Finite Group Databasebeta

← C3×#82271 #11804966

Subgroups — C3×#82271 #11804966

Order 1152.

1749 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
4C3×#5211C211yesmaximal, characteristic, complemented
5C3×#4990C212yesmaximal, complemented
6C3×#4989C212yesmaximal, complemented
7C3×#4955C211yesmaximal, characteristic
8C3×#4942C211yesmaximal, characteristic, complemented
9C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
10C3×#4940C212yesmaximal, complemented
11C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
12C3×#2342—31nomaximal
13#82271C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C32×#117—24no—
19C2×C32×C4⋊C4C2212yescomplemented
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C42C2212yescomplemented
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C418yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yescomplemented
34C2×C3×C4×Dic3C2212yescomplemented
35C3×D3×C22⋊C4—24no—
36C3×C3⋊#95C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39C3×C3⋊#95C2212yescomplemented
40C2×C3×#117—21no—
41C2×C3×#117D311yescharacteristic, complemented
42C2×C3×#117C2×C311yescharacteristic, complemented
43C22×C3×C22⋊C4—31no—
44C22×C3×C22⋊C4—31no—
45C22×(C2×D3)⋊C4C2×C311yescharacteristic
46C2×D3×C22⋊C4C2×C311yescharacteristic
47C3×#388—32no—
48C3×#388—32no—
49C3×#385—32no—
50C3×#381—31no—
51C3×#380—31no—
52C3×#379—31no—
53C3×C4×C22⋊C4—31no—
54C3×C4×C22⋊C4—32no—
55#5211C2×C311yescharacteristic, complemented
56#4990C2×C312yescomplemented
57#4989C2×C312yescomplemented
58#4955C2×C311yescharacteristic
59#4942C2×C311yescharacteristic, complemented
60Dic3×C22⋊C4C2×C311yescharacteristic, complemented
61#4940C2×C312yescomplemented
62C4×(C2×D3)⋊C4C2×C312yescomplemented
63C24×C32C2311yescharacteristic
64C23×C3×D3—22no—
65C23×C3×D3—22no—
66C23×C3×D3—24no—
67C23×C3×D3—42no—
68C23×C3×D3C2×C414yes—
69C23×C3×D3C2311yescharacteristic
70C23×C3×D3C2311yescharacteristic
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4C2×C414yescomplemented
74C22×C32×C4C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2312yes—
78C22×C3×Dic3—42no—
79C22×C3×Dic3C2×C414yescomplemented
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C2×C3×C4×D3—24no—
85C2×C3×C4×D3—24no—
86C2×C3×C4×D3—42no—
87C32×C4⋊C4—24no—
88C32×C22⋊C4—22no—
89C32×C22⋊C4D414yes—
90C32×C42—24no—
91C3×#217—22no—
92C3×#217—22no—
93C3×(C2×D3)⋊C4—24no—
94C3×(C2×D3)⋊C4—24no—
95C3×(C2×D3)⋊C4—42no—
96C3×(C2×D3)⋊C4C2×C414yes—
97C3×(C2×D3)⋊C4C2×C414yes—
98C3×(C2×D3)⋊C4C2×C414yescomplemented
99C3×(C2×D3)⋊C4C2×C414yescomplemented
100C3×Dic3⋊C4—42no—
101C3×C4×Dic3—42no—
102#2342—31noSylow
103C25×C3—31no—
104C24×D3C22×C311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4—31no—
107C23×C3×C4—32no—
108C23×C3×C4C2×D311yescharacteristic
109C23×C3×C4C22×C311yescharacteristic
110C23×Dic3C22×C311yescharacteristic
111C22×C4×D3C22×C312yes—
112C3×#117—28no—
113C3×#117—24no—
114C3×#117—24no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C4⋊C4C2×D312yescomplemented
118C2×C3×C4⋊C4C22×C312yescomplemented
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—38no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—64no—
132C2×C3×C22⋊C4C2×D311yescharacteristic
133C2×C3×C22⋊C4C2×D311yescharacteristic
134C2×C3×C22⋊C4C22×C311yescharacteristic
135C2×C3×C22⋊C4C22×C311yescharacteristic
136C2×C3×C42—22no—
137C2×C3×C42—32no—
138C2×C3×C42C2×D312yescomplemented
139C2×C3×C42C22×C312yescomplemented
140C2×#217C22×C311yescharacteristic
141C2×#217C22×C311yescharacteristic
142C2×(C2×D3)⋊C4C3×C418yescomplemented
143C2×(C2×D3)⋊C4C22×C312yes—
144C2×(C2×D3)⋊C4C22×C312yes—
145C2×(C2×D3)⋊C4C22×C312yes—
146C2×(C2×D3)⋊C4C22×C311yescharacteristic
147C2×(C2×D3)⋊C4C22×C311yescharacteristic
148C2×(C2×D3)⋊C4C22×C311yescharacteristic
149C2×(C2×D3)⋊C4C22×C311yescharacteristic
150C2×Dic3⋊C4C22×C312yescomplemented
151C2×C4×Dic3C22×C312yescomplemented
152D3×C22⋊C4—24no—
153C3×#95—32no—
154C3×#95—32no—
155C3×#95—32no—
156C3×#95—32no—
157C3⋊#95C22×C312yescomplemented
158C3⋊#95C22×C312yescomplemented
159C3⋊#95C22×C312yescomplemented
160C3⋊#95C22×C312yescomplemented
161C23×C32—22no—
162C23×C32—22no—
163C23×C32C22×C412yes—
164C23×C32C2×D412yes—
165C23×C32#4112yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—22no—
170C22×C3×D3—28no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—28no—
176C22×C3×D3—44no—
177C22×C3×D3—48no—
178C22×C3×D3—48no—
179C22×C3×D3C22×C412yes—
180C22×C3×D3C22×C412yes—
181C22×C3×D3#4114yes—
182C2×C32×C4—28no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4C22×C412yes—
193C2×C32×C4C22×C412yes—
194C2×C32×C4C2×D414yes—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—44no—
204C2×C3×Dic3C22×C412yes—
205C2×C3×Dic3C22×C412yes—
206C3×C4×D3—48no—
207C2×#117C3×D311yescharacteristic, complemented
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210#388—32no—
211#388—32no—
212#385—32no—
213#381—31no—
214#380—31no—
215#379—31no—
216C4×C22⋊C4—31no—
217C4×C22⋊C4—32no—
218C24×C3—21no—
219C24×C3—31no—
220C24×C3—31no—
221C24×C3—34no—
222C24×C3—64no—
223C24×C3—62no—
224C24×C3—62no—
225C24×C3—122no—
226C24×C3C22×D311yescharacteristic
227C24×C3C23×C311yescharacteristic
228C23×D3—22no—
229C23×D3—22no—
230C23×D3—24no—
231C23×D3—42no—
232C23×D3C2×C3×C414yes—
233C23×D3C23×C311yescharacteristic
234C23×D3C23×C311yescharacteristic
235C22×C3×C4—24no—
236C22×C3×C4—24no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—24no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—34no—
249C22×C3×C4—32no—
250C22×C3×C4—32no—
251C22×C3×C4—64no—
252C22×C3×C4—64no—
253C22×C3×C4—122no—
254C22×C3×C4—122no—
255C22×C3×C4C4×D314yescomplemented
256C22×C3×C4C2×C3×C414yescomplemented
257C22×C3×C4C22×D312yes—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D312yes—
261C22×C3×C4C23×C312yes—
262C22×C3×C4C23×C311yescharacteristic
263C22×C3×C4C23×C311yescharacteristic
264C22×C3×C4C23×C312yes—
265C22×Dic3—42no—
266C22×Dic3C2×C3×C414yescomplemented
267C22×Dic3C23×C312yes—
268C22×Dic3C23×C312yes—
269C22×Dic3C23×C311yescharacteristic
270C22×Dic3C23×C311yescharacteristic
271C2×C4×D3—24no—
272C2×C4×D3—24no—
273C2×C4×D3—42no—
274C3×C4⋊C4—28no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—122no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—24no—
282C3×C22⋊C4—34no—
283C3×C22⋊C4—34no—
284C3×C22⋊C4—34no—
285C3×C22⋊C4—34no—
286C3×C22⋊C4—64no—
287C3×C22⋊C4—62no—
288C3×C22⋊C4—62no—
289C3×C22⋊C4—64no—
290C3×C22⋊C4—122no—
291C3×C22⋊C4#6714yes—
292C3×C22⋊C4C3×D414yes—
293C3×C42—28no—
294C3×C42—24no—
295C3×C42—24no—
296C3×C42—122no—
297#217—22no—
298#217—22no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4C2×C3×C414yes—
303(C2×D3)⋊C4C2×C3×C414yes—
304(C2×D3)⋊C4C2×C3×C414yescomplemented
305(C2×D3)⋊C4C2×C3×C414yescomplemented
306Dic3⋊C4—42no—
307C4×Dic3—42no—
308C22×C32—22no—
309C22×C32—22no—
310C22×C32—24no—
311C22×C32—24no—
312C22×C32C4×D414yes—
313C22×C32C23×C411yescharacteristic
314C22×C32C22×D411yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C22×C32C2×#4112yes—
317C22×C32H(5,𝔽2)12yes—
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3—24no—
321C2×C3×D3—24no—
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—22no—
325C2×C3×D3—416no—
326C2×C3×D3—42no—
327C2×C3×D3—42no—
328C2×C3×D3#11714yescomplemented
329C32×C4—22no—
330C32×C4—22no—
331C32×C4—24no—
332C32×C4—42no—
333C3×Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336C3×Dic3—42no—
337C25—31no—
338C23×C4—31no—
339C23×C4—32no—
340C23×C4C2×C3×D311yescharacteristic
341#117—24no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4C2×C3×D312yescomplemented
344C2×C22⋊C4—38no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—32no—
352C2×C22⋊C4—32no—
353C2×C22⋊C4—32no—
354C2×C22⋊C4—64no—
355C2×C22⋊C4C2×C3×D311yescharacteristic
356C2×C22⋊C4C2×C3×D311yescharacteristic
357C2×C42—32no—
358C2×C42C2×C3×D312yescomplemented
359#95—32no—
360#95—32no—
361#95—32no—
362#95—32no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—21no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—32no—
372C23×C3—34no—
373C23×C3—32no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—68no—
377C23×C3—61no—
378C23×C3—62no—
379C23×C3—61no—
380C23×C3—68no—
381C23×C3—61no—
382C23×C3—62no—
383C23×C3—62no—
384C23×C3—61no—
385C23×C3—124no—
386C23×C3—128no—
387C23×C3—128no—
388C23×C3C2×C4×D312yes—
389C23×C3#23512yes—
390C23×C3C2×#6712yes—
391C23×C3C22×C3×C412yes—
392C23×C3C2×C3×D412yes—
393C23×C3C3×#4112yes—
394C23×C3C23×D311yescharacteristic
395C23×C3C24×C311yescharacteristic
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—22no—
399C22×D3—28no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—28no—
405C22×D3—44no—
406C22×D3—48no—
407C22×D3—48no—
408C22×D3C22×C3×C412yes—
409C22×D3C22×C3×C412yes—
410C22×D3C3×#4114yes—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—216no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—28no—
417C2×C3×C4—28no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—24no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—24no—
440C2×C3×C4—32no—
441C2×C3×C4—32no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—128no—
455C2×C3×C4—124no—
456C2×C3×C4C2×C4×D312yes—
457C2×C3×C4C2×C4×D312yes—
458C2×C3×C4C2×#6714yes—
459C2×C3×C4C22×C3×C412yes—
460C2×C3×C4C22×C3×C412yes—
461C2×C3×C4C2×C3×D414yes—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—44no—
471C2×Dic3C22×C3×C412yes—
472C2×Dic3C22×C3×C412yes—
473C4×D3—48no—
474C2×C32—24no—
475C2×C32C2×#11711yescharacteristic
476C2×C32C2×C4×D411yescharacteristic
477C2×C32#51811yescharacteristic
478C2×C32#54612yes—
479C2×C32#55112yes—
480C3×D3—24no—
481C3×D3—42no—
482C24—31no—
483C24—31no—
484C24—34no—
485C24—64no—
486C24—62no—
487C24—62no—
488C24—122no—
489C24C22×C3×D311yescharacteristic
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—31no—
493C22×C4—31no—
494C22×C4—34no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—64no—
498C22×C4—64no—
499C22×C4—122no—
500C22×C4—122no—
501C22×C4C3×C4×D314yescomplemented
502C22×C4C22×C3×D312yes—
503C22×C4C22×C3×D311yescharacteristic
504C22×C4C22×C3×D311yescharacteristic
505C22×C4C22×C3×D312yes—
506C4⋊C4—24no—
507C4⋊C4—122no—
508C22⋊C4—22no—
509C22⋊C4—34no—
510C22⋊C4—34no—
511C22⋊C4—34no—
512C22⋊C4—34no—
513C22⋊C4—64no—
514C22⋊C4—62no—
515C22⋊C4—62no—
516C22⋊C4—64no—
517C22⋊C4—122no—
518C22⋊C4C3×#6714yes—
519C42—24no—
520C42—122no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—21no—
535C22×C3—34no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—62no—
541C22×C3—64no—
542C22×C3—62no—
543C22×C3—64no—
544C22×C3—62no—
545C22×C3—62no—
546C22×C3—62no—
547C22×C3—1216no—
548C22×C3—122no—
549C22×C3—122no—
550C22×C3C4×#6714yes—
551C22×C3C3×C4×D414yes—
552C22×C3C22×C4×D311yescharacteristic
553C22×C3C2×#23511yescharacteristic
554C22×C3D3×#4112yes—
555C22×C3#100912yes—
556C22×C3C22×#6711yescharacteristic
557C22×C3C23×C3×C411yescharacteristic
558C22×C3C22×C3×D411yescharacteristic
559C22×C3C2×C3×#4111yescharacteristic
560C22×C3C2×C3×#4112yes—
561C22×C3C3×H(5,𝔽2)12yes—
562C2×D3—22no—
563C2×D3—22no—
564C2×D3—24no—
565C2×D3—24no—
566C2×D3—22no—
567C2×D3—22no—
568C2×D3—22no—
569C2×D3—416no—
570C2×D3—42no—
571C2×D3—42no—
572C2×D3C3×#11714yescomplemented
573C3×C4—24no—
574C3×C4—24no—
575C3×C4—22no—
576C3×C4—22no—
577C3×C4—24no—
578C3×C4—22no—
579C3×C4—22no—
580C3×C4—24no—
581C3×C4—44no—
582C3×C4—44no—
583C3×C4—42no—
584C3×C4—42no—
585C3×C4—62no—
586C3×C4—62no—
587C3×C4—122no—
588C3×C4—122no—
589Dic3—22no—
590Dic3—22no—
591Dic3—42no—
592Dic3—42no—
593C32#234211yescharacteristic, complemented, Sylow
594C23—22no—
595C23—22no—
596C23—32no—
597C23—34no—
598C23—32no—
599C23—68no—
600C23—61no—
601C23—62no—
602C23—61no—
603C23—68no—
604C23—61no—
605C23—62no—
606C23—62no—
607C23—61no—
608C23—124no—
609C23—128no—
610C23—128no—
611C23C2×C3×C4×D312yes—
612C23C3×#23512yes—
613C23C2×C3×#6712yes—
614C23C23×C3×D311yescharacteristic
615C2×C4—28no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—32no—
626C2×C4—32no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—128no—
636C2×C4—124no—
637C2×C4C2×C3×C4×D312yes—
638C2×C4C2×C3×C4×D312yes—
639C2×C4C2×C3×#6714yes—
640C2×C3—24no—
641C2×C3—24no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—22no—
645C2×C3—21no—
646C2×C3—22no—
647C2×C3—44no—
648C2×C3—64no—
649C2×C3—122no—
650C2×C3D3×#11711yescharacteristic
651C2×C3#552111yescharacteristic
652C2×C3#552712yes—
653C2×C3C2×C4×#6711yescharacteristic
654C2×C3#582912yes—
655C2×C3C2×C3×#11711yescharacteristic
656C2×C3C2×C3×C4×D411yescharacteristic
657C2×C3C3×#51811yescharacteristic
658C2×C3C3×#54612yes—
659C2×C3C3×#55112yes—
660D3—24no—
661D3—42no—
662C22—22no—
663C22—22no—
664C22—24no—
665C22—24no—
666C22—34no—
667C22—62no—
668C22—64no—
669C22—62no—
670C22—64no—
671C22—62no—
672C22—62no—
673C22—62no—
674C22—1216no—
675C22—122no—
676C22—122no—
677C22C3×C4×#6714yes—
678C22C22×C3×C4×D311yescharacteristic
679C22C2×C3×#23511yescharacteristic
680C22C3×D3×#4112yes—
681C22C3×#100912yes—
682C22C22×C3×#6711yescharacteristic
683C4—22no—
684C4—22no—
685C4—24no—
686C4—42no—
687C4—62no—
688C4—62no—
689C4—122no—
690C4—122no—
691C3—21no—
692C3#8227111yescharacteristic, direct product factor
693C3C3×#234211yescharacteristic, complemented
694C2—24no—
695C2—64no—
696C2—122no—
697C2C3×D3×#11711yescharacteristic
698C2C3×#552111yescharacteristic
699C2C3×#552712yes—
700C2C2×C3×C4×#6711yescharacteristic
701C2C3×#582912yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
prime radicalC24×C3×D3C22
cosocleC23×C3C24×C3
hypercenterC2×C3×#117D3
hypocenterC3C3×#2342
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
4. C3×#5211C2semidirect
5. C3×#4990C2semidirect
6. C3×#4989C2semidirect
8. C3×#4942C2semidirect
9. C3×Dic3×C22⋊C4C2semidirect
10. C3×#4940C2semidirect
11. C3×C4×(C2×D3)⋊C4C2semidirect
13. #82271C3direct (N × H)
19. C2×C32×C4⋊C4C22semidirect
22. C2×C32×C42C22semidirect
25. C2×C3×(C2×D3)⋊C4C4semidirect
33. C2×C3×Dic3⋊C4C22semidirect
34. C2×C3×C4×Dic3C22semidirect
36. C3×C3⋊#95C22semidirect
37. C3×C3⋊#95C22semidirect
38. C3×C3⋊#95C22semidirect
39. C3×C3⋊#95C22semidirect
41. C2×C3×#117D3semidirect
42. C2×C3×#117C2×C3semidirect
55. #5211C2×C3semidirect
56. #4990C2×C3semidirect
57. #4989C2×C3semidirect
59. #4942C2×C3semidirect
60. Dic3×C22⋊C4C2×C3semidirect
61. #4940C2×C3semidirect
62. C4×(C2×D3)⋊C4C2×C3semidirect
73. C22×C32×C4C2×C4semidirect
79. C22×C3×Dic3C2×C4semidirect
98. C3×(C2×D3)⋊C4C2×C4semidirect
99. C3×(C2×D3)⋊C4C2×C4semidirect
117. C2×C3×C4⋊C4C2×D3semidirect
118. C2×C3×C4⋊C4C22×C3semidirect
138. C2×C3×C42C2×D3semidirect
139. C2×C3×C42C22×C3semidirect
142. C2×(C2×D3)⋊C4C3×C4semidirect
150. C2×Dic3⋊C4C22×C3semidirect
151. C2×C4×Dic3C22×C3semidirect
157. C3⋊#95C22×C3semidirect
158. C3⋊#95C22×C3semidirect
159. C3⋊#95C22×C3semidirect
160. C3⋊#95C22×C3semidirect
207. C2×#117C3×D3semidirect
255. C22×C3×C4C4×D3semidirect
256. C22×C3×C4C2×C3×C4semidirect
266. C22×Dic3C2×C3×C4semidirect
304. (C2×D3)⋊C4C2×C3×C4semidirect
305. (C2×D3)⋊C4C2×C3×C4semidirect
328. C2×C3×D3#117semidirect
343. C2×C4⋊C4C2×C3×D3semidirect
358. C2×C42C2×C3×D3semidirect
501. C22×C4C3×C4×D3semidirect
572. C2×D3C3×#117semidirect
593. C32#2342semidirect
692. C3#82271direct (N × H)
693. C3C3×#2342semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C22×C3×(C2×D3)⋊C42
C2×C3×D3×C22⋊C42
C3×#52112
C3×#49902
C3×#49892
C3×#49552
C3×#49422
C3×Dic3×C22⋊C42
C3×#49402
C3×C4×(C2×D3)⋊C42
C3×#23423
#822713