Finite Group Databasebeta

← #11812999

Subgroups — #11812999

Order 1152.

1339 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×Dic3×#67C211yesmaximal, characteristic, complemented
3#10592921C211yesmaximal, characteristic, complemented
4C3×#5220C211yesmaximal, characteristic, complemented
5#10591721C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591717C211yesmaximal, characteristic, complemented
9#10591717C211yesmaximal, characteristic, complemented
10#10591701C211yesmaximal, characteristic, complemented
11#10591696C211yesmaximal, characteristic, complemented
12D3×C3⋊#95C211yesmaximal, characteristic, complemented
13#10591343C211yesmaximal, characteristic, complemented
14#10591278C211yesmaximal, characteristic, complemented
15#10591263C211yesmaximal, characteristic, complemented
16#82656—31nomaximal
17#74897—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C3×#938—24no—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37Dic3×#67—24no—
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C3×#121—31no—
56C2×#938D311yescharacteristic
57C2×D4×Dic3—31no—
58C2×C4×#67—31no—
59C3×#386—31no—
60#5222—31no—
61#5222—31no—
62#5222—61no—
63#5220—31no—
64#5220—31no—
65#5220—31no—
66#5220D311yescharacteristic, complemented
67#5211—31no—
68#5210—31no—
69C2×C3⋊#95—31no—
70#4986—31no—
71#4978—31no—
72#4956—31no—
73#4956—31no—
74#4956—31no—
75#4953—31no—
76#4953—31no—
77#4952—31no—
78#4952—31no—
79#4951—31no—
80#4944—31no—
81#4943—31no—
82#4668—31no—
83D3×#95—31no—
84#4660—31no—
85#4655—31no—
86C24×C32C2311yescharacteristic
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4—41no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67D414yes—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—41no—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—41no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3—41no—
122#3757—22no—
123#3757—41no—
124#3757—41no—
125#3757—41no—
126#3750—22no—
127C3×#217—22no—
128C3×#217—22no—
129C3×#217—22no—
130C3×#217—41no—
131C3×#217—41no—
132C3×C4⋊Dic3—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—41no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—22no—
137Dic32—22no—
138#2444—91noSylow
139C22×C3×D4—21no—
140C22×C3×D4—31no—
141C22×C3×D4—31no—
142C22×C3×D4C2×D311yescharacteristic
143C22×C3×D4C2×D311yescharacteristic
144C23×C3×C4—31no—
145C23×C3×C4—31no—
146C22×#67C2×D311yescharacteristic
147C22×#67C2×D311yescharacteristic
148C23×Dic3—31no—
149C23×Dic3—31no—
150C23×Dic3C2×D311yescharacteristic
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3C2×D311yescharacteristic
154C3×#121—64no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—61no—
172C2×#217—61no—
173C2×#217—61no—
174C2×#217—61no—
175C2×#217C2×D311yescharacteristic
176C2×#217C2×D311yescharacteristic
177C2×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
179C2×#217C2×D311yescharacteristic
180#938—24no—
181D4×Dic3—64no—
182C4×#67—64no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3C2×D311yescharacteristic
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—61no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—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—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—61no—
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32C2×D412yes—
234C23×C32C2411yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D412yes—
240C22×C3×D3#4112yes—
241C22×C3×D3#4112yes—
242C32×D4—44no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4#4112yes—
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—
258C3×#67—28no—
259C3×#67—44no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
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—21no—
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×Dic3#4112yes—
282C3×C4×D3—44no—
283D3×Dic3—44no—
284D3×Dic3—44no—
285C2×#121—31no—
286C2×C4×D4—91no—
287#400—91no—
288#397—91no—
289#397—91no—
290#394—91no—
291#388—91no—
292#387—91no—
293#386—31no—
294#386—91no—
295#386—91no—
296#386—91no—
297#385—91no—
298#381—91no—
299C2×#95—91no—
300C24×C3—21no—
301C24×C3—21no—
302C24×C3—31no—
303C24×C3C22×D311yescharacteristic
304C24×C3C22×D311yescharacteristic
305C24×C3C22×D311yescharacteristic
306C24×C3C22×D311yescharacteristic
307C23×D3C22×D311yescharacteristic
308C2×C3×D4—22no—
309C2×C3×D4—22no—
310C2×C3×D4—22no—
311C2×C3×D4—22no—
312C2×C3×D4—34no—
313C2×C3×D4—42no—
314C2×C3×D4—42no—
315C2×C3×D4—41no—
316C2×C3×D4—41no—
317C2×C3×D4—42no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C22×C3×C4—21no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—121no—
336C22×C3×C4—121no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—22no—
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—22no—
343C2×#67—22no—
344C2×#67#6714yes—
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—41no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—62no—
361C22×Dic3—62no—
362C22×Dic3—62no—
363C22×Dic3—121no—
364C22×Dic3—121no—
365C22×Dic3—121no—
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—41no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—121no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C3×C4⋊C4—62no—
383C3×C22⋊C4—62no—
384C3×C22⋊C4—62no—
385C3×C22⋊C4—62no—
386C3×C22⋊C4—121no—
387C3×C22⋊C4—121no—
388#217—22no—
389#217—22no—
390#217—22no—
391#217—41no—
392#217—41no—
393#217—62no—
394#217—62no—
395#217—62no—
396#217—62no—
397#217—122no—
398#217—121no—
399#217—121no—
400#217—121no—
401#217—121no—
402#217—121no—
403#217—121no—
404#217—122no—
405#217—122no—
406#217—122no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409C4⋊Dic3—22no—
410C4⋊Dic3—62no—
411C4⋊Dic3—121no—
412Dic3⋊C4—62no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—122no—
416Dic3⋊C4—121no—
417C4×Dic3—62no—
418C4×Dic3—62no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32C22×D411yescharacteristic
434C22×C32C2×#4111yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32C2×#4111yescharacteristic
438C22×C32H(5,𝔽2)11yescharacteristic
439C22×C32H(5,𝔽2)11yescharacteristic
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3#12314yes—
447C32×C4—22no—
448C3⋊Dic3—41no—
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C22×D4—31no—
460C22×D4—31no—
461C22×D4D3211yescharacteristic
462C23×C4—31no—
463C23×C4—31no—
464C23×C4—91no—
465C23×C4—91no—
466#121—64no—
467C4×D4—184no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—91no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4—91no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4—31no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C22⋊C4—91no—
481C2×C22⋊C4—91no—
482C2×C22⋊C4—91no—
483C2×C42—91no—
484#95—31no—
485#95—31no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95—91no—
492#95—91no—
493#95—91no—
494#95—91no—
495#95—91no—
496C23×C3—21no—
497C23×C3—21no—
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—21no—
508C23×C3—22no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—22no—
525C23×C3—32no—
526C23×C3—32no—
527C23×C3—32no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3D3×D412yes—
545C23×C3C2×#6712yes—
546C23×C3C23×D311yescharacteristic
547C23×C3C23×D311yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3#23712yes—
553C22×D3#23712yes—
554C22×D3C2×#6712yes—
555C3×D4—44no—
556C3×D4—44no—
557C3×D4—48no—
558C3×D4—68no—
559C3×D4—124no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—22no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
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—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—124no—
589C2×C3×C4—124no—
590C2×C3×C4#23512yes—
591C2×C3×C4#23712yes—
592#67—28no—
593#67—44no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—44no—
614C2×Dic3—62no—
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—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—124no—
651C2×Dic3—124no—
652C2×Dic3#23712yes—
653C2×Dic3C2×#6712yes—
654C4×D3—44no—
655C4×D3—124no—
656C4×D3—124no—
657C2×C32—42no—
658C2×C32—81no—
659C2×C32C2×#12311yescharacteristic
660C2×C32#52911yescharacteristic
661C2×C32#53811yescharacteristic
662C2×C32#54611yescharacteristic
663C2×C32#54611yescharacteristic
664C2×C32#55311yescharacteristic
665C2×C32#55311yescharacteristic
666C3×D3—24no—
667C24—31no—
668C24C2×D3211yescharacteristic
669C24C2×D3211yescharacteristic
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—34no—
673C2×D4—41no—
674C2×D4—62no—
675C2×D4—62no—
676C2×D4—62no—
677C2×D4—62no—
678C2×D4—62no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—91no—
691C22×C4—91no—
692C22×C4—91no—
693C22×C4—91no—
694C22×C4—121no—
695C22×C4—121no—
696C22×C4—182no—
697C22×C4—182no—
698C22×C4—182no—
699C22×C4—361no—
700C22×C4—361no—
701C22×C4—361no—
702C22×C4C2×D3211yescharacteristic
703C4⋊C4—62no—
704C4⋊C4—182no—
705C4⋊C4—182no—
706C4⋊C4—361no—
707C22⋊C4—62no—
708C22⋊C4—62no—
709C22⋊C4—62no—
710C22⋊C4—121no—
711C22⋊C4—121no—
712C22⋊C4—182no—
713C22⋊C4—182no—
714C22⋊C4—182no—
715C22⋊C4—361no—
716C22⋊C4—361no—
717C22⋊C4—361no—
718C42—182no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—34no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3C2×#23511yescharacteristic
776C22×C3C2×D3×D411yescharacteristic
777C22×C3C2×#23711yescharacteristic
778C22×C3C2×#23711yescharacteristic
779C22×C3C2×#23711yescharacteristic
780C22×C3C2×#23711yescharacteristic
781C22×C3#100411yescharacteristic
782C22×C3#100411yescharacteristic
783C22×C3#100411yescharacteristic
784C22×C3D3×#4111yescharacteristic
785C22×C3D3×#4111yescharacteristic
786C22×C3D3×#4111yescharacteristic
787C22×C3#100911yescharacteristic
788C22×C3C22×#6711yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3#93514yes—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—42no—
799C3×C4—62no—
800C3×C4—62no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4—121no—
804C3×C4—121no—
805C3×C4—121no—
806Dic3—22no—
807Dic3—22no—
808Dic3—41no—
809Dic3—41no—
810Dic3—41no—
811Dic3—41no—
812Dic3—41no—
813Dic3—122no—
814Dic3—121no—
815Dic3—121no—
816Dic3—121no—
817Dic3—121no—
818Dic3—121no—
819Dic3—121no—
820Dic3—121no—
821Dic3—121no—
822Dic3—241no—
823Dic3—241no—
824Dic3—241no—
825C32#244411yescharacteristic, complemented, Sylow
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—32no—
840C23—32no—
841C23—32no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23D3×#6712yes—
847C23C22×D3211yescharacteristic
848D4—44no—
849D4—68no—
850D4—124no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—124no—
875C2×C4—124no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—364no—
889C2×C4—364no—
890C2×C4#380412yes—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—42no—
899C2×C3—42no—
900C2×C3—64no—
901C2×C3—82no—
902C2×C3—82no—
903C2×C3—81no—
904C2×C3—81no—
905C2×C3#549011yescharacteristic
906C2×C3#555711yescharacteristic
907C2×C3#555811yescharacteristic
908C2×C3#559111yescharacteristic
909C2×C3#560011yescharacteristic
910C2×C3#560111yescharacteristic
911C2×C3#561311yescharacteristic
912C2×C3#561411yescharacteristic
913C2×C3#561711yescharacteristic
914C2×C3#561811yescharacteristic
915C2×C3D3×#12311yescharacteristic
916C2×C3C2×#93511yescharacteristic
917C2×C3#580611yescharacteristic
918C2×C3#582911yescharacteristic
919D3—24no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—34no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22D3×#23711yescharacteristic
942C22D3×#23711yescharacteristic
943C22D3×#23711yescharacteristic
944C22#6431411yescharacteristic
945C22C2×#380411yescharacteristic
946C22C2×D3×#6711yescharacteristic
947C22#6433011yescharacteristic
948C4—22no—
949C4—62no—
950C4—62no—
951C4—121no—
952C4—121no—
953C4—121no—
954C4—121no—
955C4—121no—
956C4—361no—
957C4—361no—
958C4—361no—
959C4—361no—
960C3—21no—
961C3#7489711yescharacteristic, complemented
962C3#8265611yescharacteristic, complemented
963C2—42no—
964C2—64no—
965C2—81no—
966C2D3×#93511yescharacteristic
967C2#1059517211yescharacteristic
968C2#1059517911yescharacteristic
969C2#1059518211yescharacteristic
970C2#1059530411yescharacteristic
971C2#1059531011yescharacteristic
972C2#1059549311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32#2444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×#67C2semidirect
3. #10592921C2semidirect
4. C3×#5220C2semidirect
5. #10591721C2semidirect
6. #10591721C2semidirect
7. #10591721C2semidirect
8. #10591717C2semidirect
9. #10591717C2semidirect
10. #10591701C2semidirect
11. #10591696C2semidirect
12. D3×C3⋊#95C2semidirect
13. #10591343C2semidirect
14. #10591278C2semidirect
15. #10591263C2semidirect
66. #5220D3semidirect
825. C32#2444semidirect
961. C3#74897semidirect
962. C3#82656semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×Dic3×#672
#105929212
C3×#52202
#105917212
#105917172
#105917012
#105916962
D3×C3⋊#952
#105913432
#105912782
#105912632
#826563
#748973