Finite Group Databasebeta

← #13177365

Subgroups — #13177365

Order 1728.

2356 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89028C211yesmaximal, characteristic, complemented
2C22×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3#11723980C211yesmaximal, characteristic, complemented
4C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6#11723642C211yesmaximal, characteristic, complemented
7#11723630C211yesmaximal, characteristic, complemented
8#11723622C211yesmaximal, characteristic, complemented
9#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#11723616C211yesmaximal, characteristic, complemented
11#11723614C211yesmaximal, characteristic, complemented
12#11723500C211yesmaximal, characteristic, complemented
13#11723479C211yesmaximal, characteristic, complemented
14#11723461C211yesmaximal, characteristic, complemented
15#11723459C211yesmaximal, characteristic, complemented
16#10596057—31nomaximal
17#10595129—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C2×#6293C2211yescharacteristic, complemented
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic
30C2×#6289C2211yescharacteristic, complemented
31#89028—24no—
32C2×D3×C3⋊Dic3—24no—
33C2×D3×C3⋊Dic3C2211yescharacteristic
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic
36C2×D3×C3⋊Dic3C2211yescharacteristic
37#88864C2211yescharacteristic, complemented
38#88859C2211yescharacteristic, complemented
39#88857C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic
41C3×#3757C2211yescharacteristic, complemented
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C23×C3⋊Dic3—31no—
56C2×#3830—31no—
57C2×#3804—34no—
58C22×D3×Dic3—34no—
59C32×#120—31no—
60#64162—31no—
61#64148—31no—
62#64148—31no—
63#64148—34no—
64#64148—64no—
65#64144—31no—
66D4×C3⋊Dic3—31no—
67D4×C3⋊Dic3D311yescharacteristic, complemented
68#64095—31no—
69#64090—31no—
70#64090—31no—
71#64087—31no—
72#64087—31no—
73#64086—31no—
74C3×#937D314yescomplemented
75C3×D4×Dic3—34no—
76#63982—34no—
77#63977—34no—
78Dic3×#67—34no—
79#63971—34no—
80#63969—34no—
81#63952—34no—
82#63899—34no—
83#63890—34no—
84#63880—34no—
85#63877—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C32×D3—22no—
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C33×D4—22no—
95C2×C33×C4C2311yescharacteristic
96#6312—22no—
97#6312—22no—
98C2×C3⋊(C3⋊Dic3)—22no—
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C2×C3×C3⋊Dic3—22no—
103C2×C3×C3⋊Dic3—22no—
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C32×#67—22no—
109C32×#67—22no—
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112#6293—22no—
113#6291—22no—
114#6291—22no—
115#6289—22no—
116D3×C3⋊Dic3—22no—
117D3×C3⋊Dic3—22no—
118D3×C3⋊Dic3—22no—
119D3×C3⋊Dic3D414yescomplemented
120#5586—94no—
121#5547—91no—
122C24×C32—31no—
123C23×C3×D3C2×D314yes—
124C2×C32×D4—24no—
125C2×C32×D4—31no—
126C2×C32×D4—31no—
127C2×C32×D4C2×D314yes—
128C2×C32×D4C2×D311yescharacteristic
129C2×#638—31no—
130C2×#638—31no—
131C2×#638—34no—
132C2×#638—34no—
133C2×#638—31no—
134C2×#638—31no—
135C2×#638—64no—
136C2×#638—64no—
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—34no—
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3—31no—
143C22×C3⋊Dic3—64no—
144C22×C3⋊Dic3—64no—
145C22×C3⋊Dic3C2×D311yescharacteristic
146C22×C3⋊Dic3C2×D311yescharacteristic, complemented
147#3830—64no—
148C2×C4×C3⋊D3—31no—
149C2×#634—31no—
150C2×C3×#67C2×D314yes—
151C2×C3×#67C2×D314yes—
152C22×C3×Dic3—34no—
153C22×C3×Dic3—34no—
154C2×#627—34no—
155C2×#626—34no—
156C2×#626—34no—
157C2×#624—34no—
158#3804—616no—
159C2×D3×Dic3—34no—
160C2×D3×Dic3—34no—
161C2×D3×Dic3—34no—
162C2×D3×Dic3—34no—
163C2×D3×Dic3—616no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167#3757—31no—
168#3757—34no—
169#3757—31no—
170#3757—31no—
171#3757—64no—
172#3757C2×D311yescharacteristic
173#3757C2×D311yescharacteristic, complemented
174#3752—31no—
175#3752—34no—
176#3752—31no—
177#3752—64no—
178C4⋊(C3⋊Dic3)—31no—
179C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
180#3750—31no—
181#3750—34no—
182#3750—31no—
183#3750—31no—
184#3750—31no—
185#3750—64no—
186C4×C3⋊Dic3—31no—
187C4×C3⋊Dic3C2×D311yescharacteristic, complemented
188C3×#217—34no—
189C3×#217—34no—
190C3×#217C2×D314yes—
191C3×(C2×D3)⋊C4C2×D314yes—
192C3×(C2×D3)⋊C4C2×D314yes—
193C3×C4⋊Dic3—34no—
194C3×C4×Dic3—34no—
195#3724—34no—
196#3724—34no—
197Dic3⋊Dic3—34no—
198Dic3⋊Dic3—34no—
199#3722—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202Dic32—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33#4112yescomplemented
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C32×D3—28no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3C2×D412yes—
219C2×C32×D3#4112yescomplemented
220C33×C4—21no—
221C3⋊(C3⋊Dic3)—21no—
222C3⋊(C3⋊Dic3)—21no—
223C3⋊(C3⋊Dic3)C2×D412yes—
224C3×C3⋊Dic3—21no—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3C2×D412yes—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C23×Dic3—94no—
231C2×#237—94no—
232C2×#235—91no—
233C22×C4×D3—91no—
234C3×#120—34no—
235C3×C4×D4—91no—
236#953—94no—
237#939—94no—
238#939—94no—
239#939—91no—
240#939—184no—
241#937C3⋊D311yescharacteristic, complemented
242#935—94no—
243D4×Dic3—34no—
244D4×Dic3—94no—
245C4×#67—91no—
246C4×#67—91no—
247#896—91no—
248#894—91no—
249#886—94no—
250#884—91no—
251#883—91no—
252#882—91no—
253#67⋊C4—94no—
254#67⋊C4—94no—
255#878—94no—
256#878—94no—
257#878—91no—
258#877—94no—
259C4×D12—91no—
260#872—91no—
261C23×C32—24no—
262C23×C32—24no—
263C23×C32—31no—
264C23×C32—31no—
265C23×C32—62no—
266C23×C32—62no—
267C23×C32—62no—
268C23×C32C22×D314yes—
269C23×C32C22×D314yes—
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C22×C3⋊D3—31no—
273C22×C3⋊D3—34no—
274C22×C3⋊D3—64no—
275C22×C3×D3—28no—
276C22×C3×D3—28no—
277C22×C3×D3—28no—
278C22×C3×D3C22×D314yes—
279C22×C3×D3C22×D314yes—
280C32×D4—22no—
281C32×D4—28no—
282C32×D4—48no—
283C32×D4—62no—
284C32×D4—62no—
285C2×C32×C4—24no—
286C2×C32×C4—31no—
287C2×C32×C4—31no—
288C2×C32×C4C22×D314yes—
289C2×C32×C4C22×D311yescharacteristic
290#638—62no—
291#638—62no—
292#638—62no—
293#638—62no—
294#638—68no—
295#638—68no—
296#638—128no—
297#638—128no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3—31no—
301C2×C3⋊Dic3—34no—
302C2×C3⋊Dic3—31no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—34no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—64no—
309C2×C3⋊Dic3—64no—
310C2×C3⋊Dic3—62no—
311C2×C3⋊Dic3—62no—
312C2×C3⋊Dic3—62no—
313C2×C3⋊Dic3—62no—
314C2×C3⋊Dic3—68no—
315C2×C3⋊Dic3—128no—
316C2×C3⋊Dic3C22×D311yescharacteristic
317C2×C3⋊Dic3C22×D311yescharacteristic
318C2×C3⋊Dic3C22×D311yescharacteristic
319C2×C3⋊Dic3C22×D311yescharacteristic
320C4×C3⋊D3—62no—
321#634—62no—
322C3×#67—28no—
323C3×#67—28no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—34no—
327C2×C3×Dic3—34no—
328C2×C3×Dic3—68no—
329C2×C3×Dic3—68no—
330C2×C3×Dic3C22×D314yes—
331C2×C3×Dic3C22×D314yes—
332#627—68no—
333#626—68no—
334#626—68no—
335#624—68no—
336D3×Dic3—316no—
337D3×Dic3—68no—
338D3×Dic3—68no—
339D3×Dic3—68no—
340#525—271noSylow
341C2×C33—22no—
342C2×C33—41no—
343C2×C33C22×D411yescharacteristic
344C2×C33C2×#4111yescharacteristic
345C2×C33C2×#4111yescharacteristic
346C3⋊(C3⋊D3)—41no—
347C32×D3—22no—
348C32×D3—22no—
349C24×C3—34no—
350C23×D3C2×C3⋊D311yescharacteristic
351C2×C3×D4—24no—
352C2×C3×D4—34no—
353C2×C3×D4—34no—
354C2×C3×D4D3214yes—
355C2×C3×D4C2×C3⋊D311yescharacteristic
356C22×C3×C4—91no—
357C22×C3×C4—91no—
358C2×#67—94no—
359C2×#67—94no—
360C2×#67—94no—
361C2×#67—94no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—184no—
365C2×#67—184no—
366C2×#67C2×C3⋊D311yescharacteristic
367C2×#67C2×C3⋊D311yescharacteristic
368C22×Dic3—34no—
369C22×Dic3—34no—
370C22×Dic3—94no—
371C22×Dic3—94no—
372C22×Dic3—94no—
373C22×Dic3—94no—
374C22×Dic3—94no—
375C22×Dic3—91no—
376C22×Dic3—184no—
377C22×Dic3—1816no—
378#237—1816no—
379#235—184no—
380C2×D12—91no—
381C2×D12—91no—
382C2×C4×D3—91no—
383C2×C4×D3—94no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—184no—
389C2×Dic6—94no—
390C2×Dic6—91no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C42—91no—
398#217—34no—
399#217—34no—
400#217—94no—
401#217—94no—
402#217—94no—
403#217—91no—
404#217—184no—
405#217C2×C3⋊D311yescharacteristic
406(C2×D3)⋊C4—94no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—94no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—184no—
413(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
414(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
415C4⋊Dic3—34no—
416C4⋊Dic3—94no—
417C4⋊Dic3—91no—
418Dic3⋊C4—94no—
419Dic3⋊C4—94no—
420Dic3⋊C4—94no—
421Dic3⋊C4—94no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—184no—
427C4×Dic3—34no—
428C4×Dic3—94no—
429C4×Dic3—91no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—24no—
436C22×C32—28no—
437C22×C32—24no—
438C22×C32—24no—
439C22×C32—24no—
440C22×C32—24no—
441C22×C32—24no—
442C22×C32—32no—
443C22×C32—32no—
444C22×C32—44no—
445C22×C32—44no—
446C22×C32—44no—
447C22×C32—44no—
448C22×C32—44no—
449C22×C32—68no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32#23512yescomplemented
455C22×C32#23718yescomplemented
456C22×C32C23×D314yes—
457C22×C32C23×D311yescharacteristic
458C2×C3⋊D3—61no—
459C2×C3⋊D3—61no—
460C2×C3⋊D3—61no—
461C2×C3⋊D3—64no—
462C2×C3⋊D3—64no—
463C2×C3⋊D3—64no—
464C2×C3⋊D3—124no—
465C2×C3⋊D3—124no—
466C2×C3⋊D3—124no—
467C2×C3×D3—232no—
468C2×C3×D3—24no—
469C2×C3×D3—24no—
470C2×C3×D3—24no—
471C2×C3×D3—24no—
472C2×C3×D3D3×D418yes—
473C2×C3×D3#23718yescomplemented
474C32×C4—21no—
475C32×C4—24no—
476C32×C4—44no—
477C32×C4—61no—
478C32×C4—61no—
479C3⋊Dic3—21no—
480C3⋊Dic3—21no—
481C3⋊Dic3—21no—
482C3⋊Dic3—32no—
483C3⋊Dic3—38no—
484C3⋊Dic3—68no—
485C3⋊Dic3—61no—
486C3⋊Dic3—61no—
487C3⋊Dic3—64no—
488C3⋊Dic3—64no—
489C3⋊Dic3—124no—
490C3⋊Dic3—124no—
491C3⋊Dic3D3×D412yes—
492C3×Dic3—24no—
493C3×Dic3—24no—
494C3×Dic3—38no—
495C3×Dic3—64no—
496C3×Dic3—64no—
497C3×Dic3—64no—
498C2×#41—271no—
499C23×C4—271no—
500#123—271no—
501#123—271no—
502C22⋊Q8—271no—
503C22⋊Q8—271no—
504#121—271no—
505#121—271no—
506#120—31no—
507#120—271no—
508C4×D4—91no—
509C4×D4—271no—
510C4×D4—271no—
511C4×D4—271no—
512#117—271no—
513C33#52511yescharacteristic, complemented, Sylow
514C23×C3—24no—
515C23×C3—24no—
516C23×C3—34no—
517C23×C3—34no—
518C23×C3—68no—
519C23×C3—68no—
520C23×C3—68no—
521C23×C3C2×D3214yes—
522C23×C3C2×D3214yes—
523C23×C3C22×C3⋊D311yescharacteristic
524C23×C3C22×C3⋊D311yescharacteristic
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—94no—
529C22×D3—91no—
530C22×D3—184no—
531C22×D3C22×C3⋊D311yescharacteristic
532C22×D3C22×C3⋊D311yescharacteristic
533C3×D4—28no—
534C3×D4—22no—
535C3×D4—48no—
536C3×D4—68no—
537C3×D4—68no—
538C2×C3×C4—24no—
539C2×C3×C4—34no—
540C2×C3×C4—34no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—91no—
545C2×C3×C4—182no—
546C2×C3×C4—182no—
547C2×C3×C4C2×D3214yes—
548C2×C3×C4C22×C3⋊D311yescharacteristic
549#67—22no—
550#67—22no—
551#67—188no—
552#67—188no—
553#67—182no—
554#67—188no—
555#67—188no—
556#67—182no—
557#67—368no—
558#67—368no—
559C2×Dic3—34no—
560C2×Dic3—34no—
561C2×Dic3—34no—
562C2×Dic3—34no—
563C2×Dic3—68no—
564C2×Dic3—68no—
565C2×Dic3—916no—
566C2×Dic3—94no—
567C2×Dic3—91no—
568C2×Dic3—94no—
569C2×Dic3—94no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—184no—
573C2×Dic3—184no—
574C2×Dic3—184no—
575C2×Dic3—188no—
576C2×Dic3—188no—
577C2×Dic3—188no—
578C2×Dic3—182no—
579C2×Dic3—188no—
580C2×Dic3—368no—
581C2×Dic3C22×C3⋊D311yescharacteristic
582C2×Dic3C22×C3⋊D311yescharacteristic
583D12—182no—
584D12—182no—
585C4×D3—94no—
586C4×D3—182no—
587C4×D3—188no—
588C4×D3—182no—
589C4×D3—182no—
590C4×D3—182no—
591Dic6—182no—
592Dic6—188no—
593C2×C32—22no—
594C2×C32—24no—
595C2×C32—24no—
596C2×C32—24no—
597C2×C32—28no—
598C2×C32—48no—
599C2×C32—41no—
600C2×C32—44no—
601C2×C32—62no—
602C2×C32—62no—
603C2×C32—84no—
604C2×C32C2×#23511yescharacteristic
605C2×C32C2×D3×D414yes—
606C2×C32C2×D3×D411yescharacteristic
607C2×C32C2×#23714yes—
608C2×C32C2×#23714yes—
609C2×C32D3×#4111yescharacteristic
610C3⋊D3—121no—
611C3⋊D3—124no—
612C3⋊D3—244no—
613C3×D3—28no—
614C3×D3—28no—
615C24—31no—
616#41—544no—
617C2×Q8—271no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—271no—
621C2×D4—271no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4D3×C3⋊D311yescharacteristic
625C22×C4—91no—
626C22×C4—91no—
627C22×C4—271no—
628C22×C4—271no—
629C22×C4—271no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C22×C4—544no—
634C4⋊C4—91no—
635C4⋊C4—271no—
636C4⋊C4—271no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C4⋊C4—271no—
640C22⋊C4—31no—
641C22⋊C4—31no—
642C22⋊C4—31no—
643C22⋊C4—91no—
644C22⋊C4—91no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4—271no—
650C42—91no—
651C42—271no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—24no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—24no—
663C22×C3—28no—
664C22×C3—38no—
665C22×C3—38no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3—632no—
672C22×C3—64no—
673C22×C3—64no—
674C22×C3—64no—
675C22×C3—64no—
676C22×C3#380418yescomplemented
677C22×C3#383012yescomplemented
678C22×C3C22×D3214yes—
679C22×C3C23×C3⋊D311yescharacteristic
680C2×D3—28no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—184no—
686C2×D3—184no—
687C2×D3—184no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—364no—
692C2×D3—364no—
693C2×D3—364no—
694C2×D3D4×C3⋊D312yes—
695C2×D3#383012yescomplemented
696C3×C4—24no—
697C3×C4—21no—
698C3×C4—44no—
699C3×C4—64no—
700C3×C4—64no—
701C3×C4—92no—
702C3×C4—181no—
703C3×C4—181no—
704C3×C4—181no—
705Dic3—21no—
706Dic3—21no—
707Dic3—38no—
708Dic3—64no—
709Dic3—64no—
710Dic3—64no—
711Dic3—98no—
712Dic3—92no—
713Dic3—188no—
714Dic3—184no—
715Dic3—184no—
716Dic3—181no—
717Dic3—181no—
718Dic3—364no—
719Dic3—364no—
720C32—24no—
721C32#554711yescharacteristic, complemented
722C32#558614yescomplemented
723C23—31no—
724C23—31no—
725C23—62no—
726C23—62no—
727C23—62no—
728C23—271no—
729C23C2×D3×C3⋊D311yescharacteristic
730C23C2×D3×C3⋊D311yescharacteristic
731Q8—542no—
732D4—22no—
733D4—62no—
734D4—62no—
735D4—542no—
736D4—542no—
737D4—542no—
738D4—542no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—91no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—182no—
746C2×C4—182no—
747C2×C4—274no—
748C2×C4—271no—
749C2×C4—271no—
750C2×C4—271no—
751C2×C4—542no—
752C2×C4—542no—
753C2×C4—542no—
754C2×C4—542no—
755C2×C4—542no—
756C2×C4C2×D3×C3⋊D311yescharacteristic
757C2×C3—28no—
758C2×C3—22no—
759C2×C3—24no—
760C2×C3—24no—
761C2×C3—24no—
762C2×C3—48no—
763C2×C3—44no—
764C2×C3—41no—
765C2×C3—68no—
766C2×C3—68no—
767C2×C3—84no—
768C2×C3D32×D414yes—
769C2×C3D3×#23714yes—
770C2×C3C2×#380414yes—
771C2×C3C2×D4×C3⋊D311yescharacteristic
772C2×C3C2×#383011yescharacteristic
773C2×C3C2×#383011yescharacteristic
774D3—22no—
775D3—22no—
776D3—364no—
777D3—361no—
778D3—724no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—32no—
785C22—32no—
786C22—68no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22#8902812yescomplemented
795C22C22×D3×C3⋊D311yescharacteristic
796C4—21no—
797C4—61no—
798C4—61no—
799C4—92no—
800C4—181no—
801C4—181no—
802C4—181no—
803C4—272no—
804C4—541no—
805C4—541no—
806C3—24no—
807C3#1059512914yescomplemented
808C3#1059605711yescharacteristic, complemented
809C2—22no—
810C2—41no—
811C2—62no—
812C2—62no—
813C2—1081no—
814C2D3×D4×C3⋊D311yescharacteristic
815C2D3×#383011yescharacteristic
816C2C2×#8902811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#89028C2semidirect
2. C22×D3×C3⋊Dic3C2semidirect
3. #11723980C2semidirect
4. C3×D4×C3⋊Dic3C2semidirect
5. C32×#937C2semidirect
6. #11723642C2semidirect
7. #11723630C2semidirect
8. #11723622C2semidirect
9. #67×C3⋊Dic3C2semidirect
10. #11723616C2semidirect
11. #11723614C2semidirect
12. #11723500C2semidirect
13. #11723479C2semidirect
14. #11723461C2semidirect
15. #11723459C2semidirect
21. C2×#6312C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
27. C2×#6293C22semidirect
30. C2×#6289C22semidirect
37. #88864C22semidirect
38. #88859C22semidirect
39. #88857C22semidirect
41. C3×#3757C22semidirect
42. C3×C4⋊(C3⋊Dic3)C22semidirect
43. C3×C4×C3⋊Dic3C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
49. #88806C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
67. D4×C3⋊Dic3D3semidirect
74. C3×#937D3semidirect
119. D3×C3⋊Dic3D4semidirect
146. C22×C3⋊Dic3C2×D3semidirect
173. #3757C2×D3semidirect
179. C4⋊(C3⋊Dic3)C2×D3semidirect
187. C4×C3⋊Dic3C2×D3semidirect
208. C22×C33#41semidirect
219. C2×C32×D3#41semidirect
241. #937C3⋊D3semidirect
454. C22×C32#235semidirect
455. C22×C32#237semidirect
473. C2×C3×D3#237semidirect
513. C33#525semidirect
676. C22×C3#3804semidirect
677. C22×C3#3830semidirect
695. C2×D3#3830semidirect
721. C32#5547semidirect
722. C32#5586semidirect
794. C22#89028semidirect
807. C3#10595129semidirect
808. C3#10596057semidirect

Maximal subgroups

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

subgroupindex
C2×#890282
C22×D3×C3⋊Dic32
#117239802
C3×D4×C3⋊Dic32
C32×#9372
#117236422
#117236302
#117236222
#67×C3⋊Dic32
#117236162
#117236142
#117235002
#117234792
#117234612
#117234592
#105960573
#105951293