Finite Group Databasebeta

← C3×#77282 #11808661

Subgroups — C3×#77282 #11808661

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2C2×C3×#877C211yesmaximal, characteristic
3C32×#396C211yesmaximal, characteristic
4C3×#4982C211yesmaximal, characteristic, complemented
5C3×#4981C211yesmaximal, characteristic, complemented
6C3×#4979C211yesmaximal, characteristic, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
9C3×#4949C211yesmaximal, characteristic
10C3×#4948C211yesmaximal, characteristic
11C3×#4947C211yesmaximal, characteristic
12C3×Dic3×C22⋊C4C211yesmaximal, characteristic
13C3×Dic3×C22⋊C4C211yesmaximal, characteristic
14C3×#4658C211yesmaximal, characteristic, complemented
15C3×#4649C211yesmaximal, characteristic, complemented
16C3×#2396—31nomaximal
17#77282C311yesmaximal, characteristic, direct product factor
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
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×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#887—24no—
44C3×#877—24no—
45C32×#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×#117—31no—
57C2×#887C2×C311yescharacteristic, complemented
58C2×#877C2×C311yescharacteristic
59C3×#400—31no—
60C3×#399—31no—
61C3×#398—31no—
62C3×#398—31no—
63C3×#396—21no—
64C3×#396—31no—
65C3×#396D311yescharacteristic
66C3×#396C2×C311yescharacteristic
67C3×#395—31no—
68C3×#393—31no—
69C3×C4×C4⋊C4—31no—
70C3×C4×C4⋊C4—31no—
71C3×C4×C4⋊C4—31no—
72C3×C4×C22⋊C4—31no—
73C3×C4×C22⋊C4—31no—
74#4982C2×C311yescharacteristic, complemented
75#4981C2×C311yescharacteristic, complemented
76#4979C2×C311yescharacteristic, complemented
77Dic3×C4⋊C4C2×C311yescharacteristic, complemented
78Dic3×C4⋊C4C2×C311yescharacteristic, complemented
79#4949C2×C311yescharacteristic
80#4948C2×C311yescharacteristic
81#4947C2×C311yescharacteristic
82Dic3×C22⋊C4C2×C311yescharacteristic
83Dic3×C22⋊C4C2×C311yescharacteristic
84#4658C2×C311yescharacteristic, complemented
85#4649C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3×Dic3—22no—
94C22×C3×Dic3—22no—
95C22×C3×Dic3Q814yescomplemented
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×Dic6—22no—
105C2×C3×Dic6—22no—
106C2×C3×Dic6—22no—
107C32×C4⋊C4—22no—
108C32×C4⋊C4—22no—
109C32×C4⋊C4—22no—
110C32×C22⋊C4—22no—
111C32×C22⋊C4—22no—
112C32×C22⋊C4—22no—
113C3×#217—22no—
114C3×#217—22no—
115C3×#217—22no—
116C3×C4⋊Dic3—22no—
117C3×C4⋊Dic3—22no—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×Dic3⋊C4—22no—
123C3×Dic3⋊C4—22no—
124C3×C4×Dic3—22no—
125C3×C4×Dic3—22no—
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128C3×C4×Dic3—22no—
129C3×C4×Dic3D414yes—
130#2396—31noSylow
131C22×C3×Q8—31no—
132C23×C3×C4—31no—
133C23×Dic3C22×C311yescharacteristic
134C22×Dic6C22×C311yescharacteristic
135C3×C4×Q8—64no—
136C3×#117—64no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C2×D311yescharacteristic
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C4⋊C4C22×C311yescharacteristic
153C2×C3×C4⋊C4C22×C311yescharacteristic
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4C2×D311yescharacteristic
161C2×C3×C22⋊C4C2×D311yescharacteristic
162C2×C3×C22⋊C4C2×D311yescharacteristic
163C2×C3×C22⋊C4C22×C311yescharacteristic
164C2×C3×C22⋊C4C22×C311yescharacteristic
165C2×C3×C22⋊C4C22×C311yescharacteristic
166C2×C3×C42—31no—
167C2×C3×C42—31no—
168C2×C3×C42—31no—
169C2×C3×C42—31no—
170C2×C3×C42—31no—
171C2×C3×C42—31no—
172C2×#217C22×C311yescharacteristic
173C2×#217C22×C311yescharacteristic
174C2×#217C22×C311yescharacteristic
175C2×C4⋊Dic3C22×C311yescharacteristic
176C2×C4⋊Dic3C22×C311yescharacteristic
177C2×Dic3⋊C4C22×C311yescharacteristic
178C2×Dic3⋊C4C22×C311yescharacteristic
179C2×Dic3⋊C4C22×C311yescharacteristic
180C2×Dic3⋊C4C22×C311yescharacteristic
181C2×Dic3⋊C4C22×C311yescharacteristic
182C2×Dic3⋊C4C22×C311yescharacteristic
183C2×C4×Dic3C22×C311yescharacteristic
184C2×C4×Dic3C22×C311yescharacteristic
185C2×C4×Dic3C22×C311yescharacteristic
186C2×C4×Dic3C22×C311yescharacteristic
187C2×C4×Dic3C22×C311yescharacteristic
188C2×C4×Dic3C22×C311yescharacteristic
189#887—24no—
190#877—24no—
191C3×#95—21no—
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×#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
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32C2×Q812yes—
219C23×C32C2411yescharacteristic
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×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
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×C4C2×D412yes—
236C2×C32×C4#4112yes—
237C2×C32×C4#4112yes—
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—28no—
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×Dic3C2×D412yes—
257C2×C3×Dic3C2×D412yes—
258C2×C3×Dic3C2×Q812yes—
259C2×C3×Dic3C2×Q812yes—
260C2×C3×Dic3#4112yes—
261C2×C3×Dic3#4112yes—
262C2×C3×Dic3#4112yes—
263C3×Dic6—28no—
264C2×C4×Q8—31no—
265C2×#117—31no—
266#400—31no—
267#399—31no—
268#398—31no—
269#398—31no—
270#396—31no—
271#396C3×D311yescharacteristic
272#395—31no—
273#393—31no—
274C4×C4⋊C4—31no—
275C4×C4⋊C4—31no—
276C4×C4⋊C4—31no—
277C4×C22⋊C4—31no—
278C4×C22⋊C4—31no—
279C24×C3—21no—
280C24×C3C22×D311yescharacteristic
281C24×C3C23×C311yescharacteristic
282C2×C3×Q8—62no—
283C2×C3×Q8—62no—
284C2×C3×Q8—62no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—31no—
292C22×C3×C4—34no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—62no—
301C22×C3×C4—62no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C23×C311yescharacteristic
309C22×C3×C4C23×C311yescharacteristic
310C22×C3×C4C23×C311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C22×C3×C4C23×C311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3C3×Q814yescomplemented
317C22×Dic3C23×C311yescharacteristic
318C22×Dic3C23×C311yescharacteristic
319C22×Dic3C23×C311yescharacteristic
320C22×Dic3C23×C311yescharacteristic
321C22×Dic3C23×C311yescharacteristic
322C22×Dic3C23×C311yescharacteristic
323C22×Dic3C23×C311yescharacteristic
324C22×Dic3C23×C311yescharacteristic
325C2×Dic6—22no—
326C2×Dic6—22no—
327C2×Dic6—22no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—22no—
331C3×C4⋊C4—22no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—42no—
335C3×C4⋊C4—42no—
336C3×C4⋊C4—42no—
337C3×C4⋊C4—62no—
338C3×C4⋊C4—62no—
339C3×C4⋊C4—62no—
340C3×C4⋊C4—62no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—62no—
345C3×C22⋊C4—22no—
346C3×C22⋊C4—22no—
347C3×C22⋊C4—22no—
348C3×C22⋊C4—22no—
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—42no—
352C3×C22⋊C4—42no—
353C3×C22⋊C4—42no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356C3×C22⋊C4—62no—
357C3×C42—34no—
358C3×C42—62no—
359C3×C42—62no—
360C3×C42—62no—
361C3×C42—62no—
362C3×C42—62no—
363#217—22no—
364#217—22no—
365#217—22no—
366C4⋊Dic3—22no—
367C4⋊Dic3—22no—
368Dic3⋊C4—22no—
369Dic3⋊C4—22no—
370Dic3⋊C4—22no—
371Dic3⋊C4—22no—
372Dic3⋊C4—22no—
373Dic3⋊C4—22no—
374C4×Dic3—22no—
375C4×Dic3—22no—
376C4×Dic3—22no—
377C4×Dic3—22no—
378C4×Dic3—22no—
379C4×Dic3C3×D414yes—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32C22×D411yescharacteristic
388C22×C32C22×Q811yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C32×C4—22no—
395C32×C4—22no—
396C32×C4—22no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4—41no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3C22⋊Q814yes—
408C22×Q8—31no—
409C23×C4—31no—
410C4×Q8—64no—
411#117—64no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4C2×C3×D311yescharacteristic
421C2×C4⋊C4C2×C3×D311yescharacteristic
422C2×C4⋊C4C2×C3×D311yescharacteristic
423C2×C22⋊C4—31no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4C2×C3×D311yescharacteristic
427C2×C22⋊C4C2×C3×D311yescharacteristic
428C2×C22⋊C4C2×C3×D311yescharacteristic
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—31no—
432C2×C42—31no—
433C2×C42—31no—
434C2×C42—31no—
435#95—31no—
436#95—31no—
437#95—31no—
438#95—31no—
439#95—31no—
440#95—31no—
441#95—31no—
442#95—31no—
443#95—31no—
444#95C2×C3×D311yescharacteristic
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—22no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3D3×Q812yes—
466C23×C3C2×C3×Q812yes—
467C23×C3C23×D311yescharacteristic
468C23×C3C24×C311yescharacteristic
469C3×Q8—68no—
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—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—68no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4D3×D412yes—
544C2×C3×C4#23712yes—
545C2×C3×C4#23712yes—
546C2×C3×C4C2×C3×D412yes—
547C2×C3×C4C3×#4112yes—
548C2×C3×C4C3×#4112yes—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—28no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3C2×C3×D412yes—
568C2×Dic3C2×C3×D412yes—
569C2×Dic3C2×C3×Q812yes—
570C2×Dic3C2×C3×Q812yes—
571C2×Dic3C3×#4112yes—
572C2×Dic3C3×#4112yes—
573C2×Dic3C3×#4112yes—
574Dic6—28no—
575C2×C32—42no—
576C2×C32C2×C22⋊Q811yescharacteristic
577C2×C32#52511yescharacteristic
578C2×C32#52911yescharacteristic
579C2×C32#52911yescharacteristic
580C2×C32#53211yescharacteristic
581C2×C32#53311yescharacteristic
582C2×C32#53311yescharacteristic
583C24C22×C3×D311yescharacteristic
584C2×Q8—62no—
585C2×Q8—62no—
586C2×Q8—62no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—34no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4C22×C3×D311yescharacteristic
599C22×C4C22×C3×D311yescharacteristic
600C22×C4C22×C3×D311yescharacteristic
601C22×C4C22×C3×D311yescharacteristic
602C22×C4C22×C3×D311yescharacteristic
603C22×C4C22×C3×D311yescharacteristic
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—62no—
608C4⋊C4—62no—
609C4⋊C4—62no—
610C4⋊C4—62no—
611C4⋊C4—62no—
612C4⋊C4—62no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—62no—
619C22⋊C4—62no—
620C22⋊C4—62no—
621C42—34no—
622C42—62no—
623C42—62no—
624C42—62no—
625C42—62no—
626C42—62no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×#23711yescharacteristic
657C22×C3C2×#23711yescharacteristic
658C22×C3C2×D3×Q811yescharacteristic
659C22×C3D3×#4111yescharacteristic
660C22×C3D3×#4111yescharacteristic
661C22×C3D3×#4111yescharacteristic
662C22×C3C22×C3×D411yescharacteristic
663C22×C3C22×C3×Q811yescharacteristic
664C22×C3C2×C3×#4111yescharacteristic
665C22×C3C2×C3×#4111yescharacteristic
666C22×C3C2×C3×#4111yescharacteristic
667C22×C3C2×C3×#4111yescharacteristic
668C22×C3C2×C3×#4111yescharacteristic
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—34no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—62no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—62no—
689C3×C4—81no—
690C3×C4—81no—
691C3×C4—81no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695Dic3—22no—
696Dic3—22no—
697Dic3—22no—
698Dic3—22no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3C3×C22⋊Q814yes—
703C32#239611yescharacteristic, complemented, Sylow
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23C3×D3×Q812yes—
711C23C23×C3×D311yescharacteristic
712Q8—68no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—68no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4C3×D3×D412yes—
754C2×C4C3×#23712yes—
755C2×C4C3×#23712yes—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—42no—
765C2×C3—82no—
766C2×C3#559611yescharacteristic
767C2×C3#560011yescharacteristic
768C2×C3#560611yescharacteristic
769C2×C3#562211yescharacteristic
770C2×C3#562211yescharacteristic
771C2×C3D3×C22⋊Q811yescharacteristic
772C2×C3#570611yescharacteristic
773C2×C3C2×C3×C22⋊Q811yescharacteristic
774C2×C3C3×#52511yescharacteristic
775C2×C3C3×#52911yescharacteristic
776C2×C3C3×#52911yescharacteristic
777C2×C3C3×#53211yescharacteristic
778C2×C3C3×#53311yescharacteristic
779C2×C3C3×#53311yescharacteristic
780C22—22no—
781C22—22no—
782C22—22no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22C2×C3×D3×D411yescharacteristic
788C22C2×C3×#23711yescharacteristic
789C22C2×C3×#23711yescharacteristic
790C22C2×C3×D3×Q811yescharacteristic
791C22C3×D3×#4111yescharacteristic
792C22C3×D3×#4111yescharacteristic
793C22C3×D3×#4111yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—34no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—62no—
802C4—62no—
803C4—62no—
804C4—62no—
805C4—121no—
806C4—121no—
807C4—121no—
808C3—21no—
809C3#7728211yescharacteristic, direct product factor
810C3C3×#239611yescharacteristic, complemented
811C2—42no—
812C2C3×#559611yescharacteristic
813C2C3×#560011yescharacteristic
814C2C3×#560611yescharacteristic
815C2C3×#562211yescharacteristic
816C2C3×#562211yescharacteristic
817C2C3×D3×C22⋊Q811yescharacteristic
818C2C3×#570611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#396C2
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC3×#396D3
hypocenterC3C3×#2396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#396

Complements

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

NH ≅ G/Ntype
1. C2×C3×#887C2semidirect
4. C3×#4982C2semidirect
5. C3×#4981C2semidirect
6. C3×#4979C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
8. C3×Dic3×C4⋊C4C2semidirect
14. C3×#4658C2semidirect
15. C3×#4649C2semidirect
17. #77282C3direct (N × H)
57. C2×#887C2×C3semidirect
74. #4982C2×C3semidirect
75. #4981C2×C3semidirect
76. #4979C2×C3semidirect
77. Dic3×C4⋊C4C2×C3semidirect
78. Dic3×C4⋊C4C2×C3semidirect
84. #4658C2×C3semidirect
85. #4649C2×C3semidirect
95. C22×C3×Dic3Q8semidirect
316. C22×Dic3C3×Q8semidirect
703. C32#2396semidirect
809. C3#77282direct (N × H)
810. C3C3×#2396semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×C3×#8772
C32×#3962
C3×#49822
C3×#49812
C3×#49792
C3×Dic3×C4⋊C42
C3×#49492
C3×#49482
C3×#49472
C3×Dic3×C22⋊C42
C3×#46582
C3×#46492
C3×#23963
#772823