Finite Group Databasebeta

← C3×#76199 #11803907

Subgroups — C3×#76199 #11803907

Order 1152.

1141 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#896C211yesmaximal, characteristic
2C32×#389C211yesmaximal, characteristic, complemented
3C3×#4989C211yesmaximal, characteristic
4C3×#4989C211yesmaximal, characteristic
5C3×#4987C211yesmaximal, characteristic
6C3×#4980C211yesmaximal, characteristic, complemented
7C3×#4978C211yesmaximal, characteristic, complemented
8C3×#4976C211yesmaximal, characteristic, complemented
9C3×#4973C211yesmaximal, characteristic, complemented
10C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
11C3×#4933C211yesmaximal, characteristic, complemented
12C3×#4666C211yesmaximal, characteristic
13C3×D3×#95C211yesmaximal, characteristic
14C3×#4655C211yesmaximal, characteristic, complemented
15C3×#4646C211yesmaximal, characteristic, complemented
16C3×#2329—31nomaximal
17#76199C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C42C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#896C418yescomplemented
40C32×#95C2211yescharacteristic
41C32×#95C2211yescharacteristic
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×C22⋊Q8—31no—
55C2×#896C2×C311yescharacteristic
56C3×#391—31no—
57C3×#391—31no—
58C3×#389—21no—
59C3×#389—31no—
60C3×#389D311yescharacteristic, complemented
61C3×#389C2×C311yescharacteristic, complemented
62C3×#387—31no—
63C3×#387—31no—
64C3×#387—31no—
65C3×#387—31no—
66C3×#385—31no—
67C3×#385—31no—
68C3×#380—31no—
69C3×C4×C22⋊C4—31no—
70C3×C4×C22⋊C4—31no—
71C2×C3×#95—31no—
72#4989C2×C311yescharacteristic
73#4989C2×C311yescharacteristic
74#4987C2×C311yescharacteristic
75#4980C2×C311yescharacteristic, complemented
76#4978C2×C311yescharacteristic, complemented
77#4976C2×C311yescharacteristic, complemented
78#4973C2×C311yescharacteristic, complemented
79C4×(C2×D3)⋊C4C2×C311yescharacteristic
80#4933C2×C311yescharacteristic, complemented
81#4666C2×C311yescharacteristic
82D3×#95C2×C311yescharacteristic
83#4655C2×C311yescharacteristic, complemented
84#4646C2×C311yescharacteristic, complemented
85C23×C3×D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—41no—
102C2×C3×C4×D3—41no—
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3—41no—
106C2×C3×C4×D3—41no—
107C2×C3×C4×D3C2×C414yes—
108C2×C3×C4×D3Q814yescomplemented
109C2×C3×Dic6—41no—
110C2×C3×Dic6—41no—
111C2×C3×Dic6C2×C414yescomplemented
112C32×C4⋊C4—41no—
113C32×C4⋊C4—41no—
114C32×C4⋊C4—41no—
115C32×C4⋊C4C2×C414yescomplemented
116C32×C42—41no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4C2×C414yes—
120C3×(C2×D3)⋊C4C2×C414yes—
121C3×C4⋊Dic3—41no—
122C3×Dic3⋊C4—41no—
123C3×Dic3⋊C4—41no—
124C3×Dic3⋊C4C2×C414yescomplemented
125C3×Dic3⋊C4C2×C414yescomplemented
126C3×C4×Dic3—41no—
127C3×C4×Dic3—41no—
128C3×C4×Dic3—41no—
129#2329—31noSylow
130C22×C3×Q8—31no—
131C23×C3×C4—31no—
132C23×C3×C4—31no—
133C23×C3×C4—31no—
134C22×C4×D3C22×C311yescharacteristic
135C22×C4×D3C22×C311yescharacteristic
136C22×C4×D3C22×C311yescharacteristic
137C22×Dic6C22×C311yescharacteristic
138C3×C22⋊Q8—38no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
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⋊C4C2×D311yescharacteristic
152C2×C3×C4⋊C4C22×C311yescharacteristic
153C2×C3×C4⋊C4C22×C311yescharacteristic
154C2×C3×C4⋊C4C22×C311yescharacteristic
155C2×C3×C4⋊C4C22×C311yescharacteristic
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C42—21no—
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×C3×C42—31no—
164C2×C3×C42C2×D311yescharacteristic
165C2×C3×C42C22×C311yescharacteristic
166C2×(C2×D3)⋊C4C22×C311yescharacteristic
167C2×(C2×D3)⋊C4C22×C311yescharacteristic
168C2×(C2×D3)⋊C4C22×C311yescharacteristic
169C2×(C2×D3)⋊C4C22×C311yescharacteristic
170C2×C4⋊Dic3C22×C311yescharacteristic
171C2×Dic3⋊C4C22×C311yescharacteristic
172C2×Dic3⋊C4C22×C311yescharacteristic
173C2×Dic3⋊C4C22×C311yescharacteristic
174C2×Dic3⋊C4C22×C311yescharacteristic
175C2×C4×Dic3C22×C311yescharacteristic
176C2×C4×Dic3C22×C311yescharacteristic
177C2×C4×Dic3C22×C311yescharacteristic
178#896C3×C418yescomplemented
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—31no—
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×#95C2×D311yescharacteristic
194C3×#95C2×D311yescharacteristic
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
206C3⋊#95C22×C311yescharacteristic
207C3⋊#95C22×C311yescharacteristic
208C3⋊#95C22×C311yescharacteristic
209C23×C32C2411yescharacteristic
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3C22×C412yes—
215C22×C3×D3C2×Q812yes—
216C22×C3×D3#4112yes—
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×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×C4C22×C412yes—
235C2×C32×C4C22×C412yes—
236C2×C32×C4C22×C412yes—
237C2×C32×C4C2×Q812yes—
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—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C22×C412yes—
256C2×C3×Dic3C22×C412yes—
257C2×C3×Dic3C22×C412yes—
258C2×C3×Dic3C2×Q812yes—
259C3×C4×D3—44no—
260C3×C4×D3—44no—
261C3×C4×D3—44no—
262C3×Dic6—44no—
263C2×C22⋊Q8—31no—
264#391—31no—
265#391—31no—
266#389—31no—
267#389C3×D311yescharacteristic, complemented
268#387—31no—
269#387—31no—
270#387—31no—
271#387—31no—
272#385—31no—
273#385—31no—
274#380—31no—
275C4×C22⋊C4—31no—
276C4×C22⋊C4—31no—
277C2×#95—31no—
278C24×C3—31no—
279C23×D3C23×C311yescharacteristic
280C2×C3×Q8—34no—
281C2×C3×Q8—121no—
282C2×C3×Q8—121no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—34no—
295C22×C3×C4—34no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—62no—
300C22×C3×C4—121no—
301C22×C3×C4—121no—
302C22×C3×C4—121no—
303C22×C3×C4—121no—
304C22×C3×C4—121no—
305C22×C3×C4—121no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C22×C3×C4C23×C311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C22×C3×C4C23×C311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C22×Dic3C23×C311yescharacteristic
321C22×Dic3C23×C311yescharacteristic
322C22×Dic3C23×C311yescharacteristic
323C22×Dic3C23×C311yescharacteristic
324C22×Dic3C23×C311yescharacteristic
325C22×Dic3C23×C311yescharacteristic
326C22×Dic3C23×C311yescharacteristic
327C2×C4×D3—22no—
328C2×C4×D3—41no—
329C2×C4×D3—41no—
330C2×C4×D3—41no—
331C2×C4×D3—41no—
332C2×C4×D3—41no—
333C2×C4×D3—41no—
334C2×C4×D3C2×C3×C414yes—
335C2×C4×D3C3×Q814yescomplemented
336C2×Dic6—41no—
337C2×Dic6—41no—
338C2×Dic6C2×C3×C414yescomplemented
339C3×C4⋊C4—24no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—41no—
346C3×C4⋊C4—41no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—42no—
349C3×C4⋊C4—42no—
350C3×C4⋊C4—42no—
351C3×C4⋊C4—121no—
352C3×C4⋊C4—121no—
353C3×C4⋊C4—121no—
354C3×C4⋊C4C4×D314yescomplemented
355C3×C4⋊C4C2×C3×C414yescomplemented
356C3×C22⋊C4—34no—
357C3×C22⋊C4—34no—
358C3×C22⋊C4—62no—
359C3×C22⋊C4—62no—
360C3×C42—41no—
361C3×C42—41no—
362C3×C42—42no—
363C3×C42—121no—
364C3×C42—121no—
365C3×C42—121no—
366(C2×D3)⋊C4—22no—
367(C2×D3)⋊C4—22no—
368(C2×D3)⋊C4C2×C3×C414yes—
369(C2×D3)⋊C4C2×C3×C414yes—
370C4⋊Dic3—41no—
371Dic3⋊C4—41no—
372Dic3⋊C4—41no—
373Dic3⋊C4C2×C3×C414yescomplemented
374Dic3⋊C4C2×C3×C414yescomplemented
375C4×Dic3—41no—
376C4×Dic3—41no—
377C4×Dic3—41no—
378C22×C32C23×C411yescharacteristic
379C22×C32C22×Q811yescharacteristic
380C22×C32C2×#4111yescharacteristic
381C22×C32H(5,𝔽2)11yescharacteristic
382C22×C32H(5,𝔽2)11yescharacteristic
383C22×C32H(5,𝔽2)11yescharacteristic
384C22×C322−1+411yescharacteristic
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3C4×Q814yes—
392C32×C4—22no—
393C32×C4—22no—
394C32×C4—22no—
395C32×C4—22no—
396C32×C4—41no—
397C32×C4—41no—
398C32×C4—41no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C22×Q8—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C22⋊Q8—38no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4C2×C3×D311yescharacteristic
417C2×C4⋊C4C2×C3×D311yescharacteristic
418C2×C4⋊C4C2×C3×D311yescharacteristic
419C2×C4⋊C4C2×C3×D311yescharacteristic
420C2×C22⋊C4—31no—
421C2×C22⋊C4—31no—
422C2×C22⋊C4—31no—
423C2×C22⋊C4—31no—
424C2×C42—31no—
425C2×C42—31no—
426C2×C42—31no—
427C2×C42C2×C3×D311yescharacteristic
428#95—31no—
429#95—31no—
430#95—31no—
431#95—31no—
432#95—31no—
433#95—31no—
434#95—31no—
435#95—31no—
436#95—31no—
437#95—31no—
438#95—31no—
439#95—31no—
440#95C2×C3×D311yescharacteristic
441#95C2×C3×D311yescharacteristic
442C23×C3—21no—
443C23×C3—32no—
444C23×C3—32no—
445C23×C3—32no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3C23×D311yescharacteristic
451C23×C3C24×C311yescharacteristic
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3C22×C3×C412yes—
457C22×D3C2×C3×Q812yes—
458C22×D3C3×#4112yes—
459C3×Q8—124no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
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—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—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
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—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
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—124no—
537C2×C3×C4—124no—
538C2×C3×C4—124no—
539C2×C3×C4C2×C4×D312yes—
540C2×C3×C4C2×C4×D312yes—
541C2×C3×C4C2×C4×D312yes—
542C2×C3×C4D3×Q812yes—
543C2×C3×C4C22×C3×C412yes—
544C2×C3×C4C22×C3×C412yes—
545C2×C3×C4C22×C3×C412yes—
546C2×C3×C4C2×C3×Q812yes—
547C2×Dic3—21no—
548C2×Dic3—21no—
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—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3C22×C3×C412yes—
565C2×Dic3C22×C3×C412yes—
566C2×Dic3C22×C3×C412yes—
567C2×Dic3C2×C3×Q812yes—
568C4×D3—44no—
569C4×D3—44no—
570C4×D3—44no—
571Dic6—44no—
572C2×C32C2×C4×Q811yescharacteristic
573C2×C32#51811yescharacteristic
574C2×C32#52011yescharacteristic
575C2×C32#53811yescharacteristic
576C2×C32#53911yescharacteristic
577C2×C32#54311yescharacteristic
578C2×C32#54411yescharacteristic
579C3×D3—24no—
580C24—31no—
581C2×Q8—34no—
582C2×Q8—121no—
583C2×Q8—121no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—34no—
589C22×C4—34no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—62no—
594C22×C4—121no—
595C22×C4—121no—
596C22×C4—121no—
597C22×C4—121no—
598C22×C4—121no—
599C22×C4—121no—
600C22×C4C22×C3×D311yescharacteristic
601C22×C4C22×C3×D311yescharacteristic
602C22×C4C22×C3×D311yescharacteristic
603C22×C4C22×C3×D311yescharacteristic
604C22×C4C22×C3×D311yescharacteristic
605C22×C4C22×C3×D311yescharacteristic
606C22×C4C22×C3×D311yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—34no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—121no—
613C4⋊C4—121no—
614C4⋊C4—121no—
615C4⋊C4C3×C4×D314yescomplemented
616C22⋊C4—34no—
617C22⋊C4—34no—
618C22⋊C4—62no—
619C22⋊C4—62no—
620C42—41no—
621C42—121no—
622C42—121no—
623C42—121no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—34no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3C22×C4×D311yescharacteristic
639C22×C3#100411yescharacteristic
640C22×C3#100411yescharacteristic
641C22×C3C2×D3×Q811yescharacteristic
642C22×C3#100711yescharacteristic
643C22×C3D3×#4111yescharacteristic
644C22×C3#100911yescharacteristic
645C22×C3C23×C3×C411yescharacteristic
646C22×C3C22×C3×Q811yescharacteristic
647C22×C3C2×C3×#4111yescharacteristic
648C22×C3C3×H(5,𝔽2)11yescharacteristic
649C22×C3C3×H(5,𝔽2)11yescharacteristic
650C22×C3C3×H(5,𝔽2)11yescharacteristic
651C22×C3C3×2−1+411yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3C3×C4×Q814yes—
659C3×C4—24no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—22no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—62no—
682C3×C4—81no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687Dic3—22no—
688Dic3—22no—
689Dic3—22no—
690Dic3—22no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694C32#232911yescharacteristic, complemented, Sylow
695C23—32no—
696C23—32no—
697C23—32no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23C23×C3×D311yescharacteristic
703Q8—124no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
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—32no—
722C2×C4—32no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—124no—
743C2×C4—124no—
744C2×C4—124no—
745C2×C4C2×C3×C4×D312yes—
746C2×C4C2×C3×C4×D312yes—
747C2×C4C2×C3×C4×D312yes—
748C2×C4C3×D3×Q812yes—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—64no—
757C2×C3#550411yescharacteristic
758C2×C3#554511yescharacteristic
759C2×C3C4×D3×Q811yescharacteristic
760C2×C3#561311yescharacteristic
761C2×C3#563411yescharacteristic
762C2×C3#569211yescharacteristic
763C2×C3#572911yescharacteristic
764C2×C3C2×C3×C4×Q811yescharacteristic
765C2×C3C3×#51811yescharacteristic
766C2×C3C3×#52011yescharacteristic
767C2×C3C3×#53811yescharacteristic
768C2×C3C3×#53911yescharacteristic
769C2×C3C3×#54311yescharacteristic
770C2×C3C3×#54411yescharacteristic
771D3—24no—
772C22—34no—
773C22—62no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22C22×C3×C4×D311yescharacteristic
780C22C3×#100411yescharacteristic
781C22C3×#100411yescharacteristic
782C22C2×C3×D3×Q811yescharacteristic
783C22C3×#100711yescharacteristic
784C22C3×D3×#4111yescharacteristic
785C22C3×#100911yescharacteristic
786C4—22no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—62no—
794C4—62no—
795C4—62no—
796C4—62no—
797C4—121no—
798C4—121no—
799C4—121no—
800C3—21no—
801C3#7619911yescharacteristic, direct product factor
802C3C3×#232911yescharacteristic, complemented
803C2—64no—
804C2C3×#550411yescharacteristic
805C2C3×#554511yescharacteristic
806C2C3×C4×D3×Q811yescharacteristic
807C2C3×#561311yescharacteristic
808C2C3×#563411yescharacteristic
809C2C3×#569211yescharacteristic
810C2C3×#572911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#389C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#389D3
hypocenterC3C3×#2329
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
2. C32×#389C2semidirect
6. C3×#4980C2semidirect
7. C3×#4978C2semidirect
8. C3×#4976C2semidirect
9. C3×#4973C2semidirect
11. C3×#4933C2semidirect
14. C3×#4655C2semidirect
15. C3×#4646C2semidirect
17. #76199C3direct (N × H)
39. C3×#896C4semidirect
60. C3×#389D3semidirect
61. C3×#389C2×C3semidirect
75. #4980C2×C3semidirect
76. #4978C2×C3semidirect
77. #4976C2×C3semidirect
78. #4973C2×C3semidirect
80. #4933C2×C3semidirect
83. #4655C2×C3semidirect
84. #4646C2×C3semidirect
108. C2×C3×C4×D3Q8semidirect
111. C2×C3×Dic6C2×C4semidirect
115. C32×C4⋊C4C2×C4semidirect
124. C3×Dic3⋊C4C2×C4semidirect
125. C3×Dic3⋊C4C2×C4semidirect
178. #896C3×C4semidirect
267. #389C3×D3semidirect
335. C2×C4×D3C3×Q8semidirect
338. C2×Dic6C2×C3×C4semidirect
354. C3×C4⋊C4C4×D3semidirect
355. C3×C4⋊C4C2×C3×C4semidirect
373. Dic3⋊C4C2×C3×C4semidirect
374. Dic3⋊C4C2×C3×C4semidirect
615. C4⋊C4C3×C4×D3semidirect
694. C32#2329semidirect
801. C3#76199direct (N × H)
802. C3C3×#2329semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8962
C32×#3892
C3×#49892
C3×#49872
C3×#49802
C3×#49782
C3×#49762
C3×#49732
C3×C4×(C2×D3)⋊C42
C3×#49332
C3×#46662
C3×D3×#952
C3×#46552
C3×#46462
C3×#23293
#761993