Finite Group Databasebeta

← #11813008

Subgroups — #11813008

Order 1152.

1287 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3#10592685C211yesmaximal, characteristic, complemented
4C3×#4978C211yesmaximal, characteristic, complemented
5#10591376C211yesmaximal, characteristic, complemented
6#10591376C211yesmaximal, characteristic, complemented
7#10591376C211yesmaximal, characteristic, complemented
8#10591376C211yesmaximal, characteristic, complemented
9#10591362C211yesmaximal, characteristic, complemented
10D3×C3⋊#95C211yesmaximal, characteristic, complemented
11#10591315C211yesmaximal, characteristic, complemented
12#10591300C211yesmaximal, characteristic, complemented
13#10591299C211yesmaximal, characteristic, complemented
14#10591279C211yesmaximal, characteristic, complemented
15#10591277C211yesmaximal, characteristic, complemented
16#82656—31nomaximal
17#75320—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#895—24no—
32C2×#3724C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42Dic3×D12—24no—
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C3×#121—31no—
56C2×D4×Dic3—31no—
57C2×#895D311yescharacteristic
58C2×C4×D12—31no—
59C3×#387—31no—
60#5222—31no—
61#5220—31no—
62#5220—31no—
63#5220—31no—
64#5220—31no—
65#5210—31no—
66C2×C3⋊#95—31no—
67#4991—31no—
68#4989—31no—
69#4986—31no—
70#4986—31no—
71#4986—61no—
72#4978D311yescharacteristic, complemented
73#4953—31no—
74#4952—31no—
75#4944—31no—
76#4943—31no—
77#4940—31no—
78#4675—31no—
79#4674—31no—
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4665—31no—
84#4664—31no—
85D3×#95—31no—
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
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×D12—22no—
102C2×C3×D12—22no—
103C2×C3×D12—22no—
104C2×C3×D12—22no—
105C2×C3×D12—22no—
106C2×C3×D12—22no—
107C2×C3×D12—22no—
108C2×C3×D12—41no—
109C2×C3×D12D414yes—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—41no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—41no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3—41no—
122C32×C4⋊C4—22no—
123C4⋊(C3⋊Dic3)—22no—
124C3×(C2×D3)⋊C4—22no—
125C3×(C2×D3)⋊C4—22no—
126C3×Dic3⋊C4—22no—
127C3×C4×Dic3—22no—
128#3724—41no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131(C2×D3)⋊Dic3—22no—
132(C2×D3)⋊Dic3—22no—
133(C2×D3)⋊Dic3—41no—
134(C2×D3)⋊Dic3—41no—
135(C2×D3)⋊Dic3—41no—
136(C2×D3)⋊Dic3—41no—
137(C2×D3)⋊Dic3—41no—
138#2444—91noSylow
139C22×C3×D4—31no—
140C22×C3×D4—31no—
141C22×C3×D4—31no—
142C23×C3×C4—31no—
143C23×Dic3—31no—
144C23×Dic3—31no—
145C23×Dic3—31no—
146C22×D12C2×D311yescharacteristic
147C22×D12C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3C2×D311yescharacteristic
153C3×#121—64no—
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×C3×C4⋊C4C2×D311yescharacteristic
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C42—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—
170D4×Dic3—64no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×(C2×D3)⋊C4C2×D311yescharacteristic
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—61no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×C4×Dic3C2×D311yescharacteristic
189#895—24no—
190C4×D12—64no—
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—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—61no—
212C3⋊#95—61no—
213C3⋊#95—61no—
214C3⋊#95—61no—
215C3⋊#95—61no—
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C23×C32C2411yescharacteristic
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—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D412yes—
239C22×C3×D3C2×D412yes—
240C22×C3×D3#4112yes—
241C22×C3×D3#4112yes—
242C2×C32×C4—21no—
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×C32×C4C2×D412yes—
250C2×C32×C4#4112yes—
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×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#4112yes—
278C3×D12—28no—
279C3×D12—44no—
280C3×D12—44no—
281C3×C4×D3—44no—
282D3×Dic3—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—31no—
293#386—91no—
294#386—91no—
295#386—91no—
296#386—91no—
297#385—91no—
298#381—91no—
299C2×#95—91no—
300C24×C3—31no—
301C24×C3—31no—
302C24×C3—31no—
303C23×D3C22×D311yescharacteristic
304C23×D3C22×D311yescharacteristic
305C23×D3C22×D311yescharacteristic
306C2×C3×D4—34no—
307C2×C3×D4—62no—
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C2×C3×D4—62no—
311C2×C3×D4—62no—
312C2×C3×D4—62no—
313C2×C3×D4—62no—
314C2×C3×D4—121no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4—121no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344C22×Dic3—62no—
345C22×Dic3—62no—
346C22×Dic3—62no—
347C22×Dic3—62no—
348C22×Dic3—62no—
349C22×Dic3—121no—
350C22×Dic3—121no—
351C22×Dic3—121no—
352C22×Dic3—121no—
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C2×D12—22no—
359C2×D12—22no—
360C2×D12—22no—
361C2×D12—22no—
362C2×D12—22no—
363C2×D12—22no—
364C2×D12—22no—
365C2×D12—41no—
366C2×D12#6714yes—
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—41no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—121no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—42no—
382C3×C4⋊C4—62no—
383C3×C22⋊C4—62no—
384C3×C22⋊C4—62no—
385C3×C42—62no—
386#217—62no—
387#217—62no—
388#217—62no—
389#217—62no—
390#217—121no—
391#217—121no—
392#217—121no—
393#217—121no—
394#217—121no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—121no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4—121no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406C4⋊Dic3—62no—
407C4⋊Dic3—62no—
408C4⋊Dic3—122no—
409Dic3⋊C4—22no—
410Dic3⋊C4—121no—
411Dic3⋊C4—121no—
412C4×Dic3—22no—
413C22×C32C22×D411yescharacteristic
414C22×C32C2×#4111yescharacteristic
415C22×C32C2×#4111yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32C2×#4111yescharacteristic
418C22×C32H(5,𝔽2)11yescharacteristic
419C22×C32H(5,𝔽2)11yescharacteristic
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3#12314yes—
441C32×C4—22no—
442C32×C4—22no—
443C32×C4—41no—
444C3⋊Dic3—41no—
445C3⋊Dic3—41no—
446C3⋊Dic3—41no—
447C3⋊Dic3—41no—
448C3×Dic3—22no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C22×D4—31no—
454C22×D4—31no—
455C22×D4—31no—
456C23×C4—31no—
457C23×C4—91no—
458C23×C4—91no—
459C23×C4—91no—
460#121—64no—
461C4×D4—184no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4D3211yescharacteristic
466C2×C22⋊C4—31no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—91no—
469C2×C22⋊C4—91no—
470C2×C22⋊C4—91no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—91no—
477C2×C42—31no—
478#95—31no—
479#95—31no—
480#95—31no—
481#95—31no—
482#95—91no—
483#95—91no—
484#95—91no—
485#95—91no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490C23×C3—21no—
491C23×C3—32no—
492C23×C3—32no—
493C23×C3—32no—
494C23×C3—32no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3—61no—
511C23×C3—61no—
512C23×C3C23×D311yescharacteristic
513C23×C3C23×D311yescharacteristic
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3#23712yes—
532C22×D3#23712yes—
533C22×D3C2×#6712yes—
534C22×D3C2×#6712yes—
535C3×D4—68no—
536C3×D4—124no—
537C3×D4—124no—
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—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
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—41no—
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—124no—
577C2×C3×C4#23512yes—
578C2×C3×C4D3×D412yes—
579C2×C3×C4#23712yes—
580C2×C3×C4C2×#6712yes—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
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—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
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—121no—
620C2×Dic3—121no—
621C2×Dic3—121no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—121no—
627C2×Dic3—121no—
628C2×Dic3—121no—
629C2×Dic3—121no—
630C2×Dic3—121no—
631C2×Dic3—124no—
632C2×Dic3—124no—
633C2×Dic3—124no—
634C2×Dic3#23912yes—
635D12—28no—
636D12—44no—
637D12—44no—
638C4×D3—44no—
639C4×D3—124no—
640C4×D3—124no—
641C4×D3—124no—
642C2×C32C2×#12311yescharacteristic
643C2×C32#52911yescharacteristic
644C2×C32#53811yescharacteristic
645C2×C32#54611yescharacteristic
646C2×C32#54611yescharacteristic
647C2×C32#55311yescharacteristic
648C2×C32#55311yescharacteristic
649C3×D3—24no—
650C3×D3—42no—
651C3×D3—81no—
652C24—31no—
653C24—31no—
654C24—31no—
655C2×D4—34no—
656C2×D4—62no—
657C2×D4—62no—
658C2×D4—62no—
659C2×D4—62no—
660C2×D4—62no—
661C2×D4—62no—
662C2×D4—62no—
663C2×D4—121no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—121no—
676C22×C4—182no—
677C22×C4—182no—
678C22×C4—182no—
679C22×C4—182no—
680C22×C4—182no—
681C22×C4—361no—
682C22×C4—361no—
683C22×C4—361no—
684C22×C4—361no—
685C22×C4C2×D3211yescharacteristic
686C22×C4C2×D3211yescharacteristic
687C22×C4C2×D3211yescharacteristic
688C4⋊C4—22no—
689C4⋊C4—62no—
690C4⋊C4—182no—
691C4⋊C4—361no—
692C22⋊C4—62no—
693C22⋊C4—62no—
694C22⋊C4—182no—
695C22⋊C4—182no—
696C22⋊C4—182no—
697C22⋊C4—182no—
698C22⋊C4—361no—
699C22⋊C4—361no—
700C22⋊C4—361no—
701C22⋊C4—361no—
702C22⋊C4—361no—
703C42—62no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—34no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3C2×#23511yescharacteristic
733C22×C3C2×D3×D411yescharacteristic
734C22×C3C2×#23711yescharacteristic
735C22×C3C2×#23711yescharacteristic
736C22×C3C2×#23711yescharacteristic
737C22×C3#100411yescharacteristic
738C22×C3C2×#23911yescharacteristic
739C22×C3D3×#4111yescharacteristic
740C22×C3D3×#4111yescharacteristic
741C22×C3D3×#4111yescharacteristic
742C22×C3#100911yescharacteristic
743C22×C3#100911yescharacteristic
744C22×C3#100911yescharacteristic
745C22×C3C22×#6711yescharacteristic
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3#93514yes—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—42no—
772C3×C4—42no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—62no—
776C3×C4—81no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4—121no—
781Dic3—22no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—41no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—121no—
793Dic3—121no—
794Dic3—241no—
795Dic3—241no—
796Dic3—241no—
797Dic3—241no—
798C32#244411yescharacteristic, complemented, Sylow
799C23—32no—
800C23—32no—
801C23—32no—
802C23—32no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23C22×D3211yescharacteristic
821D4—68no—
822D4—124no—
823D4—124no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—32no—
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—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—124no—
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—181no—
857C2×C4—181no—
858C2×C4—181no—
859C2×C4—364no—
860C2×C4—364no—
861C2×C4—364no—
862C2×C4#379512yes—
863C2×C4D3×#6712yes—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—64no—
872C2×C3—122no—
873C2×C3—241no—
874C2×C3#553011yescharacteristic
875C2×C3#555011yescharacteristic
876C2×C3#558011yescharacteristic
877C2×C3#560011yescharacteristic
878C2×C3#560111yescharacteristic
879C2×C3#561711yescharacteristic
880C2×C3#561811yescharacteristic
881C2×C3#563011yescharacteristic
882C2×C3D3×#12311yescharacteristic
883C2×C3#569511yescharacteristic
884C2×C3#570411yescharacteristic
885C2×C3C2×#93511yescharacteristic
886C2×C3#580611yescharacteristic
887C2×C3#582911yescharacteristic
888D3—24no—
889D3—42no—
890D3—81no—
891C22—34no—
892C22—62no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22C2×#379511yescharacteristic
913C22#6430711yescharacteristic
914C22D3×#23711yescharacteristic
915C22D3×#23711yescharacteristic
916C22D3×#23911yescharacteristic
917C22#6432011yescharacteristic
918C22C2×D3×#6711yescharacteristic
919C4—22no—
920C4—22no—
921C4—41no—
922C4—62no—
923C4—121no—
924C4—121no—
925C4—121no—
926C4—121no—
927C4—361no—
928C4—361no—
929C4—361no—
930C4—361no—
931C3—21no—
932C3#7532011yescharacteristic, complemented
933C3#8265611yescharacteristic, complemented
934C2—64no—
935C2—122no—
936C2—241no—
937C2#1059442611yescharacteristic
938C2#1059443311yescharacteristic
939C2#1059443811yescharacteristic
940C2#1059464611yescharacteristic
941C2#1059488611yescharacteristic
942C2D3×#93511yescharacteristic
943C2#1059542711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×C3×#895C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×D12C2semidirect
3. #10592685C2semidirect
4. C3×#4978C2semidirect
5. #10591376C2semidirect
6. #10591376C2semidirect
7. #10591376C2semidirect
8. #10591376C2semidirect
9. #10591362C2semidirect
10. D3×C3⋊#95C2semidirect
11. #10591315C2semidirect
12. #10591300C2semidirect
13. #10591299C2semidirect
14. #10591279C2semidirect
15. #10591277C2semidirect
72. #4978D3semidirect
798. C32#2444semidirect
932. C3#75320semidirect
933. C3#82656semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×Dic3×D122
#105926852
C3×#49782
#105913762
#105913622
D3×C3⋊#952
#105913152
#105913002
#105912992
#105912792
#105912772
#826563
#753203