Finite Group Databasebeta

← #13168728

Subgroups — #13168728

Order 1728.

1364 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89040C211yesmaximal, characteristic, complemented
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3#11723435C211yesmaximal, characteristic, complemented
4#11723425C211yesmaximal, characteristic, complemented
5Dic3×#634C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic
7C3×#63866C211yesmaximal, characteristic, complemented
8#11723035C212yesmaximal, complemented
9#11722979C212yesmaximal, complemented
10#11722978C212yesmaximal, complemented
11#11722927C212yesmaximal
12#10595403—31nomaximal
13Dic6×#67—31nomaximal
14#10593904—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6296C2212yes—
21C2×#6294C2212yes—
22#89040—24no—
23C2×C3×#627C2212yes—
24C2×C3×#626C2211yescharacteristic
25C2×C3×D3×Dic3C2212yes—
26C3×D3×Dic6—24no—
27C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29#88807C2212yes—
30#88806C2212yes—
31#88806C2212yes—
32#88803C2212yes—
33(C2×D3)⋊(C3⋊Dic3)C2212yes—
34Dic3×C3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×Dic3⋊Dic3C2212yes—
37C3×Dic3⋊Dic3C2212yes—
38C3×#3722C2211yescharacteristic
39C3×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×C3×D3×Q8—31no—
41C22×C3×Dic6—31no—
42C2×#3797—31no—
43C2×D3×Dic6—31no—
44C2×D3×Dic6—31no—
45C2×D3×Dic6D311yescharacteristic, complemented
46#64155—31no—
47#64133—31no—
48C4×#634—31no—
49C3×#944—31no—
50C3×C4×#67—31no—
51C3×C4×D12—31no—
52C3×#869—31no—
53Dic3×#67—32no—
54#63964—32no—
55#63919—32no—
56#63904—32no—
57C4×#626D311yescharacteristic
58#63899—32no—
59#63899—32no—
60#63898—32no—
61#63888—32no—
62#63887—32no—
63#63866D311yescharacteristic, complemented
64#63856—31no—
65#63856—31no—
66#63856—31no—
67#63856—31no—
68#63856—61no—
69#63856—61no—
70#63851—32no—
71Dic3×Dic6—31no—
72Dic3×Dic6—31no—
73Dic3×Dic6—61no—
74#63839—32no—
75#63839—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C3×C4×C3⋊D3—22no—
84C3×#634—22no—
85C3×#634D414yescomplemented
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2311yescharacteristic
90C32×C4×D3—22no—
91C32×Dic6—22no—
92#6296—24no—
93#6294—24no—
94C3×#627—24no—
95C3×#626Q814yescomplemented
96C3×D3×Dic3—24no—
97Q8×#67—91no—
98#5727—91no—
99D4×Dic6—91no—
100C2×C32×Q8—31no—
101C22×C32×C4—31no—
102C2×C4×C3⋊D3C2×D311yescharacteristic
103C2×#634C2×D311yescharacteristic
104C2×#634C2×D311yescharacteristic
105C2×C3×#67—31no—
106C22×C3×Dic3—32no—
107C3×D3×Q8—64no—
108C2×C3×D12—31no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—61no—
114C2×C3×C4×D3C2×D311yescharacteristic
115C2×C3×C4×D3C2×D311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6—31no—
118C2×C3×Dic6—31no—
119C2×C3×Dic6—31no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—32no—
122C2×C3×Dic6—32no—
123C2×C3×Dic6—64no—
124C2×C3×Dic6—61no—
125C2×C3×Dic6—61no—
126C2×C3×Dic6C2×D311yescharacteristic
127C2×C3×Dic6C2×D311yescharacteristic
128C2×#627—32no—
129C2×#627—32no—
130C2×#627—32no—
131C2×#627C2×D312yes—
132C2×#626C2×D311yescharacteristic
133C2×#624—32no—
134C2×D3×Dic3—32no—
135C2×D3×Dic3—32no—
136C2×D3×Dic3C2×D312yes—
137#3797—64no—
138D3×Dic6—24no—
139D3×Dic6—64no—
140D3×Dic6—64no—
141C32×C42—31no—
142#3757—32no—
143#3752—32no—
144C4⋊(C3⋊Dic3)—31no—
145C4⋊(C3⋊Dic3)—31no—
146C4⋊(C3⋊Dic3)—31no—
147C4⋊(C3⋊Dic3)—61no—
148C4⋊(C3⋊Dic3)—61no—
149C4⋊(C3⋊Dic3)—61no—
150C4⋊(C3⋊Dic3)—121no—
151#3750—32no—
152#3750—32no—
153#3750—32no—
154C4×C3⋊Dic3—32no—
155C3×#217—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×C4⋊Dic3—32no—
160C3×C4⋊Dic3—32no—
161C3×C4⋊Dic3—31no—
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4—32no—
165C3×C4×Dic3—21no—
166C3×C4×Dic3C2×D311yescharacteristic
167C3×C4×Dic3C2×D311yescharacteristic
168#3724—32no—
169#3724—32no—
170#3724—32no—
171#3724—32no—
172#3724—62no—
173#3724—62no—
174Dic3⋊Dic3—32no—
175Dic3⋊Dic3—32no—
176Dic3⋊Dic3—62no—
177Dic3⋊Dic3C2×D311yescharacteristic
178Dic3⋊Dic3C2×D312yes—
179Dic3⋊Dic3C2×D312yes—
180#3722C2×D311yescharacteristic
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—62no—
186(C2×D3)⋊Dic3—62no—
187(C2×D3)⋊Dic3C2×D311yescharacteristic
188Dic32—32no—
189Dic32—32no—
190Dic32—62no—
191C22×C33C2411yescharacteristic
192C2×C3×C3⋊D3—21no—
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3C2×Q812yescomplemented
195C2×C32×D3—21no—
196C2×C32×D3—21no—
197C2×C32×D3C2×Q812yescomplemented
198C33×C4C2×D412yes—
199C3⋊(C3⋊Dic3)—22no—
200C3×C3⋊Dic3—22no—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3C2×D414yes—
203C32×Dic3—22no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3C2×Q812yescomplemented
207C22×C3×Q8—91no—
208C2×D3×Q8—31no—
209C2×D3×Q8—91no—
210C2×D3×Q8—91no—
211C22×Dic6—31no—
212C22×Dic6—91no—
213C3×C4⋊Q8—91no—
214C3×C4×D4—91no—
215#946—92no—
216#946—91no—
217#946—91no—
218#946—91no—
219#946—181no—
220Q8×Dic3—91no—
221#944—31no—
222#944—92no—
223D4×Dic3—92no—
224C4×#67—31no—
225C4×#67—92no—
226#924—92no—
227#924—91no—
228#924—91no—
229#924—91no—
230#924—181no—
231#896—92no—
232#896—92no—
233#893—92no—
234#888—92no—
235#888—92no—
236#878—92no—
237#878—92no—
238C4×D12—31no—
239#869—31no—
240C4×Dic6—91no—
241C4×Dic6—91no—
242C4×Dic6—181no—
243C23×C32—31no—
244C22×C3⋊D3C22×D311yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—61no—
249C22×C3×D3C22×D311yescharacteristic
250C22×C3×D3C22×D311yescharacteristic
251C32×Q8—62no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—31no—
256C2×C32×C4—32no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—41no—
260C2×C32×C4—62no—
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×D312yes—
273C2×C3⋊Dic3C22×D312yes—
274C4×C3⋊D3—22no—
275#634—22no—
276#634#6714yescomplemented
277C3×#67—34no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3—61no—
291C2×C3×Dic3—64no—
292C2×C3×Dic3C22×D312yes—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299C2×C3×Dic3C22×D311yescharacteristic
300C3×D12—34no—
301C3×C4×D3—22no—
302C3×C4×D3—22no—
303C3×C4×D3—42no—
304C3×C4×D3—64no—
305C3×C4×D3—62no—
306C3×C4×D3—62no—
307C3×C4×D3—122no—
308C3×Dic6—22no—
309C3×Dic6—22no—
310C3×Dic6—34no—
311C3×Dic6—34no—
312C3×Dic6—42no—
313C3×Dic6—64no—
314C3×Dic6—64no—
315C3×Dic6—64no—
316C3×Dic6—62no—
317C3×Dic6—62no—
318C3×Dic6—122no—
319#627—24no—
320#627—64no—
321#627—64no—
322#627—64no—
323#626Dic614yescomplemented
324#624—64no—
325D3×Dic3—24no—
326D3×Dic3—64no—
327D3×Dic3—64no—
328D4×Q8—271noSylow
329C2×C33C22×D411yescharacteristic
330C2×C33C22×Q811yescharacteristic
331C2×C332−1+411yescharacteristic
332C3×C3⋊D3—22no—
333C32×D3—22no—
334C2×C3×Q8—31no—
335C2×C3×Q8—31no—
336C2×C3×Q8—61no—
337C2×C3×Q8—92no—
338C2×C3×Q8—91no—
339C2×C3×Q8—91no—
340C2×C3×Q8—184no—
341C2×C3×D4—91no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—61no—
345C22×C3×C4—92no—
346C22×C3×C4—91no—
347C2×#67—31no—
348C22×Dic3—32no—
349C22×Dic3—92no—
350D3×Q8—64no—
351D3×Q8—184no—
352D3×Q8—184no—
353C2×D12—31no—
354C2×C4×D3—32no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—61no—
358C2×C4×D3—92no—
359C2×C4×D3—92no—
360C2×C4×D3D3211yescharacteristic
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—31no—
364C2×Dic6—31no—
365C2×Dic6—32no—
366C2×Dic6—32no—
367C2×Dic6—61no—
368C2×Dic6—61no—
369C2×Dic6—64no—
370C2×Dic6—92no—
371C2×Dic6—92no—
372C2×Dic6—92no—
373C2×Dic6—184no—
374C2×Dic6D3211yescharacteristic
375C3×C4⋊C4—91no—
376C3×C4⋊C4—92no—
377C3×C4⋊C4—92no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C42—31no—
381C3×C42—31no—
382C3×C42—61no—
383#217—31no—
384#217—92no—
385#217—92no—
386#217—92no—
387#217—182no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—92no—
392(C2×D3)⋊C4—92no—
393(C2×D3)⋊C4—92no—
394(C2×D3)⋊C4—182no—
395C4⋊Dic3—32no—
396C4⋊Dic3—32no—
397C4⋊Dic3—31no—
398C4⋊Dic3—91no—
399C4⋊Dic3—91no—
400C4⋊Dic3—91no—
401C4⋊Dic3—92no—
402C4⋊Dic3—181no—
403C4⋊Dic3—181no—
404C4⋊Dic3—181no—
405C4⋊Dic3—361no—
406Dic3⋊C4—32no—
407Dic3⋊C4—31no—
408Dic3⋊C4—32no—
409Dic3⋊C4—92no—
410Dic3⋊C4—92no—
411Dic3⋊C4—92no—
412Dic3⋊C4—92no—
413Dic3⋊C4—92no—
414Dic3⋊C4—92no—
415Dic3⋊C4—92no—
416Dic3⋊C4—92no—
417Dic3⋊C4—182no—
418Dic3⋊C4—182no—
419Dic3⋊C4—182no—
420C4×Dic3—92no—
421C4×Dic3—92no—
422C4×Dic3—92no—
423C4×Dic3—182no—
424C4×Dic3D3211yescharacteristic
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—32no—
429C22×C32—41no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32C23×D311yescharacteristic
433C22×C32C23×D311yescharacteristic
434C22×C32C23×D311yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3C2×Dic612yescomplemented
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—22no—
443C2×C3×D3—32no—
444C2×C3×D3—32no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—62no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C2×C3×D3—61no—
451C2×C3×D3—61no—
452C2×C3×D3—121no—
453C2×C3×D3—121no—
454C2×C3×D3C2×Dic612yescomplemented
455C2×C3×D3D3×Q812yescomplemented
456C32×C4—22no—
457C32×C4—22no—
458C32×C4—22no—
459C32×C4—32no—
460C32×C4—42no—
461C32×C4—61no—
462C32×C4—62no—
463C32×C4—61no—
464C32×C4D3×D412yes—
465C32×C4D3×D412yes—
466C32×C4C2×#6712yes—
467C3⋊Dic3—22no—
468C3⋊Dic3—21no—
469C3⋊Dic3—62no—
470C3⋊Dic3—62no—
471C3⋊Dic3—62no—
472C3⋊Dic3—122no—
473C3⋊Dic3—122no—
474C3⋊Dic3—122no—
475C3⋊Dic3—242no—
476C3⋊Dic3C2×#6714yes—
477C3×Dic3—22no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—22no—
482C3×Dic3—21no—
483C3×Dic3—22no—
484C3×Dic3—34no—
485C3×Dic3—34no—
486C3×Dic3—42no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—64no—
490C3×Dic3—62no—
491C3×Dic3—61no—
492C3×Dic3—62no—
493C3×Dic3—61no—
494C3×Dic3—122no—
495C3×Dic3—121no—
496C3×Dic3C2×Dic612yescomplemented
497C3×Dic3D3×Q812yescomplemented
498C22×Q8—91no—
499C22×Q8—271no—
500C4⋊Q8—91no—
501C4⋊Q8—272no—
502C22⋊Q8—272no—
503C22⋊Q8—272no—
504C22⋊Q8—271no—
505C22⋊Q8—271no—
506C4×Q8—271no—
507C4×D4—91no—
508C4×D4—272no—
509C33D4×Q811yescharacteristic, complemented, Sylow
510C23×C3—31no—
511C23×C3—31no—
512C23×C3—61no—
513C23×C3—91no—
514C22×D3—31no—
515C22×D3—31no—
516C22×D3—61no—
517C22×D3C2×D3211yescharacteristic
518C3×Q8—62no—
519C3×Q8—62no—
520C3×Q8—94no—
521C3×Q8—122no—
522C3×Q8—184no—
523C3×Q8—182no—
524C3×D4—94no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—32no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—32no—
536C2×C3×C4—41no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—62no—
541C2×C3×C4—62no—
542C2×C3×C4—62no—
543C2×C3×C4—92no—
544C2×C3×C4—91no—
545C2×C3×C4—92no—
546C2×C3×C4—122no—
547C2×C3×C4—184no—
548C2×C3×C4—182no—
549C2×C3×C4C2×D3211yescharacteristic
550C2×C3×C4C2×D3211yescharacteristic
551C2×C3×C4C2×D3211yescharacteristic
552#67—34no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—32no—
559C2×Dic3—62no—
560C2×Dic3—61no—
561C2×Dic3—62no—
562C2×Dic3—64no—
563C2×Dic3—92no—
564C2×Dic3—92no—
565C2×Dic3—92no—
566C2×Dic3—182no—
567C2×Dic3—182no—
568C2×Dic3—182no—
569C2×Dic3—184no—
570C2×Dic3—362no—
571C2×Dic3C2×D3211yescharacteristic
572C2×Dic3C2×D3211yescharacteristic
573C2×Dic3C2×D3212yes—
574C2×Dic3C2×D3211yescharacteristic
575D12—34no—
576C4×D3—22no—
577C4×D3—64no—
578C4×D3—62no—
579C4×D3—62no—
580C4×D3—122no—
581C4×D3—184no—
582C4×D3—184no—
583Dic6—22no—
584Dic6—34no—
585Dic6—34no—
586Dic6—64no—
587Dic6—64no—
588Dic6—64no—
589Dic6—62no—
590Dic6—62no—
591Dic6—122no—
592Dic6—184no—
593Dic6—184no—
594Dic6—184no—
595C2×C32—21no—
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—41no—
605C2×C32—41no—
606C2×C32—41no—
607C2×C32—62no—
608C2×C32C22×Dic611yescharacteristic
609C2×C32C2×D3×D411yescharacteristic
610C2×C32C2×D3×D411yescharacteristic
611C2×C32C2×D3×Q811yescharacteristic
612C2×C32C2×D3×Q811yescharacteristic
613C2×C32#100711yescharacteristic
614C2×C32#100711yescharacteristic
615C2×C32#101011yescharacteristic
616C2×C32C22×#6711yescharacteristic
617C3⋊D3—22no—
618C3×D3—22no—
619C3×D3—22no—
620C3×D3—42no—
621C3×D3—62no—
622C3×D3—62no—
623C3×D3—122no—
624C2×Q8—31no—
625C2×Q8—92no—
626C2×Q8—91no—
627C2×Q8—91no—
628C2×Q8—184no—
629C2×Q8—272no—
630C2×Q8—544no—
631C2×D4—91no—
632C22×C4—31no—
633C22×C4—92no—
634C22×C4—91no—
635C22×C4—272no—
636C4⋊C4—91no—
637C4⋊C4—92no—
638C4⋊C4—92no—
639C4⋊C4—272no—
640C4⋊C4—272no—
641C4⋊C4—272no—
642C4⋊C4—271no—
643C22⋊C4—91no—
644C22⋊C4—91no—
645C22⋊C4—272no—
646C22⋊C4—272no—
647C42—31no—
648C42—272no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—32no—
654C22×C3—41no—
655C22×C3—62no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—92no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—181no—
664C22×C3—181no—
665C22×C3C22×D3211yescharacteristic
666C22×C3C22×D3211yescharacteristic
667C22×C3C22×D3211yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—32no—
671C2×D3—32no—
672C2×D3—62no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3D3×Dic612yescomplemented
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—32no—
684C3×C4—32no—
685C3×C4—42no—
686C3×C4—62no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—62no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—62no—
693C3×C4—94no—
694C3×C4—121no—
695C3×C4—122no—
696C3×C4—121no—
697C3×C4—181no—
698C3×C4—182no—
699C3×C4#380212yes—
700C3×C4D3×#6712yes—
701C3×C4D3×#6712yes—
702Dic3—21no—
703Dic3—22no—
704Dic3—21no—
705Dic3—34no—
706Dic3—34no—
707Dic3—64no—
708Dic3—62no—
709Dic3—61no—
710Dic3—62no—
711Dic3—61no—
712Dic3—122no—
713Dic3—121no—
714Dic3—182no—
715Dic3—182no—
716Dic3—182no—
717Dic3—362no—
718Dic3—362no—
719Dic3—362no—
720Dic3—722no—
721Dic3D3×Dic612yescomplemented
722C32—21no—
723C32—21no—
724C32—21no—
725C32—41no—
726C32D4×Dic611yescharacteristic, complemented
727C32#572711yescharacteristic, complemented
728C32Q8×#6711yescharacteristic, complemented
729C23—31no—
730C23—91no—
731Q8—62no—
732Q8—94no—
733Q8—184no—
734Q8—182no—
735Q8—544no—
736D4—94no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—32no—
741C2×C4—62no—
742C2×C4—92no—
743C2×C4—91no—
744C2×C4—92no—
745C2×C4—184no—
746C2×C4—182no—
747C2×C4—272no—
748C2×C4—544no—
749C2×C4D3311yescharacteristic
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—41no—
762C2×C3—62no—
763C2×C3—62no—
764C2×C3—122no—
765C2×C3—182no—
766C2×C3C2×D3×Dic611yescharacteristic
767C2×C3C2×D3×Dic611yescharacteristic
768C2×C3#6429711yescharacteristic
769C2×C3#6429711yescharacteristic
770C2×C3C2×#380211yescharacteristic
771C2×C3#6431611yescharacteristic
772C2×C3D32×Q811yescharacteristic
773C2×C3C2×D3×#6711yescharacteristic
774C2×C3C2×D3×#6711yescharacteristic
775D3—22no—
776D3—62no—
777D3—62no—
778D3—122no—
779C22—32no—
780C22—61no—
781C22—61no—
782C22—92no—
783C22—181no—
784C22—181no—
785C22C2×D3311yescharacteristic
786C4—32no—
787C4—61no—
788C4—61no—
789C4—62no—
790C4—94no—
791C4—181no—
792C4—182no—
793C4—542no—
794C4#8895312yes—
795C3—21no—
796C3—21no—
797C3—21no—
798C3—41no—
799C3#1059390411yescharacteristic, complemented
800C3Dic6×#6711yescharacteristic, complemented
801C3#1059540311yescharacteristic, complemented
802C2—62no—
803C2—182no—
804C2D32×Dic611yescharacteristic
805C2#1172439511yescharacteristic
806C2C2×#8895311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#626C22
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×#89040C2semidirect
2. C2×C3×D3×Dic6C2semidirect
3. #11723435C2semidirect
4. #11723425C2semidirect
5. Dic3×#634C2semidirect
7. C3×#63866C2semidirect
8. #11723035C2semidirect
9. #11722979C2semidirect
10. #11722978C2semidirect
45. C2×D3×Dic6D3semidirect
63. #63866D3semidirect
85. C3×#634D4semidirect
95. C3×#626Q8semidirect
194. C2×C3×C3⋊D3C2×Q8semidirect
197. C2×C32×D3C2×Q8semidirect
206. C32×Dic3C2×Q8semidirect
276. #634#67semidirect
323. #626Dic6semidirect
437. C2×C3⋊D3C2×Dic6semidirect
454. C2×C3×D3C2×Dic6semidirect
455. C2×C3×D3D3×Q8semidirect
496. C3×Dic3C2×Dic6semidirect
497. C3×Dic3D3×Q8semidirect
509. C33D4×Q8semidirect
679. C2×D3D3×Dic6semidirect
721. Dic3D3×Dic6semidirect
726. C32D4×Dic6semidirect
727. C32#5727semidirect
728. C32Q8×#67semidirect
799. C3#10593904semidirect
800. C3Dic6×#67semidirect
801. C3#10595403semidirect

Maximal subgroups

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

subgroupindex
C2×#890402
C2×C3×D3×Dic62
#117234352
#117234252
Dic3×#6342
C3×C4×#6262
C3×#638662
#117230352
#117229792
#117229782
#117229272
#105954033
Dic6×#673
#105939043