Finite Group Databasebeta

← #13169205

Subgroups — #13169205

Order 1728.

1456 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
2C2×C3×#3797C211yesmaximal, characteristic, complemented
3C4×#6295C211yesmaximal, characteristic
4#11723455C211yesmaximal, characteristic, complemented
5#11723431C211yesmaximal, characteristic, complemented
6C3×#63871C211yesmaximal, characteristic, complemented
7C3×#63843C211yesmaximal, characteristic, complemented
8#11723033C212yesmaximal, complemented
9#11722974C212yesmaximal, complemented
10#11722972C212yesmaximal, complemented
11#11722934C212yesmaximal
12Q8×#626—31nomaximal
13#10595400—31nomaximal
14#10594383—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×Dic6C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6293C2212yes—
22C2×Dic3×C3⋊D3C2212yes—
23C3⋊D3×Dic6—24no—
24C2×C3×#627C2212yes—
25C2×C3×#624C2212yes—
26C3×#3797—24no—
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29#88815C2211yescharacteristic
30#88814C2211yescharacteristic
31#88814C2211yescharacteristic
32#88807C2212yes—
33#88807C2212yes—
34Dic3⋊(C3⋊Dic3)C2212yes—
35#88803C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×Dic3⋊Dic3C2212yes—
38C3×#3722C2212yes—
39C3×Dic32C2212yes—
40C2×Q8×C3⋊D3—31no—
41C2×C3×D3×Q8—31no—
42C2×C3×D3×Q8—31no—
43C2×#3797D311yescharacteristic, complemented
44C2×D3×Dic6—31no—
45C2×D3×Dic6—31no—
46C2×D3×Dic6—61no—
47#64153—31no—
48#64106—31no—
49C3×#946—31no—
50C3×Q8×Dic3—31no—
51C3×#897—31no—
52C3×#887—31no—
53#63918—32no—
54C4×#626—31no—
55C4×#626—31no—
56C4×#626—32no—
57C4×#625—31no—
58#63895—32no—
59#63893—32no—
60#63887—32no—
61#63880—32no—
62#63879—32no—
63#63871—32no—
64#63871D311yescharacteristic, complemented
65#63866—31no—
66#63866—31no—
67#63866—32no—
68#63866—61no—
69#63857—31no—
70#63857—31no—
71#63857—32no—
72#63857—61no—
73#63851—32no—
74#63843D311yescharacteristic, complemented
75#63839—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2312yes—
80#6308—22no—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4×C3⋊D3—22no—
86C3×C4×C3⋊D3—22no—
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2312yes—
90C32×Dic6—22no—
91C32×Dic6D414yescomplemented
92#6295Q814yescomplemented
93#6293—24no—
94Dic3×C3⋊D3—24no—
95C3×#627—24no—
96C3×#624—24no—
97Q8×#67—91no—
98#5632—91no—
99Q8×D12—91no—
100C2×C32×Q8—31no—
101C2×C32×Q8—31no—
102Q8×C3⋊D3—64no—
103C2×C4×C3⋊D3—32no—
104C2×C4×C3⋊D3C2×D311yescharacteristic
105C2×C4×C3⋊D3C2×D311yescharacteristic
106C2×#634—31no—
107C2×#634—31no—
108C2×#634—31no—
109C2×#634—32no—
110C2×#634—61no—
111C2×#634—61no—
112C2×#634—61no—
113C2×#634—121no—
114C3×D3×Q8—64no—
115C3×D3×Q8—64no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—32no—
121C2×C3×C4×D3—32no—
122C2×C3×C4×D3—61no—
123C2×C3×C4×D3—61no—
124C2×C3×Dic6—21no—
125C2×C3×Dic6—21no—
126C2×C3×Dic6—32no—
127C2×C3×Dic6—32no—
128C2×C3×Dic6C2×D311yescharacteristic
129C2×C3×Dic6C2×D311yescharacteristic
130C2×C3×Dic6C2×D311yescharacteristic
131C2×C3×Dic6C2×D311yescharacteristic
132C2×#627—32no—
133C2×#627—32no—
134C2×#627—62no—
135C2×#627C2×D312yes—
136C2×#626—31no—
137C2×#626—31no—
138C2×#625—31no—
139C2×#624C2×D312yes—
140C2×D3×Dic3—32no—
141C2×D3×Dic3—32no—
142C2×D3×Dic3—62no—
143#3797—24no—
144D3×Dic6—68no—
145D3×Dic6—64no—
146D3×Dic6—64no—
147C32×C4⋊C4—31no—
148#3752—32no—
149C4⋊(C3⋊Dic3)—32no—
150#3750—32no—
151#3750—32no—
152C4×C3⋊Dic3C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—32no—
155C3×C4⋊Dic3—21no—
156C3×C4⋊Dic3—32no—
157C3×C4⋊Dic3—32no—
158C3×C4⋊Dic3C2×D311yescharacteristic
159C3×C4⋊Dic3C2×D311yescharacteristic
160C3×Dic3⋊C4—32no—
161C3×Dic3⋊C4—32no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—32no—
165C3×C4×Dic3—32no—
166C3×C4×Dic3—61no—
167#3724—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—32no—
171Dic3⋊Dic3—32no—
172Dic3⋊Dic3—32no—
173Dic3⋊Dic3—32no—
174Dic3⋊Dic3—32no—
175Dic3⋊Dic3—32no—
176Dic3⋊Dic3—62no—
177Dic3⋊Dic3—62no—
178Dic3⋊Dic3—62no—
179Dic3⋊Dic3C2×D312yes—
180Dic3⋊Dic3C2×D312yes—
181#3722—31no—
182#3722—31no—
183#3722C2×D312yes—
184(C2×D3)⋊Dic3—31no—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—62no—
191Dic32C2×D312yes—
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3C2×Q812yescomplemented
198C2×C3×C3⋊D3C2×Q812yescomplemented
199C33×C4C2×D412yes—
200C3⋊(C3⋊Dic3)—22no—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3—21no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3C2×Q812yescomplemented
205C32×Dic3—22no—
206C32×Dic3—22no—
207C32×Dic3C2×D414yes—
208C22×C3×Q8—91no—
209C2×D3×Q8—31no—
210C2×D3×Q8—31no—
211C2×D3×Q8—91no—
212C2×D3×Q8—91no—
213C2×D3×Q8—181no—
214C22×Dic6—91no—
215C3×C22⋊Q8—91no—
216C3×C4×Q8—91no—
217#946—31no—
218#946—92no—
219Q8×Dic3—31no—
220#944—92no—
221#944—91no—
222#944—91no—
223#944—181no—
224C4×#67—92no—
225C4×#67—91no—
226C4×#67—91no—
227#924—92no—
228#924—91no—
229#897—31no—
230#897—92no—
231#897—92no—
232#897—91no—
233#897—91no—
234#897—181no—
235#896—92no—
236#888—92no—
237#887—31no—
238#67⋊C4—92no—
239#878—92no—
240C4×D12—92no—
241C4×D12—91no—
242#869—92no—
243#869—91no—
244C22×C3⋊D3C22×D311yescharacteristic
245C22×C3⋊D3C22×D311yescharacteristic
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—31no—
250C22×C3×D3—61no—
251C22×C3×D3—61no—
252C32×Q8—34no—
253C32×Q8—62no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—32no—
258C2×C32×C4—32no—
259C2×C32×C4—32no—
260C2×C32×C4—41no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C3⋊Dic3—32no—
265C2×C3⋊Dic3—32no—
266C2×C3⋊Dic3—32no—
267C2×C3⋊Dic3—62no—
268C2×C3⋊Dic3—62no—
269C2×C3⋊Dic3—62no—
270C2×C3⋊Dic3—122no—
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D311yescharacteristic
274C2×C3⋊Dic3C22×D311yescharacteristic
275C4×C3⋊D3—22no—
276C4×C3⋊D3—22no—
277C4×C3⋊D3—64no—
278#634—64no—
279#634—62no—
280#634—64no—
281#634—62no—
282#634—62no—
283#634—122no—
284#634—122no—
285#634—124no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—61no—
299C2×C3×Dic3—61no—
300C2×C3×Dic3—61no—
301C2×C3×Dic3C22×D312yes—
302C2×C3×Dic3C22×D312yes—
303C2×C3×Dic3C22×D312yes—
304C2×C3×Dic3C22×D312yes—
305C2×C3×Dic3C22×D312yes—
306C2×C3×Dic3C22×D312yes—
307C3×C4×D3—64no—
308C3×C4×D3—64no—
309C3×C4×D3—62no—
310C3×C4×D3—62no—
311C3×C4×D3—62no—
312C3×C4×D3—62no—
313C3×C4×D3—64no—
314C3×C4×D3—122no—
315C3×Dic6—22no—
316C3×Dic6—22no—
317C3×Dic6—24no—
318C3×Dic6—42no—
319C3×Dic6—64no—
320C3×Dic6—64no—
321C3×Dic6D1214yescomplemented
322C3×Dic6#6714yescomplemented
323#627—24no—
324#627—68no—
325#627—64no—
326#627—64no—
327#626—34no—
328#626—34no—
329#625—34no—
330#624—24no—
331D3×Dic3—68no—
332D3×Dic3—64no—
333D3×Dic3—64no—
334D4×Q8—271noSylow
335C2×C33C22×D411yescharacteristic
336C2×C33C22×Q811yescharacteristic
337C2×C332−1+411yescharacteristic
338C3×C3⋊D3—22no—
339C3×C3⋊D3—22no—
340C2×C3×Q8—31no—
341C2×C3×Q8—31no—
342C2×C3×Q8—31no—
343C2×C3×Q8—31no—
344C2×C3×Q8—61no—
345C2×C3×Q8—61no—
346C2×C3×Q8—92no—
347C2×C3×Q8—184no—
348C22×C3×C4—92no—
349C22×C3×C4—91no—
350C22×C3×C4—91no—
351C2×#67—91no—
352C2×#67—91no—
353C22×Dic3—92no—
354D3×Q8—64no—
355D3×Q8—64no—
356D3×Q8—184no—
357D3×Q8—184no—
358D3×Q8—188no—
359C2×D12—91no—
360C2×C4×D3—31no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—32no—
365C2×C4×D3—32no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—92no—
369C2×C4×D3—92no—
370C2×C4×D3—182no—
371C2×Dic6—32no—
372C2×Dic6—32no—
373C2×Dic6—92no—
374C2×Dic6—92no—
375C2×Dic6—91no—
376C2×Dic6—91no—
377C2×Dic6—91no—
378C2×Dic6—92no—
379C2×Dic6—182no—
380C2×Dic6—181no—
381C2×Dic6—181no—
382C2×Dic6—181no—
383C2×Dic6—184no—
384C2×Dic6—361no—
385C2×Dic6D3211yescharacteristic
386C2×Dic6D3211yescharacteristic
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—92no—
391C3×C4⋊C4—92no—
392C3×C22⋊C4—92no—
393C3×C42—92no—
394C3×C42—91no—
395#217—91no—
396#217—91no—
397#217—92no—
398(C2×D3)⋊C4—32no—
399(C2×D3)⋊C4—32no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—92no—
405(C2×D3)⋊C4—92no—
406(C2×D3)⋊C4—182no—
407C4⋊Dic3—32no—
408C4⋊Dic3—32no—
409C4⋊Dic3—91no—
410C4⋊Dic3—92no—
411C4⋊Dic3—92no—
412C4⋊Dic3—92no—
413C4⋊Dic3—92no—
414C4⋊Dic3—182no—
415C4⋊Dic3D3211yescharacteristic
416Dic3⋊C4—32no—
417Dic3⋊C4—32no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—92no—
421Dic3⋊C4—92no—
422Dic3⋊C4—92no—
423Dic3⋊C4—92no—
424Dic3⋊C4—92no—
425Dic3⋊C4—182no—
426Dic3⋊C4—182no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—32no—
430C4×Dic3—32no—
431C4×Dic3—61no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—41no—
436C22×C32C23×D311yescharacteristic
437C22×C32C23×D311yescharacteristic
438C22×C32C23×D311yescharacteristic
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C2×C3⋊D3D3×Q812yescomplemented
444C2×C3⋊D3D3×Q812yescomplemented
445C2×C3×D3—32no—
446C2×C3×D3—32no—
447C2×C3×D3—32no—
448C2×C3×D3—32no—
449C2×C3×D3—62no—
450C2×C3×D3—62no—
451C2×C3×D3—62no—
452C2×C3×D3—62no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—121no—
462C2×C3×D3—121no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—34no—
467C32×C4—42no—
468C32×C4—62no—
469C32×C4—62no—
470C32×C4C2×D1212yes—
471C32×C4D3×D412yes—
472C32×C4C2×#6712yes—
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3⋊Dic3—62no—
477C3⋊Dic3—64no—
478C3⋊Dic3—62no—
479C3⋊Dic3—62no—
480C3⋊Dic3—122no—
481C3⋊Dic3—122no—
482C3⋊Dic3—124no—
483C3⋊Dic3D3×Q812yescomplemented
484C3×Dic3—22no—
485C3×Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—24no—
489C3×Dic3—32no—
490C3×Dic3—32no—
491C3×Dic3—42no—
492C3×Dic3—42no—
493C3×Dic3—62no—
494C3×Dic3—62no—
495C3×Dic3—62no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—121no—
503C3×Dic3C2×D1214yes—
504C3×Dic3C2×#6714yes—
505C22×Q8—91no—
506C22×Q8—271no—
507C4⋊Q8—272no—
508C4⋊Q8—271no—
509C22⋊Q8—91no—
510C22⋊Q8—272no—
511C22⋊Q8—271no—
512C22⋊Q8—272no—
513C4×Q8—91no—
514C4×D4—272no—
515C4×D4—271no—
516C33D4×Q811yescharacteristic, complemented, Sylow
517C23×C3—91no—
518C23×C3—91no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—31no—
523C22×D3—61no—
524C22×D3—61no—
525C3×Q8—34no—
526C3×Q8—34no—
527C3×Q8—64no—
528C3×Q8—62no—
529C3×Q8—62no—
530C3×Q8—122no—
531C3×Q8—184no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—41no—
542C2×C3×C4—62no—
543C2×C3×C4—62no—
544C2×C3×C4—62no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—184no—
550C2×C3×C4—182no—
551C2×C3×C4—182no—
552C2×C3×C4C2×D3211yescharacteristic
553C2×C3×C4C2×D3211yescharacteristic
554C2×C3×C4C2×D3211yescharacteristic
555#67—94no—
556#67—94no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—92no—
570C2×Dic3—92no—
571C2×Dic3—92no—
572C2×Dic3—182no—
573C2×Dic3—182no—
574C2×Dic3—182no—
575C2×Dic3—184no—
576C2×Dic3—362no—
577C2×Dic3C2×D3212yes—
578C2×Dic3C2×D3212yes—
579C2×Dic3C2×D3212yes—
580D12—94no—
581C4×D3—64no—
582C4×D3—64no—
583C4×D3—62no—
584C4×D3—62no—
585C4×D3—62no—
586C4×D3—62no—
587C4×D3—64no—
588C4×D3—122no—
589C4×D3—184no—
590C4×D3—184no—
591C4×D3—188no—
592Dic6—22no—
593Dic6—64no—
594Dic6—64no—
595Dic6—184no—
596Dic6—184no—
597Dic6—188no—
598Dic6—184no—
599Dic6—182no—
600Dic6—182no—
601Dic6—182no—
602Dic6—184no—
603Dic6—362no—
604Dic6—362no—
605Dic6—364no—
606Dic6#62614yescomplemented
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—41no—
619C2×C32C22×D1211yescharacteristic
620C2×C32C2×D3×D411yescharacteristic
621C2×C32C2×D3×Q811yescharacteristic
622C2×C32C2×D3×Q811yescharacteristic
623C2×C32C2×D3×Q811yescharacteristic
624C2×C32#100711yescharacteristic
625C2×C32#101011yescharacteristic
626C2×C32#101011yescharacteristic
627C2×C32C22×#6711yescharacteristic
628C3⋊D3—22no—
629C3⋊D3—22no—
630C3×D3—64no—
631C3×D3—62no—
632C3×D3—62no—
633C3×D3—62no—
634C3×D3—62no—
635C3×D3—122no—
636C2×Q8—31no—
637C2×Q8—31no—
638C2×Q8—92no—
639C2×Q8—184no—
640C2×Q8—272no—
641C2×Q8—271no—
642C2×Q8—544no—
643C2×D4—271no—
644C22×C4—92no—
645C22×C4—91no—
646C22×C4—91no—
647C22×C4—272no—
648C4⋊C4—31no—
649C4⋊C4—92no—
650C4⋊C4—92no—
651C4⋊C4—272no—
652C4⋊C4—272no—
653C4⋊C4—272no—
654C4⋊C4—271no—
655C22⋊C4—92no—
656C22⋊C4—272no—
657C22⋊C4—271no—
658C22⋊C4—271no—
659C42—92no—
660C42—91no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—41no—
665C22×C3—92no—
666C22×C3—92no—
667C22×C3—181no—
668C22×C3—181no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3C22×D3211yescharacteristic
672C22×C3C22×D3211yescharacteristic
673C22×C3C22×D3211yescharacteristic
674C2×D3—32no—
675C2×D3—32no—
676C2×D3—32no—
677C2×D3—32no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—121no—
691C2×D3—121no—
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—34no—
696C3×C4—34no—
697C3×C4—42no—
698C3×C4—64no—
699C3×C4—62no—
700C3×C4—62no—
701C3×C4—62no—
702C3×C4—62no—
703C3×C4—92no—
704C3×C4—122no—
705C3×C4—122no—
706C3×C4—181no—
707C3×C4—181no—
708C3×C4—181no—
709C3×C4D3×D1212yes—
710C3×C4C2×#62612yes—
711C3×C4D3×#6712yes—
712Dic3—22no—
713Dic3—22no—
714Dic3—32no—
715Dic3—32no—
716Dic3—62no—
717Dic3—62no—
718Dic3—62no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—61no—
724Dic3—61no—
725Dic3—121no—
726Dic3—184no—
727Dic3—182no—
728Dic3—182no—
729Dic3—182no—
730Dic3—362no—
731Dic3—362no—
732Dic3—364no—
733Dic3C2×#62614yes—
734C32—21no—
735C32—21no—
736C32—21no—
737C32—41no—
738C32Q8×D1211yescharacteristic, complemented
739C32#563211yescharacteristic, complemented
740C32Q8×#6711yescharacteristic, complemented
741C23—91no—
742C23—91no—
743Q8—34no—
744Q8—62no—
745Q8—184no—
746Q8—544no—
747Q8—542no—
748D4—274no—
749C2×C4—32no—
750C2×C4—32no—
751C2×C4—32no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—184no—
757C2×C4—182no—
758C2×C4—182no—
759C2×C4—272no—
760C2×C4—544no—
761C2×C4D3311yescharacteristic
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—182no—
775C2×C3—182no—
776C2×C3C2×D3×D1211yescharacteristic
777C2×C3#6430911yescharacteristic
778C2×C3#6431511yescharacteristic
779C2×C3#6431511yescharacteristic
780C2×C3D32×Q811yescharacteristic
781C2×C3D32×Q811yescharacteristic
782C2×C3D32×Q811yescharacteristic
783C2×C3C22×#62611yescharacteristic
784C2×C3C2×D3×#6711yescharacteristic
785D3—64no—
786D3—62no—
787D3—62no—
788D3—62no—
789D3—62no—
790D3—122no—
791C22—92no—
792C22—92no—
793C22—181no—
794C22—181no—
795C22—181no—
796C22—181no—
797C22C2×D3311yescharacteristic
798C4—34no—
799C4—62no—
800C4—62no—
801C4—92no—
802C4—181no—
803C4—181no—
804C4—181no—
805C4—542no—
806C4D3×#62612yes—
807C3—21no—
808C3—21no—
809C3—21no—
810C3—41no—
811C3#1059438311yescharacteristic, complemented
812C3#1059540011yescharacteristic, complemented
813C3Q8×#62611yescharacteristic, complemented
814C2—182no—
815C2—182no—
816C2#1172437811yescharacteristic
817C2#1172439411yescharacteristic
818C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6295C22
hypercenterC2×C4D33
hypocenterC33D4×Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×Dic6C2semidirect
2. C2×C3×#3797C2semidirect
4. #11723455C2semidirect
5. #11723431C2semidirect
6. C3×#63871C2semidirect
7. C3×#63843C2semidirect
8. #11723033C2semidirect
9. #11722974C2semidirect
10. #11722972C2semidirect
43. C2×#3797D3semidirect
64. #63871D3semidirect
74. #63843D3semidirect
91. C32×Dic6D4semidirect
92. #6295Q8semidirect
197. C2×C3×C3⋊D3C2×Q8semidirect
198. C2×C3×C3⋊D3C2×Q8semidirect
204. C3×C3⋊Dic3C2×Q8semidirect
321. C3×Dic6D12semidirect
322. C3×Dic6#67semidirect
443. C2×C3⋊D3D3×Q8semidirect
444. C2×C3⋊D3D3×Q8semidirect
483. C3⋊Dic3D3×Q8semidirect
516. C33D4×Q8semidirect
606. Dic6#626semidirect
738. C32Q8×D12semidirect
739. C32#5632semidirect
740. C32Q8×#67semidirect
811. C3#10594383semidirect
812. C3#10595400semidirect
813. C3Q8×#626semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×Dic62
C2×C3×#37972
C4×#62952
#117234552
#117234312
C3×#638712
C3×#638432
#117230332
#117229742
#117229722
#117229342
Q8×#6263
#105954003
#105943833