Finite Group Databasebeta

← C3×#10594985 #13174626

Subgroups — C3×#10594985 #13174626

Order 1728.

1278 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64139C211yesmaximal, characteristic, complemented
2C32×#930C211yesmaximal, characteristic, complemented
3C32×#926C211yesmaximal, characteristic, complemented
4C3×#63971C212yesmaximal, complemented
5C3×#63958C212yesmaximal, complemented
6C3×#63911C211yesmaximal, characteristic, complemented
7C3×#63894C211yesmaximal, characteristic, complemented
8C3×Dic3×D12C211yesmaximal, characteristic, complemented
9C3×#63890C212yesmaximal, complemented
10C3×#63869C211yesmaximal, characteristic, complemented
11C3×#63854C212yesmaximal, complemented
12C3×#5619—31nomaximal
13C3×#5535—31nomaximal
14#10594985C311yesmaximal, characteristic, direct product factor
15C22×C33×C4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C32×#67C2212yes—
19C2×C32×D12C2211yescharacteristic
20C2×C3×#626C2212yes—
21C2×C3×#626C2212yes—
22C2×C3×#624C2212yes—
23C2×C3×D3×Dic3C2212yes—
24C3×#3752C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C32×#217C2211yescharacteristic
27C32×#217C2211yescharacteristic
28C32×(C2×D3)⋊C4C2212yes—
29C32×C4⋊Dic3C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×C4×Dic3C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic
34C3×#3724C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C32×#121—31no—
39C32×#117—31no—
40#64139C2×C311yescharacteristic, complemented
41C3×#940—31no—
42C3×#939—32no—
43C3×#938—32no—
44C3×D4×Dic3—31no—
45C3×#930—21no—
46C3×#930—31no—
47C3×#930—31no—
48C3×#930—61no—
49C3×#930D311yescharacteristic, complemented
50C3×#930C2×C311yescharacteristic, complemented
51C3×#926—21no—
52C3×#926D311yescharacteristic, complemented
53C3×#926C2×C311yescharacteristic, complemented
54C3×#894—32no—
55C3×#894—32no—
56C3×#893—31no—
57C3×#890—31no—
58C3×#886—32no—
59C3×#884—32no—
60C3×#884—32no—
61C3×#883—32no—
62C3×#874—31no—
63C3×C4×D12—31no—
64C3×C4×D12—31no—
65C3×#870—31no—
66#63971C2×C312yescomplemented
67#63958C2×C312yescomplemented
68#63911C2×C311yescharacteristic, complemented
69#63894C2×C311yescharacteristic, complemented
70Dic3×D12C2×C311yescharacteristic, complemented
71#63890C2×C312yescomplemented
72#63869C2×C311yescharacteristic, complemented
73#63854C2×C312yescomplemented
74C23×C33C2311yescharacteristic
75C22×C3×C3⋊D3C2312yes—
76C22×C32×D3C2312yes—
77C2×C33×C4—22no—
78C2×C33×C4C2311yescharacteristic
79C2×C33×C4C2311yescharacteristic
80C3×#638—42no—
81C2×C3×C3⋊Dic3C2312yes—
82C3×C4⋊(C3⋊D3)—22no—
83C32×#67—42no—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C32×D12—22no—
90C3×#626—42no—
91C3×#626—42no—
92C3×#624—42no—
93C3×D3×Dic3—42no—
94C3×#540—91no—
95#5619—31no—
96#5535—31no—
97C2×C32×D4—32no—
98C2×C32×D4—31no—
99C22×C32×C4—21no—
100C22×C32×C4—21no—
101C22×C32×C4—21no—
102C22×C32×C4—41no—
103C22×C32×C4C2×D311yescharacteristic
104C22×C32×C4C2×D311yescharacteristic
105C22×C32×C4C22×C311yescharacteristic
106C2×#638C22×C312yes—
107C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
108C2×C3×#67—22no—
109C2×C3×#67—32no—
110C2×C3×#67—32no—
111C2×C3×#67—32no—
112C2×C3×#67—32no—
113C2×C3×#67—62no—
114C2×C3×#67C2×D312yes—
115C2×C3×#67C22×C312yes—
116C22×C3×Dic3—32no—
117C2×C3×D12—21no—
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×C3×D12—32no—
121C2×C3×D12—32no—
122C2×C3×D12—61no—
123C2×C3×D12C2×D311yescharacteristic
124C2×C3×D12C22×C311yescharacteristic
125C2×C3×C4×D3—32no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—32no—
128C2×#626C22×C312yes—
129C2×#626C22×C312yes—
130C2×#624C22×C312yes—
131C2×D3×Dic3C22×C312yes—
132C32×C4⋊C4—31no—
133C32×C4⋊C4—31no—
134C32×C4⋊C4—31no—
135C32×C22⋊C4—31no—
136C32×C22⋊C4—31no—
137C32×C22⋊C4—32no—
138C32×C42—31no—
139C32×C42—31no—
140#3752C22×C312yes—
141C4⋊(C3⋊Dic3)C22×C311yescharacteristic
142C3×#217—21no—
143C3×#217—21no—
144C3×#217—32no—
145C3×#217C2×D311yescharacteristic
146C3×#217C2×D311yescharacteristic
147C3×#217C22×C311yescharacteristic
148C3×#217C22×C311yescharacteristic
149C3×(C2×D3)⋊C4—22no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—32no—
155C3×(C2×D3)⋊C4—62no—
156C3×(C2×D3)⋊C4C2×D312yes—
157C3×(C2×D3)⋊C4C22×C312yes—
158C3×C4⋊Dic3—21no—
159C3×C4⋊Dic3—21no—
160C3×C4⋊Dic3—21no—
161C3×C4⋊Dic3—31no—
162C3×C4⋊Dic3—31no—
163C3×C4⋊Dic3—32no—
164C3×C4⋊Dic3—61no—
165C3×C4⋊Dic3C2×D311yescharacteristic
166C3×C4⋊Dic3C2×D311yescharacteristic
167C3×C4⋊Dic3C2×D311yescharacteristic
168C3×C4⋊Dic3C22×C311yescharacteristic
169C3×C4⋊Dic3C22×C311yescharacteristic
170C3×C4⋊Dic3C22×C311yescharacteristic
171C3×Dic3⋊C4—32no—
172C3×Dic3⋊C4—32no—
173C3×Dic3⋊C4—32no—
174C3×C4×Dic3—21no—
175C3×C4×Dic3—21no—
176C3×C4×Dic3C2×D311yescharacteristic
177C3×C4×Dic3C2×D311yescharacteristic
178C3×C4×Dic3C22×C311yescharacteristic
179C3×C4×Dic3C22×C311yescharacteristic
180#3724C22×C312yes—
181Dic3⋊Dic3C22×C312yes—
182#3722C22×C312yes—
183(C2×D3)⋊Dic3C22×C312yes—
184C22×C33—21no—
185C22×C33—21no—
186C22×C33—21no—
187C22×C33C2411yescharacteristic
188C2×C3×C3⋊D3—22no—
189C2×C3×C3⋊D3—22no—
190C2×C3×C3⋊D3—22no—
191C2×C32×D3—22no—
192C2×C32×D3—22no—
193C2×C32×D3—22no—
194C33×C4—21no—
195C33×C4#4112yes—
196C3×C3⋊Dic3—22no—
197C32×Dic3—21no—
198C32×Dic3—21no—
199C32×Dic3—22no—
200C32×Dic3—21no—
201C32×Dic3—21no—
202C3×#127—91no—
203C3×#125—91no—
204C3×#123—92no—
205C3×#123—92no—
206C3×#121—31no—
207C3×#121—31no—
208C3×#121—61no—
209C3×#121—92no—
210C3×#121—92no—
211C3×#121—91no—
212C3×C4×D4—91no—
213C3×C4×D4—91no—
214C3×#117—31no—
215C3×#117—31no—
216C3×#117—61no—
217#940—31no—
218#939—32no—
219#938—32no—
220D4×Dic3—31no—
221#930—31no—
222#930—31no—
223#930—61no—
224#930C3×D311yescharacteristic, complemented
225#926C3×D311yescharacteristic, complemented
226#894—32no—
227#894—32no—
228#893—31no—
229#890—31no—
230#886—32no—
231#884—32no—
232#884—32no—
233#883—32no—
234#874—31no—
235C4×D12—31no—
236C4×D12—31no—
237#870—31no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—32no—
242C23×C32—41no—
243C23×C32C22×D311yescharacteristic
244C23×C32C22×D311yescharacteristic
245C23×C32C23×C311yescharacteristic
246C22×C3⋊D3C23×C312yes—
247C22×C3×D3—22no—
248C22×C3×D3—32no—
249C22×C3×D3—32no—
250C22×C3×D3—62no—
251C22×C3×D3C22×D312yes—
252C22×C3×D3C23×C312yes—
253C32×D4—62no—
254C32×D4—122no—
255C2×C32×C4—22no—
256C2×C32×C4—24no—
257C2×C32×C4—22no—
258C2×C32×C4—22no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—32no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—41no—
271C2×C32×C4—41no—
272C2×C32×C4—42no—
273C2×C32×C4—42no—
274C2×C32×C4—44no—
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C23×C311yescharacteristic
280C2×C32×C4C23×C311yescharacteristic
281#638—42no—
282C2×C3⋊Dic3C23×C312yes—
283C4⋊(C3⋊D3)—22no—
284C3×#67—42no—
285C3×#67—42no—
286C3×#67—44no—
287C3×#67—122no—
288C3×#67—122no—
289C3×#67—122no—
290C3×#67—122no—
291C3×#67—124no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—122no—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C2×C3×Dic3C22×D311yescharacteristic
304C2×C3×Dic3C22×D311yescharacteristic
305C2×C3×Dic3C22×D312yes—
306C2×C3×Dic3C23×C311yescharacteristic
307C2×C3×Dic3C23×C311yescharacteristic
308C2×C3×Dic3C23×C312yes—
309C2×C3×Dic3C23×C311yescharacteristic
310C2×C3×Dic3C23×C311yescharacteristic
311C3×D12—22no—
312C3×D12—22no—
313C3×D12—42no—
314C3×D12—62no—
315C3×D12—62no—
316C3×D12—122no—
317C3×D12—122no—
318C3×D12—122no—
319C3×C4×D3—122no—
320C3×C4×D3—122no—
321C3×C4×D3—122no—
322#626—42no—
323#626—42no—
324#624—42no—
325D3×Dic3—42no—
326#540—91noSylow
327C2×C33—41no—
328C2×C33C2×#4111yescharacteristic
329C2×C33H(5,𝔽2)11yescharacteristic
330C2×C33H(5,𝔽2)11yescharacteristic
331C3×C3⋊D3—42no—
332C32×D3—42no—
333C2×C3×D4—32no—
334C2×C3×D4—32no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—61no—
338C2×C3×D4—62no—
339C2×C3×D4—92no—
340C2×C3×D4—92no—
341C2×C3×D4—92no—
342C2×C3×D4—91no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—41no—
347C22×C3×C4—92no—
348C22×C3×C4—92no—
349C22×C3×C4D3211yescharacteristic
350C22×C3×C4C2×C3×D311yescharacteristic
351C22×C3×C4C2×C3×D311yescharacteristic
352C2×#67—32no—
353C2×#67—32no—
354C2×#67—32no—
355C2×#67—32no—
356C2×#67—62no—
357C2×#67C2×C3×D312yes—
358C22×Dic3—32no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—32no—
362C2×D12—32no—
363C2×D12—61no—
364C2×D12C2×C3×D311yescharacteristic
365C2×C4×D3—32no—
366C2×C4×D3—32no—
367C2×C4×D3—32no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—92no—
378C3×C4⋊C4—92no—
379C3×C4⋊C4—91no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—32no—
385C3×C22⋊C4—32no—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—92no—
390C3×C22⋊C4—92no—
391C3×C22⋊C4—92no—
392C3×C42—31no—
393C3×C42—31no—
394C3×C42—31no—
395C3×C42—31no—
396C3×C42—61no—
397C3×C42—61no—
398#217—32no—
399#217C2×C3×D311yescharacteristic
400#217C2×C3×D311yescharacteristic
401(C2×D3)⋊C4—32no—
402(C2×D3)⋊C4—32no—
403(C2×D3)⋊C4—32no—
404(C2×D3)⋊C4—32no—
405(C2×D3)⋊C4—32no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4C2×C3×D312yes—
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—32no—
411C4⋊Dic3—61no—
412C4⋊Dic3C2×C3×D311yescharacteristic
413C4⋊Dic3C2×C3×D311yescharacteristic
414C4⋊Dic3C2×C3×D311yescharacteristic
415Dic3⋊C4—32no—
416Dic3⋊C4—32no—
417Dic3⋊C4—32no—
418C4×Dic3C2×C3×D311yescharacteristic
419C4×Dic3C2×C3×D311yescharacteristic
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—22no—
424C22×C32—22no—
425C22×C32—22no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32—42no—
443C22×C32—42no—
444C22×C32—42no—
445C22×C32—62no—
446C22×C32—62no—
447C22×C32—62no—
448C22×C32C23×D311yescharacteristic
449C22×C32C23×D311yescharacteristic
450C22×C32C24×C311yescharacteristic
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—42no—
461C2×C3×D3—42no—
462C2×C3×D3—42no—
463C2×C3×D3—62no—
464C2×C3×D3—62no—
465C2×C3×D3—62no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—62no—
469C2×C3×D3—122no—
470C2×C3×D3—122no—
471C2×C3×D3—122no—
472C32×C4—21no—
473C32×C4—22no—
474C32×C4—21no—
475C32×C4—21no—
476C32×C4—22no—
477C32×C4—22no—
478C32×C4—22no—
479C32×C4—42no—
480C32×C4—41no—
481C32×C4—41no—
482C32×C4—42no—
483C32×C4—61no—
484C32×C4—61no—
485C32×C4—61no—
486C32×C4—62no—
487C32×C4—61no—
488C32×C4#23512yes—
489C32×C4#23712yes—
490C32×C4C3×#4112yes—
491C3⋊Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—21no—
496C3×Dic3—21no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—22no—
500C3×Dic3—21no—
501C3×Dic3—21no—
502C3×Dic3—41no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—42no—
507C3×Dic3—62no—
508C3×Dic3—62no—
509C3×Dic3—122no—
510#127—91no—
511#125—91no—
512#123—92no—
513#123—92no—
514#121—31no—
515#121—92no—
516#121—92no—
517#121—91no—
518C4×D4—91no—
519C4×D4—91no—
520#117—31no—
521C33#54011yescharacteristic, complemented, Sylow
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—32no—
526C23×C3—32no—
527C23×C3—41no—
528C23×C3—62no—
529C23×C3—92no—
530C23×C3C2×D3211yescharacteristic
531C23×C3C22×C3×D311yescharacteristic
532C23×C3C22×C3×D311yescharacteristic
533C22×D3—32no—
534C22×D3—32no—
535C22×D3—62no—
536C22×D3C22×C3×D312yes—
537C3×D4—62no—
538C3×D4—62no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—124no—
543C3×D4—182no—
544C3×D4—362no—
545C3×D4—362no—
546C3×D4—362no—
547C2×C3×C4—24no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—32no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—32no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—42no—
568C2×C3×C4—42no—
569C2×C3×C4—44no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—62no—
577C2×C3×C4—92no—
578C2×C3×C4—362no—
579C2×C3×C4—362no—
580C2×C3×C4C2×D3211yescharacteristic
581C2×C3×C4C2×D3211yescharacteristic
582C2×C3×C4C22×C3×D311yescharacteristic
583C2×C3×C4C22×C3×D311yescharacteristic
584C2×C3×C4C22×C3×D311yescharacteristic
585C2×C3×C4C22×C3×D311yescharacteristic
586#67—42no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—124no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—62no—
595C2×Dic3—122no—
596C2×Dic3C22×C3×D311yescharacteristic
597C2×Dic3C22×C3×D311yescharacteristic
598C2×Dic3C22×C3×D311yescharacteristic
599C2×Dic3C22×C3×D311yescharacteristic
600C2×Dic3C22×C3×D312yes—
601D12—22no—
602D12—62no—
603D12—62no—
604D12—122no—
605D12—122no—
606D12—122no—
607C4×D3—122no—
608C4×D3—122no—
609C4×D3—122no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—41no—
620C2×C32—41no—
621C2×C32—41no—
622C2×C32—42no—
623C2×C32—42no—
624C2×C32—42no—
625C2×C32—44no—
626C2×C32—41no—
627C2×C32—41no—
628C2×C32—41no—
629C2×C32—122no—
630C2×C32C2×#23511yescharacteristic
631C2×C32C2×#23711yescharacteristic
632C2×C32#100411yescharacteristic
633C2×C32#100911yescharacteristic
634C2×C32#100911yescharacteristic
635C2×C32#100911yescharacteristic
636C2×C32C2×C3×#4111yescharacteristic
637C2×C32C3×H(5,𝔽2)11yescharacteristic
638C2×C32C3×H(5,𝔽2)11yescharacteristic
639C3⋊D3—42no—
640C3×D3—42no—
641C3×D3—42no—
642C3×D3—82no—
643C3×D3—122no—
644C3×D3—122no—
645C3×D3—242no—
646C2×D4—32no—
647C2×D4—31no—
648C2×D4—92no—
649C2×D4—92no—
650C2×D4—92no—
651C2×D4—91no—
652C22×C4—92no—
653C22×C4—92no—
654C22×C4C3×D3211yescharacteristic
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—31no—
658C4⋊C4—92no—
659C4⋊C4—92no—
660C4⋊C4—91no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—32no—
664C22⋊C4—92no—
665C22⋊C4—92no—
666C22⋊C4—92no—
667C42—31no—
668C42—31no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—41no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—62no—
699C22×C3—62no—
700C22×C3—122no—
701C22×C3—122no—
702C22×C3—122no—
703C22×C3—182no—
704C22×C3—182no—
705C22×C3—182no—
706C22×C3C22×D3211yescharacteristic
707C22×C3C23×C3×D311yescharacteristic
708C22×C3C23×C3×D311yescharacteristic
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—62no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—122no—
719C2×D3—122no—
720C2×D3—122no—
721C3×C4—22no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—61no—
733C3×C4—62no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—61no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4—62no—
741C3×C4—61no—
742C3×C4—122no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4—121no—
747C3×C4—182no—
748C3×C4#380412yes—
749C3×C4C3×#23512yes—
750C3×C4C3×#23712yes—
751Dic3—22no—
752Dic3—21no—
753Dic3—21no—
754Dic3—21no—
755Dic3—21no—
756Dic3—62no—
757Dic3—62no—
758Dic3—122no—
759C32—21no—
760C32—21no—
761C32—21no—
762C32—41no—
763C32#553511yescharacteristic, complemented
764C32#561911yescharacteristic, complemented
765C32C3×#54011yescharacteristic, complemented
766C23—32no—
767C23—92no—
768C23C2×C3×D3211yescharacteristic
769D4—62no—
770D4—122no—
771D4—182no—
772D4—362no—
773D4—362no—
774D4—362no—
775C2×C4—22no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—32no—
781C2×C4—92no—
782C2×C4—362no—
783C2×C4—362no—
784C2×C4C2×C3×D3211yescharacteristic
785C2×C4C2×C3×D3211yescharacteristic
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—42no—
796C2×C3—42no—
797C2×C3—42no—
798C2×C3—44no—
799C2×C3—41no—
800C2×C3—41no—
801C2×C3—41no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—41no—
805C2×C3—122no—
806C2×C3—122no—
807C2×C3—242no—
808C2×C3—362no—
809C2×C3#6430711yescharacteristic
810C2×C3#6430811yescharacteristic
811C2×C3C2×#380411yescharacteristic
812C2×C3C2×C3×#23511yescharacteristic
813C2×C3C2×C3×#23711yescharacteristic
814C2×C3C3×#100411yescharacteristic
815C2×C3C3×#100911yescharacteristic
816C2×C3C3×#100911yescharacteristic
817C2×C3C3×#100911yescharacteristic
818D3—42no—
819D3—122no—
820D3—122no—
821D3—242no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—62no—
826C22—62no—
827C22—62no—
828C22—182no—
829C22—182no—
830C22—182no—
831C22C22×C3×D3211yescharacteristic
832C4—21no—
833C4—61no—
834C4—62no—
835C4—61no—
836C4—61no—
837C4—61no—
838C4—182no—
839C4C3×#380412yes—
840C3—21no—
841C3—21no—
842C3—21no—
843C3—41no—
844C3#1059498511yescharacteristic, direct product factor
845C3C3×#553511yescharacteristic, complemented
846C3C3×#561911yescharacteristic, complemented
847C2—41no—
848C2—122no—
849C2—362no—
850C2C3×#6430711yescharacteristic
851C2C3×#6430811yescharacteristic
852C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C3×#64139C2semidirect
2. C32×#930C2semidirect
3. C32×#926C2semidirect
4. C3×#63971C2semidirect
5. C3×#63958C2semidirect
6. C3×#63911C2semidirect
7. C3×#63894C2semidirect
8. C3×Dic3×D12C2semidirect
9. C3×#63890C2semidirect
10. C3×#63869C2semidirect
11. C3×#63854C2semidirect
14. #10594985C3direct (N × H)
40. #64139C2×C3semidirect
49. C3×#930D3semidirect
50. C3×#930C2×C3semidirect
52. C3×#926D3semidirect
53. C3×#926C2×C3semidirect
66. #63971C2×C3semidirect
67. #63958C2×C3semidirect
68. #63911C2×C3semidirect
69. #63894C2×C3semidirect
70. Dic3×D12C2×C3semidirect
71. #63890C2×C3semidirect
72. #63869C2×C3semidirect
73. #63854C2×C3semidirect
224. #930C3×D3semidirect
225. #926C3×D3semidirect
521. C33#540semidirect
763. C32#5535semidirect
764. C32#5619semidirect
765. C32C3×#540semidirect
844. C3#10594985direct (N × H)
845. C3C3×#5535semidirect
846. C3C3×#5619semidirect

Maximal subgroups

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

subgroupindex
C3×#641392
C32×#9302
C32×#9262
C3×#639712
C3×#639582
C3×#639112
C3×#638942
C3×Dic3×D122
C3×#638902
C3×#638692
C3×#638542
C3×#56193
C3×#55353
#105949853