Finite Group Databasebeta

← #13169447

Subgroups — #13169447

Order 1728.

1602 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89019C211yesmaximal, characteristic
2#11723668C211yesmaximal, characteristic, complemented
3#11723503C211yesmaximal, characteristic
4C4×#6289C211yesmaximal, characteristic
5C3×#63844C211yesmaximal, characteristic, complemented
6C3×#63843C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11722943C212yesmaximal, complemented
9#11722942C212yesmaximal, complemented
10#11722912C212yesmaximal
11#11722900C212yesmaximal
12Q8×#624—31nomaximal
13#10594363—31nomaximal
14C4×#3797—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6293C2212yes—
19C2×#6289C2212yes—
20C2×#6289C2211yescharacteristic
21C2×#6289C2212yes—
22C2×#6289C2211yescharacteristic
23#89019C418yescomplemented
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88815C2212yes—
29#88813C2212yes—
30#88806C2212yes—
31Dic3×C3⋊Dic3C2211yescharacteristic
32Dic3×C3⋊Dic3C2211yescharacteristic
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic32C2212yes—
37C3×Dic32C2212yes—
38C3×Dic32C2212yes—
39C2×Q8×C3⋊D3—31no—
40C2×#3797—31no—
41C2×#3797—31no—
42C2×#3797—61no—
43C4⋊C4×C3⋊D3—31no—
44C42×C3⋊D3—31no—
45C3×Q8×Dic3—31no—
46C3×Q8×Dic3—31no—
47C3×#887—31no—
48C3×#887—31no—
49C3×C4×Dic6—31no—
50C3×C4×Dic6—31no—
51C4×#627—32no—
52#63900—31no—
53#63900—31no—
54#63900—32no—
55#63900—61no—
56#63883—32no—
57#63883—32no—
58C4×#624—31no—
59C4×#624—31no—
60C4×#624—32no—
61C4×#624—32no—
62C4×#624—32no—
63C4×#624—61no—
64#63844—31no—
65#63844—32no—
66#63844—32no—
67#63844D311yescharacteristic, complemented
68#63843—31no—
69#63843D311yescharacteristic, complemented
70Dic3×Dic6—31no—
71Dic3×Dic6D311yescharacteristic, complemented
72#63838—32no—
73#63837—32no—
74#63837—32no—
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C4×C3⋊(C3⋊D3)C2×C414yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×#634C2×C414yescomplemented
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C32×Dic6C2×C414yescomplemented
89#6293C2×C418yescomplemented
90#6289—22no—
91#6289—24no—
92#6289C2×C418yes—
93#6289Q814yescomplemented
94C4×D3×Q8—91no—
95C4×D3×Q8—91no—
96C4×D3×Q8—91no—
97C2×C32×Q8—31no—
98Q8×C3⋊D3—38no—
99C2×C4×C3⋊D3—31no—
100C2×C4×C3⋊D3—31no—
101C2×C4×C3⋊D3—31no—
102C2×C4×C3⋊D3—31no—
103C2×C4×C3⋊D3—32no—
104C2×C4×C3⋊D3—31no—
105C2×C4×C3⋊D3—32no—
106C2×C4×C3⋊D3—61no—
107C2×C4×C3⋊D3—61no—
108C2×C4×C3⋊D3—61no—
109C2×C4×C3⋊D3—121no—
110C2×#634—32no—
111C2×#634C2×D311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6—31no—
114C2×C3×Dic6—31no—
115C2×C3×Dic6—61no—
116C2×C3×Dic6C2×D311yescharacteristic
117C2×C3×Dic6C2×D311yescharacteristic
118C2×#627—32no—
119C2×#627—32no—
120C2×#627—62no—
121C2×#624—32no—
122C2×#624—32no—
123C2×#624—31no—
124C2×#624—31no—
125C2×#624—31no—
126C2×#624—32no—
127C2×#624—31no—
128C2×#624—32no—
129C2×#624—62no—
130C2×#624—61no—
131C2×#624—61no—
132C2×#624—62no—
133#3797—38no—
134#3797—38no—
135#3797—68no—
136C32×C4⋊C4—31no—
137C32×C42—31no—
138C4⋊(C3⋊Dic3)C2×D311yescharacteristic
139#3750—32no—
140C4×C3⋊Dic3—31no—
141C4×C3⋊Dic3—31no—
142C4×C3⋊Dic3C2×D311yescharacteristic
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3—31no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—32no—
147C3×C4⋊Dic3—32no—
148C3×C4⋊Dic3—61no—
149C3×C4⋊Dic3C2×D311yescharacteristic
150C3×C4⋊Dic3C2×D311yescharacteristic
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155C3×C4×Dic3—21no—
156C3×C4×Dic3—31no—
157C3×C4×Dic3—31no—
158C3×C4×Dic3—32no—
159C3×C4×Dic3—32no—
160C3×C4×Dic3—32no—
161C3×C4×Dic3—32no—
162C3×C4×Dic3—32no—
163C3×C4×Dic3—32no—
164C3×C4×Dic3—61no—
165C3×C4×Dic3C2×D311yescharacteristic
166C3×C4×Dic3C2×D311yescharacteristic
167#3724—32no—
168#3724—32no—
169#3724—32no—
170#3724—62no—
171#3724C2×D312yes—
172Dic3⋊Dic3—32no—
173Dic3⋊Dic3—32no—
174Dic3⋊Dic3C2×D312yes—
175Dic3⋊Dic3C2×D312yes—
176Dic32—32no—
177Dic32—32no—
178Dic32—32no—
179Dic32—31no—
180Dic32—31no—
181Dic32—31no—
182Dic32—31no—
183Dic32—61no—
184Dic32—61no—
185Dic32C2×D312yes—
186Dic32C2×D312yes—
187Dic32C2×D312yes—
188C22×C33C2411yescharacteristic
189C2×C3⋊(C3⋊D3)C22×C412yes—
190C2×C3⋊(C3⋊D3)C2×Q812yes—
191C2×C3⋊(C3⋊D3)#4112yes—
192C33×C4C22×C412yes—
193C3⋊(C3⋊Dic3)C22×C412yes—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3C22×C414yes—
197C3×C3⋊Dic3C2×Q812yescomplemented
198C32×Dic3—21no—
199C32×Dic3—22no—
200C32×Dic3C22×C414yes—
201C32×Dic3C2×Q812yescomplemented
202C2×D3×Q8—91no—
203C2×D3×Q8—91no—
204C2×D3×Q8—91no—
205C2×D3×Q8—181no—
206C3×C4×Q8—91no—
207C3×C4×Q8—91no—
208C3×C4×Q8—91no—
209Q8×Dic3—31no—
210Q8×Dic3—31no—
211Q8×Dic3—91no—
212D3×C4⋊C4—92no—
213D3×C4⋊C4—92no—
214D3×C4⋊C4—92no—
215D3×C4⋊C4—91no—
216D3×C4⋊C4—91no—
217D3×C4⋊C4—91no—
218D3×C4⋊C4—181no—
219#887—31no—
220#887—31no—
221#887—92no—
222#887—92no—
223#887—92no—
224#887—91no—
225C42×D3—92no—
226C42×D3—92no—
227C42×D3—92no—
228C42×D3—91no—
229C42×D3—91no—
230C42×D3—91no—
231C42×D3—181no—
232C4×Dic6—31no—
233C4×Dic6—31no—
234C4×Dic6—92no—
235C4×Dic6—92no—
236C4×Dic6—92no—
237C4×Dic6—91no—
238C22×C3⋊D3—31no—
239C22×C3⋊D3—31no—
240C22×C3⋊D3—31no—
241C22×C3⋊D3—61no—
242C22×C3⋊D3—61no—
243C22×C3⋊D3—61no—
244C22×C3⋊D3—121no—
245C32×Q8—34no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—31no—
250C2×C32×C4—32no—
251C2×C32×C4—32no—
252C2×C32×C4—31no—
253C2×C32×C4—41no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—61no—
261C2×C3⋊Dic3—61no—
262C2×C3⋊Dic3—61no—
263C2×C3⋊Dic3—121no—
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D312yes—
267C2×C3⋊Dic3C22×D311yescharacteristic
268C4×C3⋊D3—34no—
269C4×C3⋊D3—34no—
270C4×C3⋊D3—34no—
271C4×C3⋊D3—38no—
272C4×C3⋊D3—34no—
273C4×C3⋊D3—64no—
274C4×C3⋊D3—64no—
275C4×C3⋊D3—64no—
276C4×C3⋊D3—62no—
277C4×C3⋊D3—64no—
278C4×C3⋊D3—124no—
279#634—38no—
280#634C4×D314yescomplemented
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—32no—
291C2×C3×Dic3—32no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—61no—
294C2×C3×Dic3—61no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3—62no—
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299C2×C3×Dic3C22×D312yes—
300C2×C3×Dic3C22×D312yes—
301C2×C3×Dic3C22×D312yes—
302C2×C3×Dic3C22×D312yes—
303C2×C3×Dic3C22×D311yescharacteristic
304C2×C3×Dic3C22×D311yescharacteristic
305C3×Dic6—24no—
306C3×Dic6—34no—
307C3×Dic6—34no—
308C3×Dic6—64no—
309C3×Dic6C4×D314yescomplemented
310C3×Dic6C4×D314yescomplemented
311#627—38no—
312#627—38no—
313#627—68no—
314#624—38no—
315#624—38no—
316#624—34no—
317#624—34no—
318#624—68no—
319#624—64no—
320#624—62no—
321#624—62no—
322#624—64no—
323#624—64no—
324#624—64no—
325#624—124no—
326C2×C4×Q8—271noSylow
327C2×C33C23×C411yescharacteristic
328C2×C33C22×Q811yescharacteristic
329C2×C33C2×#4111yescharacteristic
330C3⋊(C3⋊D3)C4×Q814yescomplemented
331C2×C3×Q8—31no—
332C2×C3×Q8—31no—
333C2×C3×Q8—61no—
334C2×C3×Q8—91no—
335D3×Q8—98no—
336D3×Q8—98no—
337D3×Q8—98no—
338D3×Q8—188no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—92no—
342C2×C4×D3—92no—
343C2×C4×D3—91no—
344C2×C4×D3—91no—
345C2×C4×D3—91no—
346C2×C4×D3—91no—
347C2×C4×D3—92no—
348C2×C4×D3—91no—
349C2×C4×D3—92no—
350C2×C4×D3—92no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—92no—
354C2×C4×D3—181no—
355C2×C4×D3—181no—
356C2×C4×D3—182no—
357C2×C4×D3—181no—
358C2×C4×D3—181no—
359C2×C4×D3—181no—
360C2×C4×D3—182no—
361C2×C4×D3—361no—
362C2×Dic6—31no—
363C2×Dic6—31no—
364C2×Dic6—61no—
365C2×Dic6—92no—
366C2×Dic6—92no—
367C2×Dic6—92no—
368C2×Dic6—182no—
369C2×Dic6D3211yescharacteristic
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—92no—
374C3×C4⋊C4—92no—
375C3×C4⋊C4—92no—
376C3×C4⋊C4—91no—
377C3×C42—31no—
378C3×C42—31no—
379C3×C42—61no—
380C3×C42—92no—
381C3×C42—92no—
382C3×C42—92no—
383C3×C42—91no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—32no—
387C4⋊Dic3—32no—
388C4⋊Dic3—61no—
389C4⋊Dic3—92no—
390C4⋊Dic3D3211yescharacteristic
391Dic3⋊C4—32no—
392Dic3⋊C4—32no—
393Dic3⋊C4—32no—
394Dic3⋊C4—32no—
395Dic3⋊C4—92no—
396Dic3⋊C4—92no—
397Dic3⋊C4—92no—
398Dic3⋊C4—92no—
399Dic3⋊C4—92no—
400Dic3⋊C4—182no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—32no—
404C4×Dic3—32no—
405C4×Dic3—32no—
406C4×Dic3—32no—
407C4×Dic3—32no—
408C4×Dic3—32no—
409C4×Dic3—61no—
410C4×Dic3—92no—
411C4×Dic3—92no—
412C4×Dic3—92no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—91no—
419C4×Dic3—181no—
420C4×Dic3—181no—
421C4×Dic3D3211yescharacteristic
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—41no—
426C22×C32C23×D311yescharacteristic
427C22×C32C23×D311yescharacteristic
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—32no—
430C2×C3⋊D3—32no—
431C2×C3⋊D3—32no—
432C2×C3⋊D3—32no—
433C2×C3⋊D3—32no—
434C2×C3⋊D3—32no—
435C2×C3⋊D3—32no—
436C2×C3⋊D3—32no—
437C2×C3⋊D3—32no—
438C2×C3⋊D3—62no—
439C2×C3⋊D3—62no—
440C2×C3⋊D3—62no—
441C2×C3⋊D3—62no—
442C2×C3⋊D3—62no—
443C2×C3⋊D3—62no—
444C2×C3⋊D3—62no—
445C2×C3⋊D3—62no—
446C2×C3⋊D3—62no—
447C2×C3⋊D3—122no—
448C2×C3⋊D3—122no—
449C2×C3⋊D3—122no—
450C32×C4—22no—
451C32×C4—22no—
452C32×C4—22no—
453C32×C4—34no—
454C32×C4—32no—
455C32×C4—42no—
456C32×C4—61no—
457C32×C4—62no—
458C32×C4C2×C4×D312yes—
459C32×C4C2×C4×D312yes—
460C32×C4C2×C4×D312yes—
461C3⋊Dic3—21no—
462C3⋊Dic3—22no—
463C3⋊Dic3—32no—
464C3⋊Dic3—32no—
465C3⋊Dic3—32no—
466C3⋊Dic3—62no—
467C3⋊Dic3—62no—
468C3⋊Dic3—62no—
469C3⋊Dic3—122no—
470C3⋊Dic3C2×C4×D314yes—
471C3⋊Dic3D3×Q812yescomplemented
472C3×Dic3—22no—
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—24no—
479C3×Dic3—34no—
480C3×Dic3—34no—
481C3×Dic3—32no—
482C3×Dic3—32no—
483C3×Dic3—42no—
484C3×Dic3—64no—
485C3×Dic3—62no—
486C3×Dic3—62no—
487C3×Dic3—62no—
488C3×Dic3—61no—
489C3×Dic3—61no—
490C3×Dic3—62no—
491C3×Dic3—122no—
492C3×Dic3C2×C4×D314yes—
493C3×Dic3C2×C4×D314yes—
494C3×Dic3D3×Q812yescomplemented
495C3×Dic3D3×Q812yescomplemented
496C22×Q8—271no—
497C4×Q8—91no—
498C4×Q8—91no—
499C4×Q8—91no—
500C4×Q8—272no—
501C4×Q8—272no—
502C4×Q8—271no—
503C2×C4⋊C4—271no—
504C2×C4⋊C4—272no—
505C2×C42—271no—
506C2×C42—272no—
507C33C2×C4×Q811yescharacteristic, complemented, Sylow
508C22×D3—91no—
509C22×D3—91no—
510C22×D3—91no—
511C22×D3—181no—
512C22×D3—181no—
513C22×D3—181no—
514C22×D3—361no—
515C3×Q8—34no—
516C3×Q8—34no—
517C3×Q8—64no—
518C3×Q8—94no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—62no—
534C2×C3×C4—62no—
535C2×C3×C4—91no—
536C2×C3×C4—92no—
537C2×C3×C4—91no—
538C2×C3×C4—92no—
539C2×C3×C4C2×D3211yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541C2×C3×C4C2×D3211yescharacteristic
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—31no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—31no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—181no—
558C2×Dic3—181no—
559C2×Dic3—181no—
560C2×Dic3—361no—
561C2×Dic3C2×D3212yes—
562C2×Dic3C2×D3211yescharacteristic
563C2×Dic3C2×D3211yescharacteristic
564C2×Dic3C2×D3212yes—
565C4×D3—94no—
566C4×D3—94no—
567C4×D3—98no—
568C4×D3—98no—
569C4×D3—94no—
570C4×D3—94no—
571C4×D3—94no—
572C4×D3—94no—
573C4×D3—98no—
574C4×D3—184no—
575C4×D3—188no—
576C4×D3—184no—
577C4×D3—184no—
578C4×D3—184no—
579C4×D3—182no—
580C4×D3—184no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—184no—
584C4×D3—184no—
585C4×D3—184no—
586C4×D3—364no—
587C4×D3—364no—
588Dic6—34no—
589Dic6—34no—
590Dic6—64no—
591Dic6—98no—
592Dic6—98no—
593Dic6—98no—
594Dic6—188no—
595Dic6#62414yescomplemented
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—41no—
606C2×C32—41no—
607C2×C32—41no—
608C2×C32C22×C4×D311yescharacteristic
609C2×C32C22×C4×D311yescharacteristic
610C2×C32C22×C4×D311yescharacteristic
611C2×C32C2×D3×Q811yescharacteristic
612C2×C32C2×D3×Q811yescharacteristic
613C2×C32C2×D3×Q811yescharacteristic
614C2×C32D3×#4111yescharacteristic
615C2×C32D3×#4111yescharacteristic
616C2×C32D3×#4111yescharacteristic
617C3⋊D3—34no—
618C3⋊D3—34no—
619C3⋊D3—34no—
620C3⋊D3—64no—
621C3⋊D3—64no—
622C3⋊D3—64no—
623C3⋊D3—124no—
624C2×Q8—31no—
625C2×Q8—91no—
626C2×Q8—272no—
627C2×Q8—278no—
628C22×C4—271no—
629C22×C4—272no—
630C22×C4—271no—
631C22×C4—272no—
632C22×C4—271no—
633C4⋊C4—31no—
634C4⋊C4—92no—
635C4⋊C4—92no—
636C4⋊C4—92no—
637C4⋊C4—91no—
638C4⋊C4—272no—
639C4⋊C4—272no—
640C42—31no—
641C42—92no—
642C42—92no—
643C42—92no—
644C42—91no—
645C42—271no—
646C42—271no—
647C42—272no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—41no—
652C22×C3C22×D3211yescharacteristic
653C22×C3C22×D3211yescharacteristic
654C22×C3C22×D3211yescharacteristic
655C2×D3—92no—
656C2×D3—92no—
657C2×D3—92no—
658C2×D3—92no—
659C2×D3—92no—
660C2×D3—92no—
661C2×D3—92no—
662C2×D3—92no—
663C2×D3—92no—
664C2×D3—182no—
665C2×D3—182no—
666C2×D3—182no—
667C2×D3—182no—
668C2×D3—182no—
669C2×D3—182no—
670C2×D3—182no—
671C2×D3—182no—
672C2×D3—182no—
673C2×D3—362no—
674C2×D3—362no—
675C2×D3—362no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—34no—
680C3×C4—34no—
681C3×C4—32no—
682C3×C4—32no—
683C3×C4—42no—
684C3×C4—64no—
685C3×C4—62no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—62no—
691C3×C4—92no—
692C3×C4—94no—
693C3×C4—122no—
694C3×C4—181no—
695C3×C4—182no—
696C3×C4C4×D3212yes—
697C3×C4C4×D3212yes—
698C3×C4C2×#62412yes—
699Dic3—21no—
700Dic3—22no—
701Dic3—34no—
702Dic3—34no—
703Dic3—32no—
704Dic3—32no—
705Dic3—64no—
706Dic3—62no—
707Dic3—62no—
708Dic3—62no—
709Dic3—61no—
710Dic3—61no—
711Dic3—62no—
712Dic3—92no—
713Dic3—92no—
714Dic3—92no—
715Dic3—122no—
716Dic3—182no—
717Dic3—182no—
718Dic3—182no—
719Dic3—362no—
720Dic3#379712yescomplemented
721Dic3C2×#62414yes—
722C32—21no—
723C32—21no—
724C32—21no—
725C32—41no—
726C32C4×D3×Q811yescharacteristic, complemented
727C32C4×D3×Q811yescharacteristic, complemented
728C32C4×D3×Q811yescharacteristic, complemented
729C23—271no—
730Q8—34no—
731Q8—94no—
732Q8—278no—
733C2×C4—31no—
734C2×C4—32no—
735C2×C4—31no—
736C2×C4—32no—
737C2×C4—91no—
738C2×C4—92no—
739C2×C4—91no—
740C2×C4—92no—
741C2×C4—278no—
742C2×C4—274no—
743C2×C4—271no—
744C2×C4—274no—
745C2×C4—542no—
746C2×C4—544no—
747C2×C4D3311yescharacteristic
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3C2×#379711yescharacteristic
761C2×C3C2×C4×D3211yescharacteristic
762C2×C3C2×C4×D3211yescharacteristic
763C2×C3#6430611yescharacteristic
764C2×C3#6431211yescharacteristic
765C2×C3D32×Q811yescharacteristic
766C2×C3D32×Q811yescharacteristic
767C2×C3#6431911yescharacteristic
768C2×C3C22×#62411yescharacteristic
769D3—94no—
770D3—94no—
771D3—94no—
772D3—184no—
773D3—184no—
774D3—184no—
775D3—364no—
776C22—272no—
777C22—272no—
778C22—272no—
779C22C2×D3311yescharacteristic
780C4—32no—
781C4—34no—
782C4—61no—
783C4—62no—
784C4—92no—
785C4—94no—
786C4—181no—
787C4—182no—
788C4—272no—
789C4D3×#62412yes—
790C3—21no—
791C3—21no—
792C3—21no—
793C3—41no—
794C3C4×#379711yescharacteristic, complemented
795C3#1059436311yescharacteristic, complemented
796C3Q8×#62411yescharacteristic, complemented
797C2—274no—
798C2D3×#379711yescharacteristic
799C2#1172437611yescharacteristic
800C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC22×C3⋊(C3⋊D3)C23
hypercenterC2×C4D33
hypocenterC33C2×C4×Q8
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723668C2semidirect
5. C3×#63844C2semidirect
6. C3×#63843C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11722943C2semidirect
9. #11722942C2semidirect
23. #89019C4semidirect
67. #63844D3semidirect
69. #63843D3semidirect
71. Dic3×Dic6D3semidirect
83. C3×#634C2×C4semidirect
88. C32×Dic6C2×C4semidirect
89. #6293C2×C4semidirect
93. #6289Q8semidirect
197. C3×C3⋊Dic3C2×Q8semidirect
201. C32×Dic3C2×Q8semidirect
280. #634C4×D3semidirect
309. C3×Dic6C4×D3semidirect
310. C3×Dic6C4×D3semidirect
330. C3⋊(C3⋊D3)C4×Q8semidirect
471. C3⋊Dic3D3×Q8semidirect
494. C3×Dic3D3×Q8semidirect
495. C3×Dic3D3×Q8semidirect
507. C33C2×C4×Q8semidirect
595. Dic6#624semidirect
720. Dic3#3797semidirect
726. C32C4×D3×Q8semidirect
727. C32C4×D3×Q8semidirect
728. C32C4×D3×Q8semidirect
794. C3C4×#3797semidirect
795. C3#10594363semidirect
796. C3Q8×#624semidirect

Maximal subgroups

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

subgroupindex
C2×#890192
#117236682
#117235032
C4×#62892
C3×#638442
C3×#638432
C3×Dic3×Dic62
#117229432
#117229422
#117229122
#117229002
Q8×#6243
#105943633
C4×#37973