Finite Group Databasebeta

← C3×#83075 #11807376

Subgroups — C3×#83075 #11807376

Order 1152.

1115 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic
2C3×#4984C211yesmaximal, characteristic, complemented
3C3×#4980C211yesmaximal, characteristic, complemented
4C3×#4980C211yesmaximal, characteristic, complemented
5C3×#4980C211yesmaximal, characteristic, complemented
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C3×#4951C211yesmaximal, characteristic
9C3×#4951C211yesmaximal, characteristic
10C3×#4951C211yesmaximal, characteristic
11C3×#4950C211yesmaximal, characteristic
12C3×Dic3×C22⋊C4C211yesmaximal, characteristic
13C3×Dic3×C22⋊C4C211yesmaximal, characteristic
14C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
15C3×#4932C211yesmaximal, characteristic, complemented
16C3×#2373—31nomaximal
17#83075C311yesmaximal, characteristic, direct product factor
18C23×C3×Dic3C2211yescharacteristic
19C32×#126C418yescomplemented
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C42C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
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
54C2×C3×#126—21no—
55C2×C3×#126D311yescharacteristic
56C2×C3×#126C2×C311yescharacteristic
57C3×#389—31no—
58C3×#388—31no—
59C3×#388—31no—
60C3×#388—31no—
61C3×#387—31no—
62C3×#387—31no—
63C3×#387—31no—
64C3×#385—31no—
65C3×C4×C4⋊C4—31no—
66C3×C4×C4⋊C4—31no—
67C3×C4×C4⋊C4—31no—
68C3×C4×C22⋊C4—31no—
69C3×C4×C22⋊C4—31no—
70C3×#376—31no—
71#4984C2×C311yescharacteristic, complemented
72#4980C2×C311yescharacteristic, complemented
73#4980C2×C311yescharacteristic, complemented
74#4980C2×C311yescharacteristic, complemented
75Dic3×C4⋊C4C2×C311yescharacteristic, complemented
76Dic3×C4⋊C4C2×C311yescharacteristic, complemented
77#4951C2×C311yescharacteristic
78#4951C2×C311yescharacteristic
79#4951C2×C311yescharacteristic
80#4950C2×C311yescharacteristic
81Dic3×C22⋊C4C2×C311yescharacteristic
82Dic3×C22⋊C4C2×C311yescharacteristic
83C4×C4⋊Dic3C2×C311yescharacteristic, complemented
84#4932C2×C311yescharacteristic, complemented
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
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
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C32×C4⋊C4C2×C414yescomplemented
104C32×C4⋊C4C2×C414yescomplemented
105C32×C4⋊C4C2×C414yescomplemented
106C32×C22⋊C4C2×C414yes—
107C32×C22⋊C4C2×C414yes—
108C32×C22⋊C4C2×C414yes—
109C32×C42C2×C414yescomplemented
110C3×#217—22no—
111C3×#217—22no—
112C3×#217—41no—
113C3×C4⋊Dic3—22no—
114C3×C4⋊Dic3—22no—
115C3×C4⋊Dic3—22no—
116C3×C4⋊Dic3—22no—
117C3×C4⋊Dic3—41no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120C3×C4×Dic3—22no—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—41no—
123C3×C4×Dic3—41no—
124C3×C4×Dic3—41no—
125#2373—31noSylow
126C23×C3×C4—31no—
127C23×Dic3C22×C311yescharacteristic
128C3×#126—28no—
129C3×#126Dic318yescomplemented
130C3×#126C3×C418yescomplemented
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4C2×D311yescharacteristic
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C4⋊C4C2×D311yescharacteristic
142C2×C3×C4⋊C4C22×C311yescharacteristic
143C2×C3×C4⋊C4C22×C311yescharacteristic
144C2×C3×C4⋊C4C22×C311yescharacteristic
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4C2×D311yescharacteristic
152C2×C3×C22⋊C4C2×D311yescharacteristic
153C2×C3×C22⋊C4C2×D311yescharacteristic
154C2×C3×C22⋊C4C22×C311yescharacteristic
155C2×C3×C22⋊C4C22×C311yescharacteristic
156C2×C3×C22⋊C4C22×C311yescharacteristic
157C2×C3×C42—21no—
158C2×C3×C42—31no—
159C2×C3×C42—31no—
160C2×C3×C42—31no—
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×C3×C42—31no—
164C2×C3×C42—31no—
165C2×C3×C42C2×D311yescharacteristic
166C2×C3×C42C22×C311yescharacteristic
167C2×#217C22×C311yescharacteristic
168C2×#217C22×C311yescharacteristic
169C2×#217C22×C311yescharacteristic
170C2×C4⋊Dic3C22×C311yescharacteristic
171C2×C4⋊Dic3C22×C311yescharacteristic
172C2×C4⋊Dic3C22×C311yescharacteristic
173C2×C4⋊Dic3C22×C311yescharacteristic
174C2×C4⋊Dic3C22×C311yescharacteristic
175C2×C4×Dic3C22×C311yescharacteristic
176C2×C4×Dic3C22×C311yescharacteristic
177C2×C4×Dic3C22×C311yescharacteristic
178C2×C4×Dic3C22×C311yescharacteristic
179C2×C4×Dic3C22×C311yescharacteristic
180C2×C4×Dic3C22×C311yescharacteristic
181C2×C4×Dic3C22×C311yescharacteristic
182C3×#95—31no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95—31no—
194C3⋊#95C22×C311yescharacteristic
195C3⋊#95C22×C311yescharacteristic
196C3⋊#95C22×C311yescharacteristic
197C3⋊#95C22×C311yescharacteristic
198C3⋊#95C22×C311yescharacteristic
199C3⋊#95C22×C311yescharacteristic
200C3⋊#95C22×C311yescharacteristic
201C3⋊#95C22×C311yescharacteristic
202C3⋊#95C22×C311yescharacteristic
203C3⋊#95C22×C311yescharacteristic
204C3⋊#95C22×C311yescharacteristic
205C3⋊#95C22×C311yescharacteristic
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32C22×C412yes—
213C23×C32C2411yescharacteristic
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4C22×C412yes—
227C2×C32×C4C22×C412yes—
228C2×C32×C4C22×C412yes—
229C2×C32×C4C22×C412yes—
230C2×C32×C4C22×C412yes—
231C2×C32×C4C22×C412yes—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—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×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—44no—
253C2×C3×Dic3#4112yes—
254C2×C3×Dic3#4112yes—
255C2×C3×Dic3#4112yes—
256C2×C3×Dic3#4112yes—
257C2×#126C3×D311yescharacteristic
258#389—31no—
259#388—31no—
260#388—31no—
261#388—31no—
262#387—31no—
263#387—31no—
264#387—31no—
265#385—31no—
266C4×C4⋊C4—31no—
267C4×C4⋊C4—31no—
268C4×C4⋊C4—31no—
269C4×C22⋊C4—31no—
270C4×C22⋊C4—31no—
271#376—31no—
272C24×C3—21no—
273C24×C3C22×D311yescharacteristic
274C24×C3C23×C311yescharacteristic
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—62no—
290C22×C3×C4—62no—
291C22×C3×C4—121no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C23×C311yescharacteristic
299C22×C3×C4C23×C311yescharacteristic
300C22×C3×C4C23×C311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C22×C3×C4C23×C311yescharacteristic
303C22×C3×C4C23×C311yescharacteristic
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—41no—
307C22×Dic3C23×C311yescharacteristic
308C22×Dic3C23×C311yescharacteristic
309C22×Dic3C23×C311yescharacteristic
310C22×Dic3C23×C311yescharacteristic
311C22×Dic3C23×C311yescharacteristic
312C22×Dic3C23×C311yescharacteristic
313C22×Dic3C23×C311yescharacteristic
314C22×Dic3C23×C311yescharacteristic
315C3×C4⋊C4—24no—
316C3×C4⋊C4—24no—
317C3×C4⋊C4—24no—
318C3×C4⋊C4—62no—
319C3×C4⋊C4—62no—
320C3×C4⋊C4—62no—
321C3×C4⋊C4—62no—
322C3×C4⋊C4—121no—
323C3×C4⋊C4C2×Dic314yescomplemented
324C3×C4⋊C4C2×Dic314yescomplemented
325C3×C4⋊C4C2×Dic314yescomplemented
326C3×C4⋊C4C2×C3×C414yescomplemented
327C3×C4⋊C4C2×C3×C414yescomplemented
328C3×C4⋊C4C2×C3×C414yescomplemented
329C3×C22⋊C4—24no—
330C3×C22⋊C4—24no—
331C3×C22⋊C4—24no—
332C3×C22⋊C4—62no—
333C3×C22⋊C4—62no—
334C3×C22⋊C4—121no—
335C3×C22⋊C4C2×Dic314yes—
336C3×C22⋊C4C2×Dic314yes—
337C3×C22⋊C4C2×Dic314yes—
338C3×C22⋊C4C2×C3×C414yes—
339C3×C22⋊C4C2×C3×C414yes—
340C3×C22⋊C4C2×C3×C414yes—
341C3×C42—24no—
342C3×C42—62no—
343C3×C42—62no—
344C3×C42—62no—
345C3×C42—62no—
346C3×C42—121no—
347C3×C42—121no—
348C3×C42—121no—
349C3×C42C2×Dic314yescomplemented
350C3×C42C2×C3×C414yescomplemented
351#217—22no—
352#217—22no—
353#217—41no—
354C4⋊Dic3—22no—
355C4⋊Dic3—22no—
356C4⋊Dic3—22no—
357C4⋊Dic3—22no—
358C4⋊Dic3—41no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—22no—
362C4×Dic3—22no—
363C4×Dic3—41no—
364C4×Dic3—41no—
365C4×Dic3—41no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—41no—
370C22×C32—41no—
371C22×C32—41no—
372C22×C32—41no—
373C22×C32C23×C411yescharacteristic
374C22×C32C2×#4111yescharacteristic
375C22×C32C2×#4111yescharacteristic
376C22×C32C2×#4111yescharacteristic
377C22×C32C2×#4111yescharacteristic
378C22×C32H(5,𝔽2)11yescharacteristic
379C22×C322−1+411yescharacteristic
380C32×C4—22no—
381C32×C4—22no—
382C32×C4—22no—
383C32×C4—22no—
384C32×C4—22no—
385C32×C4—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C3×Dic3—22no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C23×C4—31no—
395#126C3×Dic318yescomplemented
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4C2×C3×D311yescharacteristic
402C2×C4⋊C4C2×C3×D311yescharacteristic
403C2×C4⋊C4C2×C3×D311yescharacteristic
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4C2×C3×D311yescharacteristic
408C2×C22⋊C4C2×C3×D311yescharacteristic
409C2×C22⋊C4C2×C3×D311yescharacteristic
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—31no—
417C2×C42C2×C3×D311yescharacteristic
418#95—31no—
419#95—31no—
420#95—31no—
421#95—31no—
422#95—31no—
423#95—31no—
424#95—31no—
425#95—31no—
426#95—31no—
427#95—31no—
428#95—31no—
429#95—31no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—22no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3C22×Dic312yes—
451C23×C3C22×C3×C412yes—
452C23×C3C23×D311yescharacteristic
453C23×C3C24×C311yescharacteristic
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—124no—
521C2×C3×C4C22×Dic312yes—
522C2×C3×C4C22×Dic312yes—
523C2×C3×C4C22×Dic312yes—
524C2×C3×C4C22×Dic312yes—
525C2×C3×C4C22×Dic312yes—
526C2×C3×C4C22×Dic312yes—
527C2×C3×C4C22×C3×C412yes—
528C2×C3×C4C22×C3×C412yes—
529C2×C3×C4C22×C3×C412yes—
530C2×C3×C4C22×C3×C412yes—
531C2×C3×C4C22×C3×C412yes—
532C2×C3×C4C22×C3×C412yes—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
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—21no—
552C2×Dic3—21no—
553C2×Dic3—44no—
554C2×Dic3C3×#4112yes—
555C2×Dic3C3×#4112yes—
556C2×Dic3C3×#4112yes—
557C2×Dic3C3×#4112yes—
558C2×C32—42no—
559C2×C32C4×#4111yescharacteristic
560C2×C32C4×#4111yescharacteristic
561C2×C32#52011yescharacteristic
562C2×C32#55111yescharacteristic
563C2×C32#55211yescharacteristic
564C2×C32#55311yescharacteristic
565C2×C32#55611yescharacteristic
566C24C22×C3×D311yescharacteristic
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—121no—
578C22×C4C22×C3×D311yescharacteristic
579C22×C4C22×C3×D311yescharacteristic
580C22×C4C22×C3×D311yescharacteristic
581C22×C4C22×C3×D311yescharacteristic
582C22×C4C22×C3×D311yescharacteristic
583C22×C4C22×C3×D311yescharacteristic
584C4⋊C4—62no—
585C4⋊C4—62no—
586C4⋊C4—62no—
587C4⋊C4—62no—
588C4⋊C4—121no—
589C4⋊C4C2×C3×Dic314yescomplemented
590C4⋊C4C2×C3×Dic314yescomplemented
591C4⋊C4C2×C3×Dic314yescomplemented
592C22⋊C4—62no—
593C22⋊C4—62no—
594C22⋊C4—121no—
595C22⋊C4C2×C3×Dic314yes—
596C22⋊C4C2×C3×Dic314yes—
597C22⋊C4C2×C3×Dic314yes—
598C42—62no—
599C42—62no—
600C42—62no—
601C42—62no—
602C42—121no—
603C42—121no—
604C42—121no—
605C42C2×C3×Dic314yescomplemented
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3D3×#4111yescharacteristic
635C22×C3D3×#4111yescharacteristic
636C22×C3D3×#4111yescharacteristic
637C22×C3D3×#4111yescharacteristic
638C22×C3#100911yescharacteristic
639C22×C3#101011yescharacteristic
640C22×C3C23×Dic311yescharacteristic
641C22×C3C23×C3×C411yescharacteristic
642C22×C3C2×C3×#4111yescharacteristic
643C22×C3C2×C3×#4111yescharacteristic
644C22×C3C2×C3×#4111yescharacteristic
645C22×C3C2×C3×#4111yescharacteristic
646C22×C3C3×H(5,𝔽2)11yescharacteristic
647C22×C3C3×2−1+411yescharacteristic
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—62no—
667C3×C4—62no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674Dic3—22no—
675Dic3—22no—
676Dic3—22no—
677Dic3—22no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682C32#237311yescharacteristic, complemented, Sylow
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23C22×C3×Dic312yes—
690C23C23×C3×D311yescharacteristic
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—124no—
728C2×C4C22×C3×Dic312yes—
729C2×C4C22×C3×Dic312yes—
730C2×C4C22×C3×Dic312yes—
731C2×C4C22×C3×Dic312yes—
732C2×C4C22×C3×Dic312yes—
733C2×C4C22×C3×Dic312yes—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—42no—
743C2×C3—82no—
744C2×C3#570211yescharacteristic
745C2×C3#570511yescharacteristic
746C2×C3#570811yescharacteristic
747C2×C3#570911yescharacteristic
748C2×C3Dic3×#4111yescharacteristic
749C2×C3Dic3×#4111yescharacteristic
750C2×C3#582711yescharacteristic
751C2×C3C3×C4×#4111yescharacteristic
752C2×C3C3×C4×#4111yescharacteristic
753C2×C3C3×#52011yescharacteristic
754C2×C3C3×#55111yescharacteristic
755C2×C3C3×#55211yescharacteristic
756C2×C3C3×#55311yescharacteristic
757C2×C3C3×#55611yescharacteristic
758C22—22no—
759C22—22no—
760C22—22no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22C3×D3×#4111yescharacteristic
766C22C3×D3×#4111yescharacteristic
767C22C3×D3×#4111yescharacteristic
768C22C3×D3×#4111yescharacteristic
769C22C3×#100911yescharacteristic
770C22C3×#101011yescharacteristic
771C22C23×C3×Dic311yescharacteristic
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—62no—
779C4—62no—
780C4—62no—
781C4—62no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—121no—
786C3—21no—
787C3#8307511yescharacteristic, direct product factor
788C3C3×#237311yescharacteristic, complemented
789C2—42no—
790C2C3×#570211yescharacteristic
791C2C3×#570511yescharacteristic
792C2C3×#570811yescharacteristic
793C2C3×#570911yescharacteristic
794C2C3×Dic3×#4111yescharacteristic
795C2C3×Dic3×#4111yescharacteristic
796C2C3×#582711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#126C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC2×C3×#126D3
hypocenterC3C3×#2373
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#126

Complements

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

NH ≅ G/Ntype
2. C3×#4984C2semidirect
3. C3×#4980C2semidirect
4. C3×#4980C2semidirect
5. C3×#4980C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
14. C3×C4×C4⋊Dic3C2semidirect
15. C3×#4932C2semidirect
17. #83075C3direct (N × H)
19. C32×#126C4semidirect
71. #4984C2×C3semidirect
72. #4980C2×C3semidirect
73. #4980C2×C3semidirect
74. #4980C2×C3semidirect
75. Dic3×C4⋊C4C2×C3semidirect
76. Dic3×C4⋊C4C2×C3semidirect
83. C4×C4⋊Dic3C2×C3semidirect
84. #4932C2×C3semidirect
103. C32×C4⋊C4C2×C4semidirect
104. C32×C4⋊C4C2×C4semidirect
105. C32×C4⋊C4C2×C4semidirect
109. C32×C42C2×C4semidirect
129. C3×#126Dic3semidirect
130. C3×#126C3×C4semidirect
323. C3×C4⋊C4C2×Dic3semidirect
324. C3×C4⋊C4C2×Dic3semidirect
325. C3×C4⋊C4C2×Dic3semidirect
326. C3×C4⋊C4C2×C3×C4semidirect
327. C3×C4⋊C4C2×C3×C4semidirect
328. C3×C4⋊C4C2×C3×C4semidirect
349. C3×C42C2×Dic3semidirect
350. C3×C42C2×C3×C4semidirect
395. #126C3×Dic3semidirect
589. C4⋊C4C2×C3×Dic3semidirect
590. C4⋊C4C2×C3×Dic3semidirect
591. C4⋊C4C2×C3×Dic3semidirect
605. C42C2×C3×Dic3semidirect
682. C32#2373semidirect
787. C3#83075direct (N × H)
788. C3C3×#2373semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1262
C3×#49842
C3×#49802
C3×Dic3×C4⋊C42
C3×#49512
C3×#49502
C3×Dic3×C22⋊C42
C3×C4×C4⋊Dic32
C3×#49322
C3×#23733
#830753