Finite Group Databasebeta

← C3×#73481 #11808778

Subgroups — C3×#73481 #11808778

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×C4×#217C211yesmaximal, characteristic, complemented
5C3×#4961C211yesmaximal, characteristic
6C3×#4959C211yesmaximal, characteristic
7C3×#4952C211yesmaximal, characteristic, complemented
8C3×#4947C211yesmaximal, characteristic, complemented
9C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C3×#4932C211yesmaximal, characteristic, complemented
12C3×#4675C211yesmaximal, characteristic, complemented
13C3×#4673C211yesmaximal, characteristic, complemented
14C3×#4660C211yesmaximal, characteristic, complemented
15C3×#4658C211yesmaximal, characteristic, complemented
16C3×#2398—31nomaximal
17#73481C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C3×C4×#67—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×C4×Dic6—24no—
43C32×#95C2211yescharacteristic
44C32×#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×C4×Q8—31no—
56C2×C3×C4×D4—31no—
57C2×C4×#67C2×C311yescharacteristic
58C2×C4×Dic6C2×C311yescharacteristic, complemented
59C3×#400—31no—
60C3×#400—31no—
61C3×#397—31no—
62C3×#397—31no—
63C3×#394—31no—
64C3×#394—31no—
65C3×#393—31no—
66C3×#393—31no—
67C3×C4×C22⋊C4—21no—
68C3×C4×C22⋊C4—31no—
69C3×C4×C22⋊C4—31no—
70C3×C4×C22⋊C4—31no—
71C3×C4×C22⋊C4D311yescharacteristic, complemented
72C3×C4×C22⋊C4C2×C311yescharacteristic, complemented
73C3×#376—31no—
74C4×#217C2×C311yescharacteristic, complemented
75#4961C2×C311yescharacteristic
76#4959C2×C311yescharacteristic
77#4952C2×C311yescharacteristic, complemented
78#4947C2×C311yescharacteristic, complemented
79C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
80C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
81#4932C2×C311yescharacteristic, complemented
82#4675C2×C311yescharacteristic, complemented
83#4673C2×C311yescharacteristic, complemented
84#4660C2×C311yescharacteristic, complemented
85#4658C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4—22no—
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×Dic6—22no—
111C2×C3×Dic6—22no—
112C2×C3×Dic6—22no—
113C32×C22⋊C4—22no—
114C32×C22⋊C4—22no—
115C32×C42—22no—
116C32×C42—22no—
117C3×#217—22no—
118C3×#217—22no—
119C3×#217—22no—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—22no—
122C3×(C2×D3)⋊C4—22no—
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4—22no—
125C3×C4⋊Dic3—22no—
126C3×Dic3⋊C4—22no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4—22no—
129C3×C4×Dic3—22no—
130C3×C4×Dic3—22no—
131C3×C4×Dic3D414yes—
132#2398—31noSylow
133C22×C3×Q8—31no—
134C22×C3×D4—31no—
135C23×C3×C4—21no—
136C23×C3×C4—31no—
137C23×C3×C4C2×D311yescharacteristic
138C23×C3×C4C22×C311yescharacteristic
139C22×#67C22×C311yescharacteristic
140C22×C4×D3C22×C311yescharacteristic
141C22×Dic6C22×C311yescharacteristic
142C3×C4×Q8—64no—
143C3×C4×D4—64no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4C2×D311yescharacteristic
159C2×C3×C22⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4C22×C311yescharacteristic
161C2×C3×C22⋊C4C22×C311yescharacteristic
162C2×C3×C42—21no—
163C2×C3×C42—21no—
164C2×C3×C42—31no—
165C2×C3×C42—31no—
166C2×C3×C42—31no—
167C2×C3×C42C2×D311yescharacteristic
168C2×C3×C42C2×D311yescharacteristic
169C2×C3×C42C22×C311yescharacteristic
170C2×C3×C42C22×C311yescharacteristic
171C2×#217C22×C311yescharacteristic
172C2×#217C22×C311yescharacteristic
173C2×#217C22×C311yescharacteristic
174C4×#67—24no—
175C2×(C2×D3)⋊C4C22×C311yescharacteristic
176C2×(C2×D3)⋊C4C22×C311yescharacteristic
177C2×(C2×D3)⋊C4C22×C311yescharacteristic
178C2×(C2×D3)⋊C4C22×C311yescharacteristic
179C2×(C2×D3)⋊C4C22×C311yescharacteristic
180C2×C4⋊Dic3C22×C311yescharacteristic
181C2×Dic3⋊C4C22×C311yescharacteristic
182C2×Dic3⋊C4C22×C311yescharacteristic
183C2×Dic3⋊C4C22×C311yescharacteristic
184C2×C4×Dic3C22×C311yescharacteristic
185C2×C4×Dic3C22×C311yescharacteristic
186C2×C4×Dic3C22×C311yescharacteristic
187C4×Dic6—24no—
188C3×#95—21no—
189C3×#95—21no—
190C3×#95—31no—
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×#95C2×D311yescharacteristic
201C3×#95C2×D311yescharacteristic
202C3×#95C22×C311yescharacteristic
203C3×#95C22×C311yescharacteristic
204C3⋊#95C22×C311yescharacteristic
205C3⋊#95C22×C311yescharacteristic
206C3⋊#95C22×C311yescharacteristic
207C3⋊#95C22×C311yescharacteristic
208C3⋊#95C22×C311yescharacteristic
209C3⋊#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32#4112yes—
221C23×C32C2411yescharacteristic
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#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—44no—
244C2×C32×C4C2×D412yes—
245C2×C32×C4#4112yes—
246C2×C32×C4#4112yes—
247C2×C32×C4#4112yes—
248C3×#67—28no—
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—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×Dic3C2×D412yes—
268C2×C3×Dic3C2×D412yes—
269C2×C3×Dic3#4112yes—
270C3×C4×D3—44no—
271C3×Dic6—28no—
272C2×C4×Q8—31no—
273C2×C4×D4—31no—
274#400—31no—
275#400—31no—
276#397—31no—
277#397—31no—
278#394—31no—
279#394—31no—
280#393—31no—
281#393—31no—
282C4×C22⋊C4—31no—
283C4×C22⋊C4—31no—
284C4×C22⋊C4—31no—
285C4×C22⋊C4C3×D311yescharacteristic, complemented
286#376—31no—
287C24×C3—21no—
288C24×C3—31no—
289C24×C3C22×D311yescharacteristic
290C24×C3C23×C311yescharacteristic
291C23×D3C23×C311yescharacteristic
292C2×C3×Q8—62no—
293C2×C3×Q8—62no—
294C2×C3×Q8—62no—
295C2×C3×D4—62no—
296C2×C3×D4—62no—
297C2×C3×D4—62no—
298C22×C3×C4—24no—
299C22×C3×C4—22no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—42no—
319C22×C3×C4—42no—
320C22×C3×C4—62no—
321C22×C3×C4—62no—
322C22×C3×C4—62no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C23×C311yescharacteristic
330C22×C3×C4C23×C311yescharacteristic
331C22×C3×C4C23×C311yescharacteristic
332C22×C3×C4C23×C311yescharacteristic
333C22×C3×C4C23×C311yescharacteristic
334C22×C3×C4C23×C311yescharacteristic
335C2×#67—22no—
336C2×#67—22no—
337C2×#67—22no—
338C22×Dic3C23×C311yescharacteristic
339C22×Dic3C23×C311yescharacteristic
340C22×Dic3C23×C311yescharacteristic
341C22×Dic3C23×C311yescharacteristic
342C22×Dic3C23×C311yescharacteristic
343C22×Dic3C23×C311yescharacteristic
344C22×Dic3C23×C311yescharacteristic
345C2×C4×D3—22no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×Dic6—22no—
349C2×Dic6—22no—
350C2×Dic6—22no—
351C3×C4⋊C4—62no—
352C3×C4⋊C4—62no—
353C3×C4⋊C4—62no—
354C3×C4⋊C4—62no—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—24no—
357C3×C22⋊C4—22no—
358C3×C22⋊C4—22no—
359C3×C22⋊C4—22no—
360C3×C22⋊C4—22no—
361C3×C22⋊C4—62no—
362C3×C22⋊C4—62no—
363C3×C22⋊C4—62no—
364C3×C22⋊C4—62no—
365C3×C22⋊C4—62no—
366C3×C22⋊C4—62no—
367C3×C22⋊C4—62no—
368C3×C22⋊C4—62no—
369C3×C42—22no—
370C3×C42—22no—
371C3×C42—22no—
372C3×C42—22no—
373C3×C42—34no—
374C3×C42—42no—
375C3×C42—42no—
376C3×C42—62no—
377C3×C42—62no—
378#217—22no—
379#217—22no—
380#217—22no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—22no—
384(C2×D3)⋊C4—22no—
385(C2×D3)⋊C4—22no—
386C4⋊Dic3—22no—
387Dic3⋊C4—22no—
388Dic3⋊C4—22no—
389Dic3⋊C4—22no—
390C4×Dic3—22no—
391C4×Dic3—22no—
392C4×Dic3C3×D414yes—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C22×C32C2×#4111yescharacteristic
405C22×C32C2×#4111yescharacteristic
406C22×C32C2×#4111yescharacteristic
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—22no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4#12414yes—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×Q8—31no—
428C22×D4—31no—
429C23×C4—31no—
430C23×C4C2×C3×D311yescharacteristic
431C4×Q8—64no—
432C4×D4—64no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4C2×C3×D311yescharacteristic
446C2×C22⋊C4C2×C3×D311yescharacteristic
447C2×C42—31no—
448C2×C42—31no—
449C2×C42—31no—
450C2×C42C2×C3×D311yescharacteristic
451C2×C42C2×C3×D311yescharacteristic
452#95—31no—
453#95—31no—
454#95—31no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95—31no—
459#95—31no—
460#95—31no—
461#95—31no—
462#95C2×C3×D311yescharacteristic
463#95C2×C3×D311yescharacteristic
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—22no—
480C23×C3—32no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3#23512yes—
492C23×C3C3×#4112yes—
493C23×C3C23×D311yescharacteristic
494C23×C3C24×C311yescharacteristic
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3C3×#4112yes—
502C3×Q8—68no—
503C3×D4—68no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—48no—
554C2×C3×C4—44no—
555C2×C3×C4—44no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
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—124no—
575C2×C3×C4#23512yes—
576C2×C3×C4#23512yes—
577C2×C3×C4D3×D412yes—
578C2×C3×C4#23712yes—
579C2×C3×C4C2×C3×D412yes—
580C2×C3×C4C3×#4112yes—
581C2×C3×C4C3×#4112yes—
582C2×C3×C4C3×#4112yes—
583#67—28no—
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—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3C2×C3×D412yes—
603C2×Dic3C2×C3×D412yes—
604C2×Dic3C3×#4112yes—
605C4×D3—44no—
606Dic6—28no—
607C2×C32—42no—
608C2×C32#52511yescharacteristic
609C2×C32#52511yescharacteristic
610C2×C32C2×#12411yescharacteristic
611C2×C32#52911yescharacteristic
612C2×C32#52911yescharacteristic
613C2×C32#52911yescharacteristic
614C2×C32#52911yescharacteristic
615C3×D3—42no—
616C24—31no—
617C24C22×C3×D311yescharacteristic
618C2×Q8—62no—
619C2×Q8—62no—
620C2×Q8—62no—
621C2×D4—62no—
622C2×D4—62no—
623C2×D4—62no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4C22×C3×D311yescharacteristic
638C22×C4C22×C3×D311yescharacteristic
639C22×C4C22×C3×D311yescharacteristic
640C22×C4C22×C3×D311yescharacteristic
641C22×C4C22×C3×D311yescharacteristic
642C22×C4C22×C3×D311yescharacteristic
643C4⋊C4—62no—
644C4⋊C4—62no—
645C4⋊C4—62no—
646C4⋊C4—62no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—62no—
650C22⋊C4—62no—
651C22⋊C4—62no—
652C22⋊C4—62no—
653C22⋊C4—62no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—62no—
657C42—22no—
658C42—22no—
659C42—34no—
660C42—62no—
661C42—62no—
662C22×C3—24no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3C2×#23511yescharacteristic
698C22×C3C2×#23511yescharacteristic
699C22×C3C2×#23511yescharacteristic
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C2×#23711yescharacteristic
702C22×C3D3×#4111yescharacteristic
703C22×C3D3×#4111yescharacteristic
704C22×C3C22×C3×D411yescharacteristic
705C22×C3C2×C3×#4111yescharacteristic
706C22×C3C2×C3×#4111yescharacteristic
707C22×C3C2×C3×#4111yescharacteristic
708C22×C3C2×C3×#4111yescharacteristic
709C22×C3C2×C3×#4111yescharacteristic
710C22×C3C2×C3×#4111yescharacteristic
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—24no—
721C3×C4—42no—
722C3×C4—42no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—121no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4#88514yes—
742C3×C4C3×#12414yes—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—41no—
747Dic3—41no—
748Dic3—41no—
749Dic3—41no—
750C32#239811yescharacteristic, complemented, Sylow
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—32no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23C3×#23512yes—
765C23C23×C3×D311yescharacteristic
766Q8—68no—
767D4—68no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—44no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—124no—
805C2×C4C3×#23512yes—
806C2×C4C3×#23512yes—
807C2×C4C3×D3×D412yes—
808C2×C4C3×#23712yes—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—44no—
817C2×C3—42no—
818C2×C3—42no—
819C2×C3—122no—
820C2×C3#547911yescharacteristic
821C2×C3C2×#88511yescharacteristic
822C2×C3#552811yescharacteristic
823C2×C3#553811yescharacteristic
824C2×C3#554711yescharacteristic
825C2×C3#554711yescharacteristic
826C2×C3#555711yescharacteristic
827C2×C3C3×#52511yescharacteristic
828C2×C3C3×#52511yescharacteristic
829C2×C3C2×C3×#12411yescharacteristic
830C2×C3C3×#52911yescharacteristic
831C2×C3C3×#52911yescharacteristic
832C2×C3C3×#52911yescharacteristic
833C2×C3C3×#52911yescharacteristic
834D3—42no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22C2×C3×#23511yescharacteristic
850C22C2×C3×#23511yescharacteristic
851C22C2×C3×#23511yescharacteristic
852C22C2×C3×D3×D411yescharacteristic
853C22C2×C3×#23711yescharacteristic
854C22C3×D3×#4111yescharacteristic
855C22C3×D3×#4111yescharacteristic
856C4—22no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—62no—
862C4—62no—
863C4—62no—
864C4—121no—
865C4—121no—
866C4—121no—
867C4—121no—
868C4C3×#88514yes—
869C3—21no—
870C3#7348111yescharacteristic, direct product factor
871C3C3×#239811yescharacteristic, complemented
872C2—42no—
873C2—122no—
874C2C3×#547911yescharacteristic
875C2C2×C3×#88511yescharacteristic
876C2C3×#552811yescharacteristic
877C2C3×#553811yescharacteristic
878C2C3×#554711yescharacteristic
879C2C3×#554711yescharacteristic
880C2C3×#555711yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#2398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C32×C4×C22⋊C4C2semidirect
4. C3×C4×#217C2semidirect
7. C3×#4952C2semidirect
8. C3×#4947C2semidirect
9. C3×C4×(C2×D3)⋊C4C2semidirect
10. C3×C4×(C2×D3)⋊C4C2semidirect
11. C3×#4932C2semidirect
12. C3×#4675C2semidirect
13. C3×#4673C2semidirect
14. C3×#4660C2semidirect
15. C3×#4658C2semidirect
17. #73481C3direct (N × H)
58. C2×C4×Dic6C2×C3semidirect
71. C3×C4×C22⋊C4D3semidirect
72. C3×C4×C22⋊C4C2×C3semidirect
74. C4×#217C2×C3semidirect
77. #4952C2×C3semidirect
78. #4947C2×C3semidirect
79. C4×(C2×D3)⋊C4C2×C3semidirect
80. C4×(C2×D3)⋊C4C2×C3semidirect
81. #4932C2×C3semidirect
82. #4675C2×C3semidirect
83. #4673C2×C3semidirect
84. #4660C2×C3semidirect
85. #4658C2×C3semidirect
285. C4×C22⋊C4C3×D3semidirect
750. C32#2398semidirect
870. C3#73481direct (N × H)
871. C3C3×#2398semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×C3×C4×Dic62
C32×C4×C22⋊C42
C3×C4×#2172
C3×#49612
C3×#49592
C3×#49522
C3×#49472
C3×C4×(C2×D3)⋊C42
C3×#49322
C3×#46752
C3×#46732
C3×#46602
C3×#46582
C3×#23983
#734813