Finite Group Databasebeta

← C3×#82357 #11812947

Subgroups — C3×#82357 #11812947

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic
3C3×#5220C211yesmaximal, characteristic, complemented
4C3×#5213C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6C3×#5211C211yesmaximal, characteristic, complemented
7C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4992C211yesmaximal, characteristic, complemented
9C3×#4985C211yesmaximal, characteristic, complemented
10C3×#4959C211yesmaximal, characteristic, complemented
11C3×#4958C211yesmaximal, characteristic, complemented
12C3×#4952C211yesmaximal, characteristic, complemented
13C3×#4946C211yesmaximal, characteristic, complemented
14C3×#4940C211yesmaximal, characteristic, complemented
15C3×#4933C211yesmaximal, characteristic, complemented
16C3×#2444—31nomaximal
17#82357C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C32×C4×D4—24no—
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C42C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C3×#939—24no—
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C2×C3×#121—31no—
56C2×C3×C4×D4—21no—
57C2×C3×C4×D4D311yescharacteristic, complemented
58C2×C3×C4×D4C2×C311yescharacteristic, complemented
59C2×#939C2×C311yescharacteristic
60C3×#400—31no—
61C3×#397—31no—
62C3×#397—31no—
63C3×#394—31no—
64C3×#388—31no—
65C3×#387—31no—
66C3×#386—31no—
67C3×#386—31no—
68C3×#386—31no—
69C3×#386—31no—
70C3×#385—31no—
71C3×#381—31no—
72C2×C3×#95—31no—
73#5220C2×C311yescharacteristic, complemented
74#5213C2×C311yescharacteristic, complemented
75#5213C2×C311yescharacteristic, complemented
76#5211C2×C311yescharacteristic, complemented
77C2×C3⋊#95C2×C311yescharacteristic, complemented
78#4992C2×C311yescharacteristic, complemented
79#4985C2×C311yescharacteristic, complemented
80#4959C2×C311yescharacteristic, complemented
81#4958C2×C311yescharacteristic, complemented
82#4952C2×C311yescharacteristic, complemented
83#4946C2×C311yescharacteristic, complemented
84#4940C2×C311yescharacteristic, complemented
85#4933C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4D414yes—
92C22×C32×C4—22no—
93C22×C32×C4—22no—
94C22×C32×C4—22no—
95C22×C32×C4—22no—
96C22×C32×C4—41no—
97C22×C32×C4—41no—
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—41no—
109C22×C3×Dic3—22no—
110C22×C3×Dic3—22no—
111C22×C3×Dic3—22no—
112C22×C3×Dic3—41no—
113C22×C3×Dic3—41no—
114C22×C3×Dic3—41no—
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C32×C4⋊C4—22no—
123C32×C22⋊C4—22no—
124C32×C22⋊C4—22no—
125C32×C42—22no—
126C3×#217—22no—
127C3×#217—22no—
128C3×#217—41no—
129C3×#217—41no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—41no—
133C3×(C2×D3)⋊C4—41no—
134C3×(C2×D3)⋊C4—41no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—22no—
137C3×Dic3⋊C4—41no—
138#2444—31noSylow
139C22×C3×D4—21no—
140C22×C3×D4—31no—
141C22×C3×D4—31no—
142C22×C3×D4C2×D311yescharacteristic
143C22×C3×D4C22×C311yescharacteristic
144C23×C3×C4—21no—
145C23×C3×C4—21no—
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C23×C3×C4C2×D311yescharacteristic
149C23×C3×C4C2×D311yescharacteristic
150C23×C3×C4C22×C311yescharacteristic
151C23×C3×C4C22×C311yescharacteristic
152C22×#67C22×C311yescharacteristic
153C22×#67C22×C311yescharacteristic
154C23×Dic3C22×C311yescharacteristic
155C23×Dic3C22×C311yescharacteristic
156C3×#121—64no—
157C3×C4×D4—28no—
158C3×C4×D4—24no—
159C3×C4×D4—24no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4C2×D311yescharacteristic
165C2×C3×C4⋊C4C22×C311yescharacteristic
166C2×C3×C22⋊C4—21no—
167C2×C3×C22⋊C4—21no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4C2×D311yescharacteristic
178C2×C3×C22⋊C4C2×D311yescharacteristic
179C2×C3×C22⋊C4C22×C311yescharacteristic
180C2×C3×C22⋊C4C22×C311yescharacteristic
181C2×C3×C42—21no—
182C2×C3×C42C2×D311yescharacteristic
183C2×C3×C42C22×C311yescharacteristic
184C2×#217C22×C311yescharacteristic
185C2×#217C22×C311yescharacteristic
186C2×#217C22×C311yescharacteristic
187C2×#217C22×C311yescharacteristic
188#939—24no—
189C2×(C2×D3)⋊C4C22×C311yescharacteristic
190C2×(C2×D3)⋊C4C22×C311yescharacteristic
191C2×(C2×D3)⋊C4C22×C311yescharacteristic
192C2×(C2×D3)⋊C4C22×C311yescharacteristic
193C2×(C2×D3)⋊C4C22×C311yescharacteristic
194C2×Dic3⋊C4C22×C311yescharacteristic
195C2×Dic3⋊C4C22×C311yescharacteristic
196C2×Dic3⋊C4C22×C311yescharacteristic
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⋊#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C3⋊#95C22×C311yescharacteristic
215C3⋊#95C22×C311yescharacteristic
216C3⋊#95C22×C311yescharacteristic
217C3⋊#95C22×C311yescharacteristic
218C3⋊#95C22×C311yescharacteristic
219C3⋊#95C22×C311yescharacteristic
220C3⋊#95C22×C311yescharacteristic
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×C32C2×D412yes—
232C23×C32C2×D412yes—
233C23×C32#4112yes—
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×D3—21no—
243C32×D4—28no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—44no—
258C2×C32×C4—44no—
259C2×C32×C4C2×D412yes—
260C2×C32×C4#4112yes—
261C3×#67—44no—
262C3×#67—44no—
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—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—44no—
284C2×C3×Dic3—44no—
285C2×C3×Dic3#4112yes—
286C2×#121—31no—
287C2×C4×D4C3×D311yescharacteristic, complemented
288#400—31no—
289#397—31no—
290#397—31no—
291#394—31no—
292#388—31no—
293#387—31no—
294#386—31no—
295#386—31no—
296#386—31no—
297#386—31no—
298#385—31no—
299#381—31no—
300C2×#95—31no—
301C24×C3—21no—
302C24×C3—21no—
303C24×C3—31no—
304C24×C3C22×D311yescharacteristic
305C24×C3C22×D311yescharacteristic
306C24×C3C23×C311yescharacteristic
307C24×C3C23×C311yescharacteristic
308C23×D3C23×C311yescharacteristic
309C2×C3×D4—24no—
310C2×C3×D4—24no—
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4—22no—
314C2×C3×D4—22no—
315C2×C3×D4—24no—
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—121no—
322C2×C3×D4#6714yes—
323C2×C3×D4C3×D414yes—
324C22×C3×C4—24no—
325C22×C3×C4—24no—
326C22×C3×C4—22no—
327C22×C3×C4—22no—
328C22×C3×C4—22no—
329C22×C3×C4—22no—
330C22×C3×C4—22no—
331C22×C3×C4—22no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—42no—
347C22×C3×C4—42no—
348C22×C3×C4—41no—
349C22×C3×C4—41no—
350C22×C3×C4—41no—
351C22×C3×C4—41no—
352C22×C3×C4—42no—
353C22×C3×C4—42no—
354C22×C3×C4—62no—
355C22×C3×C4—62no—
356C22×C3×C4—62no—
357C22×C3×C4—121no—
358C22×C3×C4—121no—
359C22×C3×C4—121no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C23×C311yescharacteristic
366C22×C3×C4C23×C311yescharacteristic
367C22×C3×C4C23×C311yescharacteristic
368C22×C3×C4C23×C311yescharacteristic
369C22×C3×C4C23×C311yescharacteristic
370C2×#67—22no—
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—22no—
374C2×#67—22no—
375C2×#67—41no—
376C22×Dic3—22no—
377C22×Dic3—22no—
378C22×Dic3—22no—
379C22×Dic3—41no—
380C22×Dic3—41no—
381C22×Dic3—41no—
382C22×Dic3C23×C311yescharacteristic
383C22×Dic3C23×C311yescharacteristic
384C22×Dic3C23×C311yescharacteristic
385C22×Dic3C23×C311yescharacteristic
386C22×Dic3C23×C311yescharacteristic
387C22×Dic3C23×C311yescharacteristic
388C22×Dic3C23×C311yescharacteristic
389C3×C4⋊C4—24no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—62no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4—121no—
395C3×C22⋊C4—24no—
396C3×C22⋊C4—24no—
397C3×C22⋊C4—22no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—62no—
405C3×C22⋊C4—121no—
406C3×C22⋊C4—121no—
407C3×C22⋊C4—121no—
408C3×C22⋊C4—121no—
409C3×C22⋊C4—121no—
410C3×C42—24no—
411C3×C42—22no—
412C3×C42—22no—
413#217—22no—
414#217—22no—
415#217—41no—
416#217—41no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—41no—
420(C2×D3)⋊C4—41no—
421(C2×D3)⋊C4—41no—
422Dic3⋊C4—22no—
423Dic3⋊C4—22no—
424Dic3⋊C4—41no—
425C22×C32—22no—
426C22×C32—22no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32#12314yes—
439C22×C32C22×D411yescharacteristic
440C22×C32C2×#4111yescharacteristic
441C22×C32C2×#4111yescharacteristic
442C22×C32C2×#4111yescharacteristic
443C22×C32C2×#4111yescharacteristic
444C22×C32H(5,𝔽2)11yescharacteristic
445C22×C32H(5,𝔽2)11yescharacteristic
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C32×C4—22no—
454C32×C4—22no—
455C32×C4—41no—
456C32×C4—41no—
457C32×C4—41no—
458C3×Dic3—22no—
459C3×Dic3—41no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C22×D4—31no—
466C22×D4—31no—
467C22×D4C2×C3×D311yescharacteristic
468C23×C4—31no—
469C23×C4—31no—
470C23×C4C2×C3×D311yescharacteristic
471C23×C4C2×C3×D311yescharacteristic
472#121—64no—
473C4×D4—24no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4C2×C3×D311yescharacteristic
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—31no—
484C2×C22⋊C4—31no—
485C2×C22⋊C4—31no—
486C2×C22⋊C4—31no—
487C2×C22⋊C4C2×C3×D311yescharacteristic
488C2×C22⋊C4C2×C3×D311yescharacteristic
489C2×C42C2×C3×D311yescharacteristic
490#95—31no—
491#95—31no—
492#95—31no—
493#95—31no—
494#95—31no—
495#95—31no—
496#95—31no—
497#95—31no—
498#95—31no—
499#95—31no—
500#95—31no—
501#95—31no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—22no—
511C23×C3—22no—
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—21no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
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—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3#23512yes—
545C23×C3#23512yes—
546C23×C3C2×#6712yes—
547C23×C3C2×#6712yes—
548C23×C3C2×C3×D412yes—
549C23×C3C2×C3×D412yes—
550C23×C3C3×#4112yes—
551C23×C3C3×#4112yes—
552C23×C3C23×D311yescharacteristic
553C23×C3C24×C311yescharacteristic
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C3×D4—216no—
562C3×D4—28no—
563C3×D4—28no—
564C3×D4—124no—
565C3×D4—124no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—32no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—44no—
609C2×C3×C4—44no—
610C2×C3×C4—44no—
611C2×C3×C4—44no—
612C2×C3×C4—48no—
613C2×C3×C4—48no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—124no—
635C2×C3×C4—124no—
636C2×C3×C4#23712yes—
637C2×C3×C4C2×#6712yes—
638C2×C3×C4C2×C3×D412yes—
639C2×C3×C4C3×#4112yes—
640#67—44no—
641#67—44no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—44no—
663C2×Dic3—44no—
664C2×Dic3C3×#4112yes—
665C2×C32—24no—
666C2×C32—42no—
667C2×C32C2×#12311yescharacteristic
668C2×C32#52911yescharacteristic
669C2×C32#53811yescharacteristic
670C2×C32#54611yescharacteristic
671C2×C32#54611yescharacteristic
672C2×C32#55311yescharacteristic
673C2×C32#55311yescharacteristic
674C3×D3—81no—
675C24—31no—
676C24C22×C3×D311yescharacteristic
677C24C22×C3×D311yescharacteristic
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—62no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—121no—
686C2×D4C3×#6714yes—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—121no—
704C22×C4—121no—
705C22×C4—121no—
706C22×C4C22×C3×D311yescharacteristic
707C22×C4C22×C3×D311yescharacteristic
708C22×C4C22×C3×D311yescharacteristic
709C22×C4C22×C3×D311yescharacteristic
710C22×C4C22×C3×D311yescharacteristic
711C4⋊C4—22no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—121no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C22⋊C4—121no—
722C22⋊C4—121no—
723C22⋊C4—121no—
724C22⋊C4—121no—
725C22⋊C4—121no—
726C42—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—24no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—24no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3#92914yes—
782C22×C3C3×#12314yes—
783C22×C3C2×#23511yescharacteristic
784C22×C3C2×#23511yescharacteristic
785C22×C3C2×#23711yescharacteristic
786C22×C3#100411yescharacteristic
787C22×C3D3×#4111yescharacteristic
788C22×C3#100911yescharacteristic
789C22×C3C22×#6711yescharacteristic
790C22×C3C22×C3×D411yescharacteristic
791C22×C3C2×C3×#4111yescharacteristic
792C22×C3C2×C3×#4111yescharacteristic
793C22×C3C2×C3×#4111yescharacteristic
794C22×C3C2×C3×#4111yescharacteristic
795C22×C3C3×H(5,𝔽2)11yescharacteristic
796C22×C3C3×H(5,𝔽2)11yescharacteristic
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3—41no—
804C3×C4—24no—
805C3×C4—24no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—42no—
813C3×C4—41no—
814C3×C4—41no—
815C3×C4—41no—
816C3×C4—41no—
817C3×C4—41no—
818C3×C4—41no—
819C3×C4—62no—
820C3×C4—121no—
821C3×C4—121no—
822C3×C4—121no—
823C3×C4—121no—
824C3×C4—121no—
825C3×C4—121no—
826Dic3—22no—
827Dic3—41no—
828Dic3—41no—
829Dic3—41no—
830Dic3—41no—
831Dic3—41no—
832Dic3—41no—
833C32#244411yescharacteristic, complemented, Sylow
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23C3×#23512yes—
852C23C3×#23512yes—
853C23C2×C3×#6712yes—
854C23C2×C3×#6712yes—
855C23C23×C3×D311yescharacteristic
856D4—28no—
857D4—124no—
858D4—124no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—32no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—124no—
896C2×C4—124no—
897C2×C4C3×#23712yes—
898C2×C4C2×C3×#6712yes—
899C2×C3—24no—
900C2×C3—24no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—44no—
909C2×C3—44no—
910C2×C3—42no—
911C2×C3—42no—
912C2×C3—241no—
913C2×C3#553811yescharacteristic
914C2×C3#554011yescharacteristic
915C2×C3#556011yescharacteristic
916C2×C3#556511yescharacteristic
917C2×C3C2×#92911yescharacteristic
918C2×C3#580611yescharacteristic
919C2×C3#582911yescharacteristic
920C2×C3C2×C3×#12311yescharacteristic
921C2×C3C3×#52911yescharacteristic
922C2×C3C3×#53811yescharacteristic
923C2×C3C3×#54611yescharacteristic
924C2×C3C3×#54611yescharacteristic
925C2×C3C3×#55311yescharacteristic
926C2×C3C3×#55311yescharacteristic
927D3—81no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22C3×#92914yes—
949C22C2×C3×#23511yescharacteristic
950C22C2×C3×#23511yescharacteristic
951C22C2×C3×#23711yescharacteristic
952C22C3×#100411yescharacteristic
953C22C3×D3×#4111yescharacteristic
954C22C3×#100911yescharacteristic
955C22C22×C3×#6711yescharacteristic
956C4—22no—
957C4—22no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—62no—
962C4—121no—
963C4—121no—
964C4—121no—
965C4—121no—
966C4—121no—
967C4—121no—
968C3—21no—
969C3#8235711yescharacteristic, direct product factor
970C3C3×#244411yescharacteristic, complemented
971C2—24no—
972C2—42no—
973C2—241no—
974C2C3×#553811yescharacteristic
975C2C3×#554011yescharacteristic
976C2C3×#556011yescharacteristic
977C2C3×#556511yescharacteristic
978C2C2×C3×#92911yescharacteristic
979C2C3×#580611yescharacteristic
980C2C3×#582911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#939C2
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C3×#5220C2semidirect
4. C3×#5213C2semidirect
5. C3×#5213C2semidirect
6. C3×#5211C2semidirect
7. C2×C3×C3⋊#95C2semidirect
8. C3×#4992C2semidirect
9. C3×#4985C2semidirect
10. C3×#4959C2semidirect
11. C3×#4958C2semidirect
12. C3×#4952C2semidirect
13. C3×#4946C2semidirect
14. C3×#4940C2semidirect
15. C3×#4933C2semidirect
17. #82357C3direct (N × H)
57. C2×C3×C4×D4D3semidirect
58. C2×C3×C4×D4C2×C3semidirect
73. #5220C2×C3semidirect
74. #5213C2×C3semidirect
75. #5213C2×C3semidirect
76. #5211C2×C3semidirect
77. C2×C3⋊#95C2×C3semidirect
78. #4992C2×C3semidirect
79. #4985C2×C3semidirect
80. #4959C2×C3semidirect
81. #4958C2×C3semidirect
82. #4952C2×C3semidirect
83. #4946C2×C3semidirect
84. #4940C2×C3semidirect
85. #4933C2×C3semidirect
287. C2×C4×D4C3×D3semidirect
833. C32#2444semidirect
969. C3#82357direct (N × H)
970. C3C3×#2444semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9392
C3×#52202
C3×#52132
C3×#52112
C2×C3×C3⋊#952
C3×#49922
C3×#49852
C3×#49592
C3×#49582
C3×#49522
C3×#49462
C3×#49402
C3×#49332
C3×#24443
#823573