Finite Group Databasebeta

← C3×#10595136 #13174784

Subgroups — C3×#10595136 #13174784

Order 1728.

1504 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C212yesmaximal, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic, complemented
4C32×D4×Dic3C211yesmaximal, characteristic, complemented
5C3×#63975C212yesmaximal, complemented
6C3×#63969C212yesmaximal, complemented
7C3×#63964C212yesmaximal, complemented
8C3×#63918C211yesmaximal, characteristic, complemented
9C3×C4×#626C211yesmaximal, characteristic, complemented
10C3×#63900C211yesmaximal, characteristic, complemented
11C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12C3×#5611—31nomaximal
13C3×#5551—31nomaximal
14#10595136C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×#67C2212yes—
19C22×C32×Dic3C2212yes—
20C2×C32×C4×D3C2211yescharacteristic
21C2×C3×#627C2212yes—
22C2×C3×#626C2211yescharacteristic
23C2×C3×#624C2212yes—
24C3×#3804—28no—
25C2×C3×D3×Dic3C2212yes—
26C3×#3757C2212yes—
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C32×#217C2212yes—
29C32×#217C2212yes—
30C32×C4⋊Dic3C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×C4×Dic3C2211yescharacteristic
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×#3722C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×C3×#237—32no—
40C2×C3×#235—32no—
41C2×#3804C2×C312yescomplemented
42C32×#121—31no—
43C32×C4×D4—31no—
44#64147C2×C311yescharacteristic, complemented
45C3×#938—21no—
46C3×#938—31no—
47C3×#938—31no—
48C3×#938—61no—
49C3×#938D311yescharacteristic, complemented
50C3×#938C2×C311yescharacteristic, complemented
51C3×#935—32no—
52C3×D4×Dic3—21no—
53C3×D4×Dic3D311yescharacteristic, complemented
54C3×D4×Dic3C2×C311yescharacteristic, complemented
55C3×C4×#67—31no—
56C2×C3×C4⋊Dic3—31no—
57C3×#924—32no—
58C3×D3×C4⋊C4—31no—
59C3×D3×C4⋊C4—31no—
60C3×D3×C4⋊C4—31no—
61C3×#888—31no—
62C3×#883—32no—
63C3×#883—32no—
64C3×#883—32no—
65C3×#878—32no—
66C3×C4×D12—31no—
67C3×#869—31no—
68#63975C2×C312yescomplemented
69#63969C2×C312yescomplemented
70#63964C2×C312yescomplemented
71#63918C2×C311yescharacteristic, complemented
72C4×#626C2×C311yescharacteristic, complemented
73#63900C2×C311yescharacteristic, complemented
74D3×C4⋊Dic3C2×C311yescharacteristic, complemented
75C23×C33C2312yes—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C33×D4—22no—
79C2×C33×C4C2311yescharacteristic
80C3×#638—24no—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—22no—
84C32×#67—24no—
85C2×C32×Dic3—24no—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C32×C4×D3—22no—
92C3×#627—24no—
93C3×#626D414yescomplemented
94C3×#624—24no—
95C3×D3×Dic3—24no—
96C3×#547—91no—
97#5611—31no—
98#5551—31no—
99C2×C32×D4—21no—
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4—32no—
103C2×C32×D4—41no—
104C2×C32×D4C2×D311yescharacteristic
105C2×C32×D4C2×D311yescharacteristic
106C2×C32×D4C22×C311yescharacteristic
107C22×C32×C4—32no—
108C22×C32×C4—31no—
109C2×#638C22×C312yes—
110C2×C4×C3⋊D3C22×C311yescharacteristic
111C2×C3×#67—22no—
112C2×C3×#67—32no—
113C2×C3×#67—32no—
114C2×C3×#67—31no—
115C2×C3×#67—62no—
116C2×C3×#67C2×D312yes—
117C2×C3×#67C22×C312yes—
118C22×C3×Dic3—22no—
119C22×C3×Dic3—32no—
120C22×C3×Dic3C2×D312yes—
121C22×C3×Dic3C22×C312yes—
122C3×#237—68no—
123C3×#235—68no—
124C2×C3×D12—31no—
125C2×C3×C4×D3—21no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—32no—
130C2×C3×C4×D3—32no—
131C2×C3×C4×D3—61no—
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×C4×D3C22×C311yescharacteristic
134C2×C3×Dic6—32no—
135C2×C3×Dic6—32no—
136C2×#627C22×C312yes—
137C2×#626C22×C311yescharacteristic
138C2×#624C22×C312yes—
139#3804—28no—
140C2×D3×Dic3C22×C312yes—
141C32×C4⋊C4—31no—
142C32×C4⋊C4—31no—
143C32×C22⋊C4—32no—
144C32×C22⋊C4—32no—
145C32×C42—31no—
146#3757C22×C312yes—
147C4⋊(C3⋊Dic3)C22×C311yescharacteristic
148C3×#217—22no—
149C3×#217—22no—
150C3×#217—32no—
151C3×#217—32no—
152C3×#217—31no—
153C3×#217—62no—
154C3×#217C2×D312yes—
155C3×#217C2×D312yes—
156C3×#217C22×C312yes—
157C3×#217C22×C312yes—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×C4⋊Dic3—21no—
162C3×C4⋊Dic3—21no—
163C3×C4⋊Dic3—31no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—32no—
166C3×C4⋊Dic3—32no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—61no—
169C3×C4⋊Dic3C2×D311yescharacteristic
170C3×C4⋊Dic3C2×D311yescharacteristic
171C3×C4⋊Dic3C22×C311yescharacteristic
172C3×C4⋊Dic3C22×C311yescharacteristic
173C3×Dic3⋊C4—31no—
174C3×Dic3⋊C4—32no—
175C3×Dic3⋊C4—32no—
176C3×Dic3⋊C4—32no—
177C3×Dic3⋊C4—32no—
178C3×C4×Dic3—21no—
179C3×C4×Dic3C2×D311yescharacteristic
180C3×C4×Dic3C22×C311yescharacteristic
181#3724C22×C312yes—
182Dic3⋊Dic3C22×C312yes—
183Dic3⋊Dic3C22×C311yescharacteristic
184Dic3⋊Dic3C22×C312yes—
185#3722C22×C311yescharacteristic
186(C2×D3)⋊Dic3C22×C311yescharacteristic
187C22×C33—22no—
188C22×C33—22no—
189C22×C33—22no—
190C22×C33C2411yescharacteristic
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—21no—
193C2×C3×C3⋊D3C2×D412yes—
194C2×C32×D3—21no—
195C2×C32×D3—21no—
196C2×C32×D3C2×D412yes—
197C33×C4#4112yescomplemented
198C3×C3⋊Dic3—22no—
199C3×C3⋊Dic3—21no—
200C32×Dic3—22no—
201C32×Dic3—22no—
202C32×Dic3—21no—
203C32×Dic3—21no—
204C32×Dic3C2×D412yes—
205C2×C3×#41—92no—
206C2×#237—32no—
207C2×#235—32no—
208C3×C4⋊Q8—91no—
209C3×#123—92no—
210C3×#123—92no—
211C3×C22⋊Q8—92no—
212C3×#121—31no—
213C3×#121—31no—
214C3×#121—61no—
215C3×#121—91no—
216C3×C4×D4—31no—
217C3×C4×D4—31no—
218C3×C4×D4—61no—
219C3×C4×D4—91no—
220C2×C3×C4⋊C4—91no—
221C2×C3×C4⋊C4—91no—
222#938—31no—
223#938—31no—
224#938—61no—
225#938C3×D311yescharacteristic, complemented
226#935—32no—
227D4×Dic3C3×D311yescharacteristic, complemented
228C4×#67—31no—
229C2×C4⋊Dic3—31no—
230#924—32no—
231D3×C4⋊C4—31no—
232D3×C4⋊C4—31no—
233D3×C4⋊C4—31no—
234#888—31no—
235#883—32no—
236#883—32no—
237#883—32no—
238#878—32no—
239C4×D12—31no—
240#869—31no—
241C23×C32—22no—
242C23×C32—22no—
243C23×C32—22no—
244C23×C32—31no—
245C23×C32—42no—
246C23×C32C22×D312yes—
247C23×C32C22×D312yes—
248C23×C32C23×C312yes—
249C22×C3⋊D3C23×C311yescharacteristic
250C22×C3×D3—21no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—61no—
254C22×C3×D3C22×D311yescharacteristic
255C22×C3×D3C23×C311yescharacteristic
256C32×D4—22no—
257C32×D4—24no—
258C32×D4—22no—
259C32×D4—22no—
260C32×D4—42no—
261C32×D4—42no—
262C32×D4—44no—
263C32×D4—64no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—31no—
268C2×C32×C4—32no—
269C2×C32×C4—32no—
270C2×C32×C4—31no—
271C2×C32×C4—31no—
272C2×C32×C4—41no—
273C2×C32×C4—64no—
274C2×C32×C4—62no—
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C23×C311yescharacteristic
278#638—24no—
279C2×C3⋊Dic3C23×C311yescharacteristic
280C2×C3⋊Dic3C23×C312yes—
281C4×C3⋊D3—22no—
282C3×#67—24no—
283C3×#67—24no—
284C3×#67—34no—
285C3×#67—44no—
286C3×#67—64no—
287C3×#67—64no—
288C3×#67—124no—
289C2×C3×Dic3—24no—
290C2×C3×Dic3—24no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—32no—
300C2×C3×Dic3—44no—
301C2×C3×Dic3—62no—
302C2×C3×Dic3—61no—
303C2×C3×Dic3—64no—
304C2×C3×Dic3C22×D311yescharacteristic
305C2×C3×Dic3C22×D311yescharacteristic
306C2×C3×Dic3C22×D312yes—
307C2×C3×Dic3C22×D312yes—
308C2×C3×Dic3C22×D311yescharacteristic
309C2×C3×Dic3C23×C311yescharacteristic
310C2×C3×Dic3C23×C311yescharacteristic
311C2×C3×Dic3C23×C312yes—
312C2×C3×Dic3C23×C312yes—
313C2×C3×Dic3C23×C311yescharacteristic
314C3×D12—34no—
315C3×C4×D3—22no—
316C3×C4×D3—22no—
317C3×C4×D3—42no—
318C3×C4×D3—64no—
319C3×C4×D3—64no—
320C3×C4×D3—64no—
321C3×C4×D3—62no—
322C3×C4×D3—62no—
323C3×C4×D3—122no—
324C3×Dic6—64no—
325C3×Dic6—64no—
326#627—24no—
327#626C3×D414yescomplemented
328#624—24no—
329D3×Dic3—24no—
330#547—91noSylow
331C2×C33—42no—
332C2×C33C22×D411yescharacteristic
333C2×C33C2×#4111yescharacteristic
334C2×C332−1+411yescharacteristic
335C3×C3⋊D3—22no—
336C32×D3—22no—
337C3×#41—188no—
338C2×C3×Q8—92no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—32no—
343C2×C3×D4—32no—
344C2×C3×D4—41no—
345C2×C3×D4—62no—
346C2×C3×D4—91no—
347C2×C3×D4—92no—
348C2×C3×D4D3211yescharacteristic
349C2×C3×D4C2×C3×D311yescharacteristic
350C2×C3×D4C2×C3×D311yescharacteristic
351C22×C3×C4—32no—
352C22×C3×C4—32no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—61no—
356C22×C3×C4—62no—
357C22×C3×C4—92no—
358C22×C3×C4—92no—
359C22×C3×C4—91no—
360C2×#67—32no—
361C2×#67—32no—
362C2×#67—31no—
363C2×#67—62no—
364C2×#67C2×C3×D312yes—
365C22×Dic3—32no—
366C22×Dic3C2×C3×D312yes—
367#237—68no—
368#235—68no—
369C2×D12—31no—
370C2×C4×D3—32no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—32no—
374C2×C4×D3—32no—
375C2×C4×D3—61no—
376C2×C4×D3C2×C3×D311yescharacteristic
377C2×Dic6—32no—
378C2×Dic6—32no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—92no—
386C3×C4⋊C4—92no—
387C3×C4⋊C4—91no—
388C3×C4⋊C4—92no—
389C3×C4⋊C4—91no—
390C3×C22⋊C4—32no—
391C3×C22⋊C4—32no—
392C3×C22⋊C4—32no—
393C3×C22⋊C4—32no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—92no—
399C3×C42—31no—
400C3×C42—31no—
401C3×C42—61no—
402#217—32no—
403#217—32no—
404#217—31no—
405#217—62no—
406#217C2×C3×D312yes—
407#217C2×C3×D312yes—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—32no—
414C4⋊Dic3—31no—
415C4⋊Dic3—32no—
416C4⋊Dic3—61no—
417C4⋊Dic3C2×C3×D311yescharacteristic
418C4⋊Dic3C2×C3×D311yescharacteristic
419Dic3⋊C4—31no—
420Dic3⋊C4—32no—
421Dic3⋊C4—32no—
422Dic3⋊C4—32no—
423Dic3⋊C4—32no—
424C4×Dic3C2×C3×D311yescharacteristic
425C22×C32—22no—
426C22×C32—24no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—32no—
439C22×C32—41no—
440C22×C32—42no—
441C22×C32—42no—
442C22×C32—44no—
443C22×C32—42no—
444C22×C32—42no—
445C22×C32—42no—
446C22×C32—42no—
447C22×C32—42no—
448C22×C32—42no—
449C22×C32—61no—
450C22×C32—61no—
451C22×C32—82no—
452C22×C32—82no—
453C22×C32C23×D311yescharacteristic
454C22×C32C23×D311yescharacteristic
455C22×C32C24×C311yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3C2×C3×D412yes—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—22no—
464C2×C3×D3—32no—
465C2×C3×D3—32no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—62no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—121no—
474C2×C3×D3—121no—
475C2×C3×D3D3×D412yes—
476C2×C3×D3C2×C3×D412yes—
477C32×C4—22no—
478C32×C4—22no—
479C32×C4—22no—
480C32×C4—32no—
481C32×C4—42no—
482C32×C4—61no—
483C32×C4—62no—
484C32×C4—62no—
485C32×C4—61no—
486C32×C4#23512yescomplemented
487C32×C4#23712yescomplemented
488C32×C4C3×#4112yescomplemented
489C3⋊Dic3—22no—
490C3⋊Dic3—21no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—22no—
496C3×Dic3—22no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—22no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C3×Dic3—42no—
503C3×Dic3—42no—
504C3×Dic3—61no—
505C3×Dic3—62no—
506C3×Dic3—62no—
507C3×Dic3—61no—
508C3×Dic3—121no—
509C3×Dic3—122no—
510C3×Dic3D3×D412yes—
511C3×Dic3C2×C3×D412yes—
512C2×#41—92no—
513C4⋊Q8—91no—
514#123—92no—
515#123—92no—
516C22⋊Q8—92no—
517#121—31no—
518#121—91no—
519C4×D4—31no—
520C4×D4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C33#54711yescharacteristic, complemented, Sylow
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—42no—
530C23×C3—61no—
531C23×C3—91no—
532C23×C3C2×D3212yes—
533C23×C3C22×C3×D312yes—
534C23×C3C22×C3×D312yes—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—61no—
538C22×D3C22×C3×D311yescharacteristic
539C3×Q8—184no—
540C3×D4—24no—
541C3×D4—22no—
542C3×D4—22no—
543C3×D4—22no—
544C3×D4—42no—
545C3×D4—42no—
546C3×D4—44no—
547C3×D4—64no—
548C3×D4—64no—
549C3×D4—94no—
550C3×D4—124no—
551C3×D4—184no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—64no—
572C2×C3×C4—64no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—91no—
576C2×C3×C4—92no—
577C2×C3×C4—122no—
578C2×C3×C4—124no—
579C2×C3×C4—184no—
580C2×C3×C4—184no—
581C2×C3×C4—182no—
582C2×C3×C4C2×D3211yescharacteristic
583C2×C3×C4C22×C3×D311yescharacteristic
584C2×C3×C4C22×C3×D311yescharacteristic
585#67—24no—
586#67—34no—
587#67—64no—
588#67—64no—
589#67—124no—
590C2×Dic3—24no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—62no—
596C2×Dic3—61no—
597C2×Dic3—64no—
598C2×Dic3C22×C3×D311yescharacteristic
599C2×Dic3C22×C3×D311yescharacteristic
600C2×Dic3C22×C3×D312yes—
601C2×Dic3C22×C3×D312yes—
602C2×Dic3C22×C3×D311yescharacteristic
603D12—34no—
604C4×D3—22no—
605C4×D3—64no—
606C4×D3—64no—
607C4×D3—64no—
608C4×D3—62no—
609C4×D3—62no—
610C4×D3—122no—
611Dic6—64no—
612Dic6—64no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—41no—
623C2×C32—41no—
624C2×C32—41no—
625C2×C32—42no—
626C2×C32—44no—
627C2×C32—42no—
628C2×C32—42no—
629C2×C32—62no—
630C2×C32—82no—
631C2×C32—82no—
632C2×C32—84no—
633C2×C32C2×#23511yescharacteristic
634C2×C32C2×D3×D411yescharacteristic
635C2×C32C2×D3×D411yescharacteristic
636C2×C32C2×#23711yescharacteristic
637C2×C32#101011yescharacteristic
638C2×C32#101011yescharacteristic
639C2×C32C22×C3×D411yescharacteristic
640C2×C32C2×C3×#4111yescharacteristic
641C2×C32C3×2−1+411yescharacteristic
642C3⋊D3—22no—
643C3×D3—22no—
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—62no—
647C3×D3—62no—
648C3×D3—122no—
649#41—188no—
650C2×Q8—92no—
651C2×D4—32no—
652C2×D4—91no—
653C2×D4—92no—
654C2×D4C3×D3211yescharacteristic
655C22×C4—32no—
656C22×C4—31no—
657C22×C4—92no—
658C22×C4—92no—
659C22×C4—91no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—92no—
663C4⋊C4—92no—
664C4⋊C4—91no—
665C4⋊C4—92no—
666C4⋊C4—91no—
667C22⋊C4—32no—
668C22⋊C4—32no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—92no—
672C42—31no—
673C22×C3—24no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—32no—
687C22×C3—32no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—44no—
697C22×C3—41no—
698C22×C3—62no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—82no—
704C22×C3—82no—
705C22×C3—92no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—181no—
709C22×C3—181no—
710C22×C3C22×D3211yescharacteristic
711C22×C3C23×C3×D311yescharacteristic
712C22×C3C23×C3×D311yescharacteristic
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—32no—
716C2×D3—32no—
717C2×D3—62no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3C3×D3×D412yes—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—32no—
729C3×C4—32no—
730C3×C4—42no—
731C3×C4—62no—
732C3×C4—61no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—61no—
740C3×C4—121no—
741C3×C4—122no—
742C3×C4—122no—
743C3×C4—121no—
744C3×C4—182no—
745C3×C4—181no—
746C3×C4#380412yescomplemented
747C3×C4C3×#23512yescomplemented
748C3×C4C3×#23712yescomplemented
749Dic3—22no—
750Dic3—22no—
751Dic3—21no—
752Dic3—21no—
753Dic3—61no—
754Dic3—62no—
755Dic3—62no—
756Dic3—61no—
757Dic3—121no—
758Dic3—122no—
759Dic3C3×D3×D412yes—
760C32—21no—
761C32—21no—
762C32—21no—
763C32—41no—
764C32#555111yescharacteristic, complemented
765C32#561111yescharacteristic, complemented
766C32C3×#54711yescharacteristic, complemented
767C23—31no—
768C23—91no—
769C23C2×C3×D3212yes—
770Q8—184no—
771D4—22no—
772D4—64no—
773D4—94no—
774D4—184no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—64no—
781C2×C4—62no—
782C2×C4—91no—
783C2×C4—92no—
784C2×C4—184no—
785C2×C4—184no—
786C2×C4—182no—
787C2×C4C2×C3×D3211yescharacteristic
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—44no—
798C2×C3—42no—
799C2×C3—42no—
800C2×C3—42no—
801C2×C3—41no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—62no—
805C2×C3—62no—
806C2×C3—82no—
807C2×C3—82no—
808C2×C3—84no—
809C2×C3—122no—
810C2×C3—182no—
811C2×C3#6430911yescharacteristic
812C2×C3D32×D411yescharacteristic
813C2×C3C2×#380411yescharacteristic
814C2×C3C2×C3×#23511yescharacteristic
815C2×C3C2×C3×D3×D411yescharacteristic
816C2×C3C2×C3×D3×D411yescharacteristic
817C2×C3C2×C3×#23711yescharacteristic
818C2×C3C3×#101011yescharacteristic
819C2×C3C3×#101011yescharacteristic
820D3—22no—
821D3—62no—
822D3—62no—
823D3—122no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—32no—
828C22—61no—
829C22—61no—
830C22—92no—
831C22—181no—
832C22—181no—
833C22C22×C3×D3211yescharacteristic
834C4—32no—
835C4—61no—
836C4—61no—
837C4—62no—
838C4—62no—
839C4—181no—
840C4—182no—
841C4C3×#380412yescomplemented
842C3—21no—
843C3—21no—
844C3—21no—
845C3—41no—
846C3#1059513611yescharacteristic, direct product factor
847C3C3×#555111yescharacteristic, complemented
848C3C3×#561111yescharacteristic, complemented
849C2—42no—
850C2—62no—
851C2—182no—
852C2C3×#6430911yescharacteristic
853C2C3×D32×D411yescharacteristic
854C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3804C2semidirect
2. C3×#64147C2semidirect
3. C32×#938C2semidirect
4. C32×D4×Dic3C2semidirect
5. C3×#63975C2semidirect
6. C3×#63969C2semidirect
7. C3×#63964C2semidirect
8. C3×#63918C2semidirect
9. C3×C4×#626C2semidirect
10. C3×#63900C2semidirect
11. C3×D3×C4⋊Dic3C2semidirect
14. #10595136C3direct (N × H)
41. C2×#3804C2×C3semidirect
44. #64147C2×C3semidirect
49. C3×#938D3semidirect
50. C3×#938C2×C3semidirect
53. C3×D4×Dic3D3semidirect
54. C3×D4×Dic3C2×C3semidirect
68. #63975C2×C3semidirect
69. #63969C2×C3semidirect
70. #63964C2×C3semidirect
71. #63918C2×C3semidirect
72. C4×#626C2×C3semidirect
73. #63900C2×C3semidirect
74. D3×C4⋊Dic3C2×C3semidirect
93. C3×#626D4semidirect
197. C33×C4#41semidirect
225. #938C3×D3semidirect
227. D4×Dic3C3×D3semidirect
327. #626C3×D4semidirect
486. C32×C4#235semidirect
487. C32×C4#237semidirect
488. C32×C4C3×#41semidirect
523. C33#547semidirect
746. C3×C4#3804semidirect
747. C3×C4C3×#235semidirect
748. C3×C4C3×#237semidirect
764. C32#5551semidirect
765. C32#5611semidirect
766. C32C3×#547semidirect
841. C4C3×#3804semidirect
846. C3#10595136direct (N × H)
847. C3C3×#5551semidirect
848. C3C3×#5611semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C3×#641472
C32×#9382
C32×D4×Dic32
C3×#639752
C3×#639692
C3×#639642
C3×#639182
C3×C4×#6262
C3×#639002
C3×D3×C4⋊Dic32
C3×#56113
C3×#55513
#105951363