Finite Group Databasebeta

← #13161834

Subgroups — #13161834

Order 1728.

1106 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3750C211yesmaximal, characteristic
2C2×C3×C4×C3⋊Dic3C211yesmaximal, characteristic
3C2×#88815C211yesmaximal, characteristic
4C2×#88813C211yesmaximal, characteristic
5C2×#88813C211yesmaximal, characteristic
6C3×#63658C211yesmaximal, characteristic
7#11722082C211yesmaximal, characteristic
8#10591243—31nomaximal
9#10591241—31nomaximal
10Dic3×Dic3⋊C4—31nomaximal
11C22×C33×C4C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C3×#3750C414yescomplemented
19C3×C4×C3⋊Dic3—22no—
20#88815C414yescomplemented
21#88813—22no—
22#88813C414yescomplemented
23C2×#3750D311yescharacteristic
24C2×C4×C3⋊Dic3D311yescharacteristic
25C2×C3×Dic3⋊C4—31no—
26C2×C3×Dic3⋊C4—31no—
27C2×C3×Dic3⋊C4—61no—
28C2×C3×C4×Dic3—31no—
29C2×C3×C4×Dic3—31no—
30C2×C3×C4×Dic3—61no—
31C2×#3724—31no—
32C2×Dic3⋊Dic3—31no—
33C2×Dic3⋊Dic3—31no—
34C2×Dic32—31no—
35C2×Dic32—31no—
36C2×Dic32—31no—
37C2×Dic32—31no—
38C2×Dic32—31no—
39C2×Dic32—31no—
40#63658D311yescharacteristic
41C3×C3⋊#95—31no—
42C3×C3⋊#95—31no—
43C3×C3⋊#95—61no—
44#63579—31no—
45#63579—31no—
46#63579—31no—
47C23×C33C2311yescharacteristic
48C2×C33×C4—21no—
49C2×C33×C4—21no—
50C2×C33×C4C2×C412yes—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3—21no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3—21no—
56C2×C3×C3⋊Dic3—21no—
57C2×C3×C3⋊Dic3—21no—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3C2×C412yes—
60C2×C3×C3⋊Dic3C2×C412yes—
61C2×C3×C3⋊Dic3C2×C412yes—
62C2×C3×C3⋊Dic3C2×C412yes—
63C2×C3×C3⋊Dic3C2×C412yes—
64C2×C3×C3⋊Dic3C2×C412yes—
65C2×C3×C3⋊Dic3C2×C412yes—
66C2×C3×C3⋊Dic3C2×C412yes—
67C2×C3×C3⋊Dic3D412yes—
68C2×C3×C3⋊Dic3Q812yes—
69Dic3×C4⋊C4—91no—
70C4×Dic3⋊C4—91no—
71#4649—91no—
72C22×C32×C4—21no—
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4—41no—
76C22×C32×C4C2×D311yescharacteristic
77C22×C32×C4C2×D311yescharacteristic
78C22×C32×C4C2×D311yescharacteristic
79C22×C3⋊Dic3C2×D311yescharacteristic
80C22×C3⋊Dic3C2×D311yescharacteristic
81C22×C3⋊Dic3C2×D311yescharacteristic
82C22×C3⋊Dic3C2×D311yescharacteristic
83C22×C3⋊Dic3C2×D311yescharacteristic
84C22×C3⋊Dic3C2×D311yescharacteristic
85C22×C3×Dic3—31no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—61no—
98C22×C3×Dic3—61no—
99C22×C3×Dic3—61no—
100C22×C3×Dic3—61no—
101C22×C3×Dic3—61no—
102C22×C3×Dic3—61no—
103#3750Dic314yescomplemented
104C4×C3⋊Dic3—22no—
105C3×Dic3⋊C4—34no—
106C3×Dic3⋊C4—34no—
107C3×Dic3⋊C4—64no—
108C3×C4×Dic3—62no—
109C3×C4×Dic3—62no—
110C3×C4×Dic3—64no—
111#3724—34no—
112Dic3⋊Dic3—34no—
113Dic3⋊Dic3—34no—
114Dic32—34no—
115Dic32—34no—
116Dic32—34no—
117Dic32—62no—
118Dic32—62no—
119Dic32—62no—
120C22×C33C22×C411yescharacteristic
121C22×C33C22×C411yescharacteristic
122C22×C33C22×C411yescharacteristic
123C22×C33C2×D411yescharacteristic
124C22×C33C2×Q811yescharacteristic
125C22×C33#4111yescharacteristic
126C22×C33#4111yescharacteristic
127C33×C4—22no—
128C3×C3⋊Dic3—22no—
129C3×C3⋊Dic3—22no—
130C3×C3⋊Dic3—22no—
131C3×C3⋊Dic3—22no—
132C3×C3⋊Dic3C4214yescomplemented
133C3×C3⋊Dic3C4⋊C414yescomplemented
134C2×C3×C4⋊C4—91no—
135C2×C3×C42—91no—
136C2×C4⋊Dic3—91no—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—61no—
140C2×Dic3⋊C4—91no—
141C2×Dic3⋊C4—91no—
142C2×C4×Dic3—31no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—61no—
145C2×C4×Dic3—91no—
146C2×C4×Dic3—91no—
147C2×C4×Dic3—91no—
148C2×C4×Dic3—91no—
149C2×C4×Dic3—91no—
150C2×C4×Dic3—91no—
151C3×#95—91no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—61no—
155C3⋊#95—91no—
156C3⋊#95—91no—
157C3⋊#95—91no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—41no—
162C23×C32C22×D311yescharacteristic
163C23×C32C22×D311yescharacteristic
164C23×C32C22×D311yescharacteristic
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—42no—
177C2×C32×C4—41no—
178C2×C32×C4—41no—
179C2×C32×C4—41no—
180C2×C32×C4—41no—
181C2×C32×C4—42no—
182C2×C32×C4—42no—
183C2×C32×C4C4×D312yes—
184C2×C32×C4C4×D312yes—
185C2×C32×C4C2×Dic312yes—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3Dic612yes—
195C2×C3⋊Dic3C4×D312yes—
196C2×C3⋊Dic3C4×D312yes—
197C2×C3⋊Dic3C4×D312yes—
198C2×C3⋊Dic3C4×D312yes—
199C2×C3⋊Dic3C4×D312yes—
200C2×C3⋊Dic3C4×D312yes—
201C2×C3⋊Dic3C2×Dic312yes—
202C2×C3⋊Dic3C2×Dic312yes—
203C2×C3⋊Dic3#6712yes—
204C2×C3×Dic3—32no—
205C2×C3×Dic3—32no—
206C2×C3×Dic3—32no—
207C2×C3×Dic3—32no—
208C2×C3×Dic3—32no—
209C2×C3×Dic3—32no—
210C2×C3×Dic3—32no—
211C2×C3×Dic3—32no—
212C2×C3×Dic3—32no—
213C2×C3×Dic3—32no—
214C2×C3×Dic3—32no—
215C2×C3×Dic3—32no—
216C2×C3×Dic3—32no—
217C2×C3×Dic3—32no—
218C2×C3×Dic3—32no—
219C2×C3×Dic3—32no—
220C2×C3×Dic3—32no—
221C2×C3×Dic3—32no—
222C2×C3×Dic3—32no—
223C2×C3×Dic3—32no—
224C2×C3×Dic3—62no—
225C2×C3×Dic3—62no—
226C2×C3×Dic3—62no—
227C2×C3×Dic3—62no—
228C2×C3×Dic3—62no—
229C2×C3×Dic3—62no—
230C2×C3×Dic3—62no—
231C2×C3×Dic3—62no—
232C2×C3×Dic3—62no—
233C2×C3×Dic3—62no—
234C2×C3×Dic3—62no—
235C2×C3×Dic3—62no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—61no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—61no—
246C2×C3×Dic3—61no—
247C2×C3×Dic3—61no—
248C2×C3×Dic3—61no—
249C2×C3×Dic3—61no—
250C2×C3×Dic3—61no—
251C2×C3×Dic3—61no—
252C2×C3×Dic3—121no—
253C2×C3×Dic3—121no—
254C2×C3×Dic3—121no—
255C2×C3×Dic3—121no—
256C2×C3×Dic3—121no—
257C2×C3×Dic3—121no—
258C4×C4⋊C4—271noSylow
259C2×C33C2×C4211yescharacteristic
260C2×C33C2×C4⋊C411yescharacteristic
261C2×C33#11711yescharacteristic
262C2×C33C4×D411yescharacteristic
263C2×C33C4×D411yescharacteristic
264C2×C33C4×Q811yescharacteristic
265C2×C33C4×Q811yescharacteristic
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—41no—
270C22×C3×C4—91no—
271C22×C3×C4—91no—
272C22×C3×C4—91no—
273C22×C3×C4—91no—
274C22×C3×C4—91no—
275C22×C3×C4—91no—
276C22×C3×C4D3211yescharacteristic
277C22×C3×C4D3211yescharacteristic
278C22×C3×C4D3211yescharacteristic
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C3×C4⋊C4—94no—
298C3×C42—182no—
299C4⋊Dic3—94no—
300Dic3⋊C4—34no—
301Dic3⋊C4—34no—
302Dic3⋊C4—64no—
303Dic3⋊C4—94no—
304Dic3⋊C4—94no—
305C4×Dic3—62no—
306C4×Dic3—62no—
307C4×Dic3—64no—
308C4×Dic3—94no—
309C4×Dic3—94no—
310C4×Dic3—94no—
311C4×Dic3—182no—
312C4×Dic3—182no—
313C4×Dic3—182no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32C2×Dic611yescharacteristic
343C22×C32C2×C4×D311yescharacteristic
344C22×C32C2×C4×D311yescharacteristic
345C22×C32C2×C4×D311yescharacteristic
346C22×C32C2×C4×D311yescharacteristic
347C22×C32C2×C4×D311yescharacteristic
348C22×C32C2×C4×D311yescharacteristic
349C22×C32C2×C4×D311yescharacteristic
350C22×C32C2×C4×D311yescharacteristic
351C22×C32#23511yescharacteristic
352C22×C32#23511yescharacteristic
353C22×C32D3×D411yescharacteristic
354C22×C32D3×D411yescharacteristic
355C22×C32#23711yescharacteristic
356C22×C32#23711yescharacteristic
357C22×C32#23711yescharacteristic
358C22×C32D3×Q811yescharacteristic
359C22×C32D3×Q811yescharacteristic
360C22×C32#23911yescharacteristic
361C22×C32C22×Dic311yescharacteristic
362C22×C32C2×#6711yescharacteristic
363C32×C4—22no—
364C32×C4—24no—
365C32×C4—22no—
366C32×C4—22no—
367C32×C4—42no—
368C32×C4—42no—
369C32×C4—44no—
370C3⋊Dic3—22no—
371C3⋊Dic3—22no—
372C3⋊Dic3—22no—
373C3⋊Dic3—22no—
374C3⋊Dic3C4×Dic314yescomplemented
375C3⋊Dic3Dic3⋊C414yescomplemented
376C3×Dic3—34no—
377C3×Dic3—34no—
378C3×Dic3—34no—
379C3×Dic3—34no—
380C3×Dic3—64no—
381C3×Dic3—64no—
382C3×Dic3—64no—
383C3×Dic3—62no—
384C3×Dic3—62no—
385C3×Dic3—62no—
386C3×Dic3—62no—
387C3×Dic3—62no—
388C3×Dic3—62no—
389C3×Dic3—62no—
390C3×Dic3—62no—
391C3×Dic3—122no—
392C3×Dic3—122no—
393C3×Dic3—122no—
394C2×C4⋊C4—91no—
395C2×C4⋊C4—271no—
396C2×C42—91no—
397C2×C42—271no—
398C2×C42—271no—
399#95—91no—
400#95—271no—
401C33C4×C4⋊C411yescharacteristic, complemented, Sylow
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—41no—
406C23×C3C2×D3211yescharacteristic
407C23×C3C2×D3211yescharacteristic
408C23×C3C2×D3211yescharacteristic
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—92no—
428C2×C3×C4—92no—
429C2×C3×C4—92no—
430C2×C3×C4—92no—
431C2×C3×C4—92no—
432C2×C3×C4—92no—
433C2×C3×C4—92no—
434C2×C3×C4—92no—
435C2×C3×C4—92no—
436C2×C3×C4—92no—
437C2×C3×C4—181no—
438C2×C3×C4—181no—
439C2×C3×C4—181no—
440C2×C3×C4—181no—
441C2×C3×C4—181no—
442C2×C3×C4—181no—
443C2×C3×C4—181no—
444C2×C3×C4—181no—
445C2×C3×C4D3×Dic312yes—
446C2×C3×C4D3×Dic312yes—
447C2×C3×C4#62412yes—
448C2×Dic3—32no—
449C2×Dic3—32no—
450C2×Dic3—32no—
451C2×Dic3—32no—
452C2×Dic3—32no—
453C2×Dic3—32no—
454C2×Dic3—32no—
455C2×Dic3—32no—
456C2×Dic3—32no—
457C2×Dic3—32no—
458C2×Dic3—32no—
459C2×Dic3—32no—
460C2×Dic3—32no—
461C2×Dic3—32no—
462C2×Dic3—32no—
463C2×Dic3—32no—
464C2×Dic3—32no—
465C2×Dic3—32no—
466C2×Dic3—32no—
467C2×Dic3—32no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—62no—
479C2×Dic3—62no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—121no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—21no—
519C2×C32—21no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—41no—
524C2×C32—41no—
525C2×C32—41no—
526C2×C32—41no—
527C2×C32—41no—
528C2×C32—41no—
529C2×C32—41no—
530C2×C32C4×Dic611yescharacteristic
531C2×C32C4×Dic611yescharacteristic
532C2×C32C42×D311yescharacteristic
533C2×C32C42×D311yescharacteristic
534C2×C32#87211yescharacteristic
535C2×C32#87711yescharacteristic
536C2×C32#67⋊C411yescharacteristic
537C2×C32#67⋊C411yescharacteristic
538C2×C32#88711yescharacteristic
539C2×C32#88711yescharacteristic
540C2×C32#88711yescharacteristic
541C2×C32D3×C4⋊C411yescharacteristic
542C2×C32D3×C4⋊C411yescharacteristic
543C2×C32#89211yescharacteristic
544C2×C32#89311yescharacteristic
545C2×C32C2×C4×Dic311yescharacteristic
546C2×C32C2×Dic3⋊C411yescharacteristic
547C2×C32C4×#6711yescharacteristic
548C2×C32C4×#6711yescharacteristic
549C2×C32D4×Dic311yescharacteristic
550C2×C32Q8×Dic311yescharacteristic
551C22×C4—91no—
552C22×C4—91no—
553C22×C4—91no—
554C22×C4—91no—
555C22×C4—91no—
556C22×C4—91no—
557C22×C4#111311yescharacteristic
558C4⋊C4—94no—
559C4⋊C4—274no—
560C42—182no—
561C42—274no—
562C42—542no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3D3×Dic611yescharacteristic
592C22×C3D3×Dic611yescharacteristic
593C22×C3#379511yescharacteristic
594C22×C3#379611yescharacteristic
595C22×C3#379711yescharacteristic
596C22×C3#379911yescharacteristic
597C22×C3C4×D3211yescharacteristic
598C22×C3C4×D3211yescharacteristic
599C22×C3C4×D3211yescharacteristic
600C22×C3C4×D3211yescharacteristic
601C22×C3C4×D3211yescharacteristic
602C22×C3C4×D3211yescharacteristic
603C22×C3C2×D3×Dic311yescharacteristic
604C22×C3C2×D3×Dic311yescharacteristic
605C22×C3#380411yescharacteristic
606C22×C3#380411yescharacteristic
607C22×C3#380511yescharacteristic
608C22×C3C2×#62411yescharacteristic
609C22×C3D3×#6711yescharacteristic
610C22×C3D3×#6711yescharacteristic
611C22×C3#381111yescharacteristic
612C3×C4—24no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—44no—
619C3×C4—94no—
620C3×C4—94no—
621C3×C4—182no—
622C3×C4—182no—
623C3×C4—182no—
624C3×C4—182no—
625Dic3—34no—
626Dic3—34no—
627Dic3—34no—
628Dic3—34no—
629Dic3—64no—
630Dic3—64no—
631Dic3—64no—
632Dic3—62no—
633Dic3—62no—
634Dic3—62no—
635Dic3—62no—
636Dic3—62no—
637Dic3—62no—
638Dic3—62no—
639Dic3—62no—
640Dic3—122no—
641Dic3—122no—
642Dic3—122no—
643C32—21no—
644C32—21no—
645C32—21no—
646C32—41no—
647C32#464911yescharacteristic, complemented
648C32C4×Dic3⋊C411yescharacteristic, complemented
649C32Dic3×C4⋊C411yescharacteristic, complemented
650C23C2×#111311yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—92no—
654C2×C4—92no—
655C2×C4—92no—
656C2×C4—92no—
657C2×C4—92no—
658C2×C4—92no—
659C2×C4—92no—
660C2×C4—92no—
661C2×C4—92no—
662C2×C4—92no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4#629412yes—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—41no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—41no—
700C2×C3#6383611yescharacteristic
701C2×C3#6383711yescharacteristic
702C2×C3#6383711yescharacteristic
703C2×C3#6383811yescharacteristic
704C2×C3Dic3×Dic611yescharacteristic
705C2×C3#6384311yescharacteristic
706C2×C3#6384411yescharacteristic
707C2×C3C4×D3×Dic311yescharacteristic
708C2×C3C4×D3×Dic311yescharacteristic
709C2×C3D3×Dic3⋊C411yescharacteristic
710C2×C3D3×Dic3⋊C411yescharacteristic
711C2×C3#6387711yescharacteristic
712C2×C3#6387811yescharacteristic
713C2×C3#6387911yescharacteristic
714C2×C3#6388111yescharacteristic
715C2×C3C4×#62411yescharacteristic
716C2×C3#6388311yescharacteristic
717C2×C3#6390411yescharacteristic
718C2×C3#6395211yescharacteristic
719C2×C3Dic3×#6711yescharacteristic
720C2×C3#67⋊Dic311yescharacteristic
721C22#8904011yescharacteristic
722C22#8904111yescharacteristic
723C22C4×#111311yescharacteristic
724C22C4×#111311yescharacteristic
725C22C2×#629411yescharacteristic
726C22#8904611yescharacteristic
727C22#8904911yescharacteristic
728C4—22no—
729C4—94no—
730C4—94no—
731C4—182no—
732C4—182no—
733C4—182no—
734C4—182no—
735C3—21no—
736C3—21no—
737C3—21no—
738C3—41no—
739C3Dic3×Dic3⋊C411yescharacteristic, complemented
740C3#1059124111yescharacteristic, complemented
741C3#1059124311yescharacteristic, complemented
742C2#1172366511yescharacteristic
743C2#1172366811yescharacteristic
744C2C4×#629411yescharacteristic
745C2#1172368211yescharacteristic
746C2#1172368311yescharacteristic
747C2#1172368411yescharacteristic
748C2#1172372611yescharacteristic
subgroupG/H
center, FrattiniC23C2×#1113
commutatorC2×C33C2×C42
FittingC22×C33×C4C22
socle, prime radical, cosocleC23×C33C23
hypercenterC22×C4#1113
hypocenterC33C4×C4⋊C4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
18. C3×#3750C4semidirect
20. #88815C4semidirect
22. #88813C4semidirect
103. #3750Dic3semidirect
132. C3×C3⋊Dic3C42semidirect
133. C3×C3⋊Dic3C4⋊C4semidirect
374. C3⋊Dic3C4×Dic3semidirect
375. C3⋊Dic3Dic3⋊C4semidirect
401. C33C4×C4⋊C4semidirect
647. C32#4649semidirect
648. C32C4×Dic3⋊C4semidirect
649. C32Dic3×C4⋊C4semidirect
739. C3Dic3×Dic3⋊C4semidirect
740. C3#10591241semidirect
741. C3#10591243semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37502
C2×C3×C4×C3⋊Dic32
C2×#888152
C2×#888132
C3×#636582
#117220822
#105912433
#105912413
Dic3×Dic3⋊C43