Finite Group Databasebeta

← C3×#74387 #11803898

Subgroups — C3×#74387 #11803898

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#878C211yesmaximal, characteristic
2C32×#385C211yesmaximal, characteristic
3C3×#5210C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C3×#4978C211yesmaximal, characteristic, complemented
6C3×#4976C211yesmaximal, characteristic, complemented
7C3×#4973C211yesmaximal, characteristic, complemented
8C3×#4972C211yesmaximal, characteristic, complemented
9C3×#4942C211yesmaximal, characteristic
10C3×Dic3×C22⋊C4C211yesmaximal, characteristic
11C3×Dic3×C22⋊C4C211yesmaximal, characteristic
12C3×#4653C211yesmaximal, characteristic, complemented
13C3×#4652C211yesmaximal, characteristic, complemented
14C3×#4652C211yesmaximal, characteristic, complemented
15C3×#4646C211yesmaximal, characteristic, complemented
16C3×#2329—31nomaximal
17#74387C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#878C418yescomplemented
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×#878C2×C311yescharacteristic
56C3×#391—31no—
57C3×#391—31no—
58C3×#389—31no—
59C3×#389—31no—
60C3×#387—31no—
61C3×#387—31no—
62C3×#387—31no—
63C3×#387—31no—
64C3×#385—21no—
65C3×#385—31no—
66C3×#385D311yescharacteristic
67C3×#385C2×C311yescharacteristic
68C3×#380—31no—
69C3×C4×C22⋊C4—31no—
70C3×C4×C22⋊C4—31no—
71C2×C3×#95—31no—
72#5210C2×C311yescharacteristic
73C2×C3⋊#95C2×C311yescharacteristic
74#4978C2×C311yescharacteristic, complemented
75#4976C2×C311yescharacteristic, complemented
76#4973C2×C311yescharacteristic, complemented
77#4972C2×C311yescharacteristic, complemented
78#4942C2×C311yescharacteristic
79Dic3×C22⋊C4C2×C311yescharacteristic
80Dic3×C22⋊C4C2×C311yescharacteristic
81#4653C2×C311yescharacteristic, complemented
82#4652C2×C311yescharacteristic, complemented
83#4652C2×C311yescharacteristic, complemented
84#4646C2×C311yescharacteristic, complemented
85C24×C32C2311yescharacteristic
86C22×C32×C4—22no—
87C22×C32×C4—41no—
88C22×C32×C4—41no—
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3×Dic3—41no—
96C22×C3×Dic3—41no—
97C22×C3×Dic3—41no—
98C22×C3×Dic3—41no—
99C22×C3×Dic3C2×C414yes—
100C22×C3×Dic3Q814yescomplemented
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×C3×Dic6—41no—
110C2×C3×Dic6—41no—
111C2×C3×Dic6C2×C414yescomplemented
112C32×C4⋊C4—41no—
113C32×C4⋊C4—41no—
114C32×C22⋊C4—22no—
115C32×C22⋊C4C2×C414yes—
116C3×#217—22no—
117C3×#217C2×C414yes—
118C3×C4⋊Dic3C2×C414yescomplemented
119C3×Dic3⋊C4—41no—
120C3×Dic3⋊C4—41no—
121C3×Dic3⋊C4—41no—
122C3×Dic3⋊C4—41no—
123C3×Dic3⋊C4C2×C414yescomplemented
124C3×Dic3⋊C4C2×C414yescomplemented
125C3×C4×Dic3—41no—
126C3×C4×Dic3—41no—
127C3×C4×Dic3—41no—
128C3×C4×Dic3—41no—
129#2329—31noSylow
130C22×C3×Q8—31no—
131C23×C3×C4—21no—
132C23×C3×C4—31no—
133C23×C3×C4—31no—
134C23×C3×C4C2×D311yescharacteristic
135C23×C3×C4C22×C311yescharacteristic
136C23×Dic3C22×C311yescharacteristic
137C23×Dic3C22×C311yescharacteristic
138C22×Dic6C22×C311yescharacteristic
139C3×C22⋊Q8—38no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
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⋊C4—31no—
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C2×D311yescharacteristic
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C4⋊C4C22×C311yescharacteristic
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4C2×D311yescharacteristic
158C2×C3×C22⋊C4C2×D311yescharacteristic
159C2×C3×C22⋊C4C22×C311yescharacteristic
160C2×C3×C22⋊C4C22×C311yescharacteristic
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×C3×C42—31no—
164C2×C3×C42—31no—
165C2×#217C22×C311yescharacteristic
166C2×#217C22×C311yescharacteristic
167C2×C4⋊Dic3C22×C311yescharacteristic
168C2×Dic3⋊C4C22×C311yescharacteristic
169C2×Dic3⋊C4C22×C311yescharacteristic
170C2×Dic3⋊C4C22×C311yescharacteristic
171C2×Dic3⋊C4C22×C311yescharacteristic
172C2×Dic3⋊C4C22×C311yescharacteristic
173C2×Dic3⋊C4C22×C311yescharacteristic
174C2×C4×Dic3C22×C311yescharacteristic
175C2×C4×Dic3C22×C311yescharacteristic
176C2×C4×Dic3C22×C311yescharacteristic
177C2×C4×Dic3C22×C311yescharacteristic
178#878C3×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×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32—21no—
213C23×C32C22×C412yes—
214C23×C32C2×Q812yes—
215C23×C32#4112yes—
216C23×C32C2411yescharacteristic
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—44no—
234C2×C32×C4C22×C412yes—
235C2×C32×C4C22×C412yes—
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—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—44no—
255C2×C3×Dic3—44no—
256C2×C3×Dic3C22×C412yes—
257C2×C3×Dic3C22×C412yes—
258C2×C3×Dic3C22×C412yes—
259C2×C3×Dic3C22×C412yes—
260C2×C3×Dic3C2×Q812yes—
261C2×C3×Dic3C2×Q812yes—
262C3×Dic6—44no—
263C2×C22⋊Q8—31no—
264#391—31no—
265#391—31no—
266#389—31no—
267#389—31no—
268#387—31no—
269#387—31no—
270#387—31no—
271#387—31no—
272#385—31no—
273#385C3×D311yescharacteristic
274#380—31no—
275C4×C22⋊C4—31no—
276C4×C22⋊C4—31no—
277C2×#95—31no—
278C24×C3—21no—
279C24×C3C22×D311yescharacteristic
280C24×C3C23×C311yescharacteristic
281C2×C3×Q8—34no—
282C2×C3×Q8—121no—
283C2×C3×Q8—121no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—34no—
299C22×C3×C4—34no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—42no—
303C22×C3×C4—41no—
304C22×C3×C4—41no—
305C22×C3×C4—41no—
306C22×C3×C4—41no—
307C22×C3×C4—42no—
308C22×C3×C4—42no—
309C22×C3×C4—121no—
310C22×C3×C4—121no—
311C22×C3×C4—121no—
312C22×C3×C4—121no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C22×C3×C4C23×C311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C22×C3×C4C23×C311yescharacteristic
323C22×C3×C4C23×C311yescharacteristic
324C22×C3×C4C23×C311yescharacteristic
325C22×Dic3—41no—
326C22×Dic3—41no—
327C22×Dic3—41no—
328C22×Dic3—41no—
329C22×Dic3C2×C3×C414yes—
330C22×Dic3C3×Q814yescomplemented
331C22×Dic3C23×C311yescharacteristic
332C22×Dic3C23×C311yescharacteristic
333C22×Dic3C23×C311yescharacteristic
334C22×Dic3C23×C311yescharacteristic
335C22×Dic3C23×C311yescharacteristic
336C22×Dic3C23×C311yescharacteristic
337C22×Dic3C23×C311yescharacteristic
338C22×Dic3C23×C311yescharacteristic
339C2×Dic6—41no—
340C2×Dic6—41no—
341C2×Dic6C2×C3×C414yescomplemented
342C3×C4⋊C4—34no—
343C3×C4⋊C4—34no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—41no—
346C3×C4⋊C4—41no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—41no—
349C3×C4⋊C4—42no—
350C3×C4⋊C4—42no—
351C3×C4⋊C4—121no—
352C3×C4⋊C4—121no—
353C3×C4⋊C4—121no—
354C3×C4⋊C4—121no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—34no—
359C3×C22⋊C4—42no—
360C3×C22⋊C4—62no—
361C3×C22⋊C4C4×D314yes—
362C3×C22⋊C4C2×C3×C414yes—
363C3×C42—121no—
364C3×C42—121no—
365C3×C42—121no—
366C3×C42—121no—
367#217—22no—
368#217C2×C3×C414yes—
369C4⋊Dic3C2×C3×C414yescomplemented
370Dic3⋊C4—41no—
371Dic3⋊C4—41no—
372Dic3⋊C4—41no—
373Dic3⋊C4—41no—
374Dic3⋊C4C2×C3×C414yescomplemented
375Dic3⋊C4C2×C3×C414yescomplemented
376C4×Dic3—41no—
377C4×Dic3—41no—
378C4×Dic3—41no—
379C4×Dic3—41no—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—22no—
386C22×C32C4×Q814yes—
387C22×C32C23×C411yescharacteristic
388C22×C32C22×Q811yescharacteristic
389C22×C32C2×#4111yescharacteristic
390C22×C32H(5,𝔽2)11yescharacteristic
391C22×C32H(5,𝔽2)11yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C322−1+411yescharacteristic
394C32×C4—22no—
395C32×C4—22no—
396C32×C4—41no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4—41no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C22×Q8—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4C2×C3×D311yescharacteristic
412C22⋊Q8—38no—
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×C22⋊C4—31no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4C2×C3×D311yescharacteristic
425C2×C22⋊C4C2×C3×D311yescharacteristic
426C2×C42—31no—
427C2×C42—31no—
428C2×C42—31no—
429C2×C42—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#95—31no—
441#95—31no—
442#95C2×C3×D311yescharacteristic
443#95C2×C3×D311yescharacteristic
444C23×C3—21no—
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—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3C2×C4×D312yes—
461C23×C3#23712yes—
462C23×C3D3×Q812yes—
463C23×C3C22×C3×C412yes—
464C23×C3C2×C3×Q812yes—
465C23×C3C3×#4112yes—
466C23×C3C23×D311yescharacteristic
467C23×C3C24×C311yescharacteristic
468C3×Q8—124no—
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—22no—
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—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
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—44no—
526C2×C3×C4—44no—
527C2×C3×C4—48no—
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×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—124no—
547C2×C3×C4—124no—
548C2×C3×C4C2×C4×D312yes—
549C2×C3×C4C2×C4×D312yes—
550C2×C3×C4C22×C3×C412yes—
551C2×C3×C4C22×C3×C412yes—
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×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—44no—
571C2×Dic3—44no—
572C2×Dic3C22×C3×C412yes—
573C2×Dic3C22×C3×C412yes—
574C2×Dic3C22×C3×C412yes—
575C2×Dic3C22×C3×C412yes—
576C2×Dic3C2×C3×Q812yes—
577C2×Dic3C2×C3×Q812yes—
578Dic6—44no—
579C2×C32—24no—
580C2×C32C2×C4×Q811yescharacteristic
581C2×C32#51811yescharacteristic
582C2×C32#52011yescharacteristic
583C2×C32#53811yescharacteristic
584C2×C32#53911yescharacteristic
585C2×C32#54311yescharacteristic
586C2×C32#54411yescharacteristic
587C24C22×C3×D311yescharacteristic
588C2×Q8—34no—
589C2×Q8—121no—
590C2×Q8—121no—
591C22×C4—22no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—34no—
599C22×C4—34no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—121no—
605C22×C4—121no—
606C22×C4—121no—
607C22×C4—121no—
608C22×C4C22×C3×D311yescharacteristic
609C22×C4C22×C3×D311yescharacteristic
610C22×C4C22×C3×D311yescharacteristic
611C22×C4C22×C3×D311yescharacteristic
612C22×C4C22×C3×D311yescharacteristic
613C22×C4C22×C3×D311yescharacteristic
614C4⋊C4—34no—
615C4⋊C4—34no—
616C4⋊C4—34no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—121no—
620C4⋊C4—121no—
621C4⋊C4—121no—
622C4⋊C4—121no—
623C22⋊C4—22no—
624C22⋊C4—34no—
625C22⋊C4—62no—
626C22⋊C4C3×C4×D314yes—
627C42—121no—
628C42—121no—
629C42—121no—
630C42—121no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—24no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3#88714yes—
658C22×C3C3×C4×Q814yes—
659C22×C3C22×C4×D311yescharacteristic
660C22×C3C2×#23711yescharacteristic
661C22×C3#100411yescharacteristic
662C22×C3#100411yescharacteristic
663C22×C3C2×D3×Q811yescharacteristic
664C22×C3#100911yescharacteristic
665C22×C3#101011yescharacteristic
666C22×C3C23×C3×C411yescharacteristic
667C22×C3C22×C3×Q811yescharacteristic
668C22×C3C2×C3×#4111yescharacteristic
669C22×C3C3×H(5,𝔽2)11yescharacteristic
670C22×C3C3×H(5,𝔽2)11yescharacteristic
671C22×C3C3×H(5,𝔽2)11yescharacteristic
672C22×C3C3×2−1+411yescharacteristic
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—62no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—62no—
693C3×C4—62no—
694C3×C4—62no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4—121no—
699Dic3—22no—
700Dic3—22no—
701Dic3—22no—
702Dic3—22no—
703Dic3—22no—
704Dic3—22no—
705Dic3—41no—
706Dic3—41no—
707C32#232911yescharacteristic, complemented, Sylow
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23C2×C3×C4×D312yes—
713C23C3×#23712yes—
714C23C3×D3×Q812yes—
715C23C23×C3×D311yescharacteristic
716Q8—124no—
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—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—44no—
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×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—124no—
759C2×C4—124no—
760C2×C4C2×C3×C4×D312yes—
761C2×C4C2×C3×C4×D312yes—
762C2×C3—24no—
763C2×C3—24no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—44no—
772C2×C3C2×#88711yescharacteristic
773C2×C3#554511yescharacteristic
774C2×C3#554611yescharacteristic
775C2×C3#559311yescharacteristic
776C2×C3#562311yescharacteristic
777C2×C3#563411yescharacteristic
778C2×C3#566511yescharacteristic
779C2×C3C2×C3×C4×Q811yescharacteristic
780C2×C3C3×#51811yescharacteristic
781C2×C3C3×#52011yescharacteristic
782C2×C3C3×#53811yescharacteristic
783C2×C3C3×#53911yescharacteristic
784C2×C3C3×#54311yescharacteristic
785C2×C3C3×#54411yescharacteristic
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22C3×#88714yes—
793C22C22×C3×C4×D311yescharacteristic
794C22C2×C3×#23711yescharacteristic
795C22C3×#100411yescharacteristic
796C22C3×#100411yescharacteristic
797C22C2×C3×D3×Q811yescharacteristic
798C22C3×#100911yescharacteristic
799C22C3×#101011yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—62no—
807C4—62no—
808C4—62no—
809C4—62no—
810C4—62no—
811C4—62no—
812C4—121no—
813C4—121no—
814C3—21no—
815C3#7438711yescharacteristic, direct product factor
816C3C3×#232911yescharacteristic, complemented
817C2—24no—
818C2C2×C3×#88711yescharacteristic
819C2C3×#554511yescharacteristic
820C2C3×#554611yescharacteristic
821C2C3×#559311yescharacteristic
822C2C3×#562311yescharacteristic
823C2C3×#563411yescharacteristic
824C2C3×#566511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#385C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC3×#385D3
hypocenterC3C3×#2329
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
5. C3×#4978C2semidirect
6. C3×#4976C2semidirect
7. C3×#4973C2semidirect
8. C3×#4972C2semidirect
12. C3×#4653C2semidirect
13. C3×#4652C2semidirect
14. C3×#4652C2semidirect
15. C3×#4646C2semidirect
17. #74387C3direct (N × H)
39. C3×#878C4semidirect
74. #4978C2×C3semidirect
75. #4976C2×C3semidirect
76. #4973C2×C3semidirect
77. #4972C2×C3semidirect
81. #4653C2×C3semidirect
82. #4652C2×C3semidirect
83. #4652C2×C3semidirect
84. #4646C2×C3semidirect
100. C22×C3×Dic3Q8semidirect
111. C2×C3×Dic6C2×C4semidirect
118. C3×C4⋊Dic3C2×C4semidirect
123. C3×Dic3⋊C4C2×C4semidirect
124. C3×Dic3⋊C4C2×C4semidirect
178. #878C3×C4semidirect
330. C22×Dic3C3×Q8semidirect
341. C2×Dic6C2×C3×C4semidirect
369. C4⋊Dic3C2×C3×C4semidirect
374. Dic3⋊C4C2×C3×C4semidirect
375. Dic3⋊C4C2×C3×C4semidirect
707. C32#2329semidirect
815. C3#74387direct (N × H)
816. C3C3×#2329semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8782
C32×#3852
C3×#52102
C2×C3×C3⋊#952
C3×#49782
C3×#49762
C3×#49732
C3×#49722
C3×#49422
C3×Dic3×C22⋊C42
C3×#46532
C3×#46522
C3×#46462
C3×#23293
#743873