642
C2×#638512
#105926412
C3×#49422
#105917132
#105917102
#105913402
#105913302
#105913092
#105913062
#105912952
#105912002
#105911912
#823533
#738893