Finite Group Databasebeta

← #13162054

Subgroups — #13162054

Order 1728.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic
2C2×C3×#3757C211yesmaximal, characteristic, complemented
3C2×C3×#3757C211yesmaximal, characteristic, complemented
4C2×#88815C211yesmaximal, characteristic, complemented
5C2×#88814C211yesmaximal, characteristic, complemented
6C2×#88814C211yesmaximal, characteristic, complemented
7#11722082C211yesmaximal, characteristic, complemented
8#10591712—31nomaximal
9#10591709—31nomaximal
10#10591708—31nomaximal
11C24×C33C2211yescharacteristic
12C23×C3×C3⋊D3C2211yescharacteristic
13C2×C3×#638—22no—
14C2×C3×#638—22no—
15C2×C3×#638—22no—
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C3×#3757—22no—
22C3×#3757—22no—
23#88815—22no—
24#88814—22no—
25#88814—22no—
26C22×#638D311yescharacteristic
27C22×C3×#67—31no—
28C22×C3×#67—31no—
29C22×C3×#67—61no—
30C2×#3757D311yescharacteristic, complemented
31C2×#3757D311yescharacteristic, complemented
32C2×C3×#217—31no—
33C2×C3×#217—31no—
34C2×C3×#217—31no—
35C2×C3×#217—31no—
36C2×C3×#217—61no—
37C2×C3×#217—61no—
38C2×#3724—31no—
39C2×Dic3⋊Dic3—31no—
40C2×Dic3⋊Dic3—31no—
41C2×#3722—31no—
42C2×#3722—31no—
43C2×(C2×D3)⋊Dic3—31no—
44C2×(C2×D3)⋊Dic3—31no—
45C2×(C2×D3)⋊Dic3—31no—
46C2×(C2×D3)⋊Dic3—31no—
47#63579—31no—
48#63579—31no—
49#63579—31no—
50C23×C33—21no—
51C23×C33—21no—
52C23×C33—21no—
53C23×C33—21no—
54C23×C33—21no—
55C23×C33—21no—
56C23×C33D412yes—
57C23×C33C2311yescharacteristic
58C22×C3×C3⋊D3—21no—
59C22×C3×C3⋊D3—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3—21no—
62C22×C3×C3⋊D3—21no—
63C22×C3×C3⋊D3—21no—
64C22×C3×C3⋊D3D412yes—
65C3×#638—28no—
66C2×C3×C3⋊Dic3—21no—
67C2×C3×C3⋊Dic3—21no—
68C2×C3×C3⋊Dic3—21no—
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3—21no—
71C2×C3×C3⋊Dic3—21no—
72C2×C3×C3⋊Dic3—21no—
73C2×C3×C3⋊Dic3—21no—
74C2×C3×C3⋊Dic3—21no—
75C2×C3×C3⋊Dic3—21no—
76C2×C3×C3⋊Dic3—21no—
77C2×C3×C3⋊Dic3—21no—
78C2×C3×C3⋊Dic3—21no—
79C2×C3×C3⋊Dic3D412yes—
80C2×C3×C3⋊Dic3D412yescomplemented
81#5222—91no—
82#4961—91no—
83#4959—91no—
84C24×C32—21no—
85C24×C32—21no—
86C24×C32—21no—
87C24×C32—41no—
88C24×C32C2×D311yescharacteristic
89C24×C32C2×D311yescharacteristic
90C24×C32C2×D311yescharacteristic
91C23×C3⋊D3C2×D311yescharacteristic
92C23×C3×D3—31no—
93C23×C3×D3—31no—
94C23×C3×D3—61no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—22no—
98C22×C3⋊Dic3C2×D311yescharacteristic
99C22×C3⋊Dic3C2×D311yescharacteristic
100C22×C3⋊Dic3C2×D311yescharacteristic
101C22×C3⋊Dic3C2×D311yescharacteristic
102C22×C3⋊Dic3C2×D311yescharacteristic
103C2×C3×#67—62no—
104C2×C3×#67—62no—
105C2×C3×#67—62no—
106C2×C3×#67—62no—
107C2×C3×#67—64no—
108C2×C3×#67—64no—
109C2×C3×#67—64no—
110C2×C3×#67—62no—
111C2×C3×#67—62no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3—31no—
119C22×C3×Dic3—31no—
120C22×C3×Dic3—31no—
121C22×C3×Dic3—31no—
122C22×C3×Dic3—61no—
123C22×C3×Dic3—61no—
124C22×C3×Dic3—61no—
125C22×C3×Dic3—61no—
126C22×C3×Dic3—61no—
127#3757—22no—
128#3757—22no—
129C3×#217—62no—
130C3×#217—62no—
131C3×#217—64no—
132C3×#217—64no—
133C3×#217—62no—
134C3×#217—62no—
135#3724—62no—
136Dic3⋊Dic3—62no—
137Dic3⋊Dic3—62no—
138#3722—62no—
139#3722—62no—
140(C2×D3)⋊Dic3—62no—
141(C2×D3)⋊Dic3—62no—
142(C2×D3)⋊Dic3—62no—
143(C2×D3)⋊Dic3—62no—
144C22×C33—22no—
145C22×C33—22no—
146C22×C33—22no—
147C22×C33—41no—
148C22×C33—41no—
149C22×C33—41no—
150C22×C33—41no—
151C22×C33C2×D411yescharacteristic
152C22×C33C2×D411yescharacteristic
153C22×C33C2×D411yescharacteristic
154C22×C33C2×D411yescharacteristic
155C22×C33#4111yescharacteristic
156C22×C33#4111yescharacteristic
157C22×C33#4111yescharacteristic
158C2×C3×C3⋊D3—22no—
159C2×C3×C3⋊D3—22no—
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3—41no—
162C2×C3×C3⋊D3—41no—
163C2×C3×C3⋊D3—41no—
164C2×C3×C3⋊D3—41no—
165C3×C3⋊Dic3—22no—
166C3×C3⋊Dic3—22no—
167C3×C3⋊Dic3—41no—
168C3×C3⋊Dic3—41no—
169C3×C3⋊Dic3—41no—
170C22×C3×D4—91no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—61no—
174C2×C3×C22⋊C4—91no—
175C2×C3×C22⋊C4—91no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—61no—
181C2×#217—61no—
182C2×#217—91no—
183C2×#217—91no—
184C2×(C2×D3)⋊C4—91no—
185C2×(C2×D3)⋊C4—91no—
186C2×(C2×D3)⋊C4—91no—
187C2×(C2×D3)⋊C4—91no—
188C2×C4⋊Dic3—91no—
189C2×Dic3⋊C4—91no—
190C2×Dic3⋊C4—91no—
191C3⋊#95—91no—
192C3⋊#95—91no—
193C3⋊#95—91no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—22no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—22no—
219C23×C32—22no—
220C23×C32—22no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—42no—
225C23×C32—41no—
226C23×C32—41no—
227C23×C32—41no—
228C23×C32—41no—
229C23×C32—41no—
230C23×C32—41no—
231C23×C32—41no—
232C23×C32—41no—
233C23×C32—41no—
234C23×C32—41no—
235C23×C32—41no—
236C23×C32—41no—
237C23×C32—41no—
238C23×C32—42no—
239C23×C32—42no—
240C23×C32—42no—
241C23×C32—42no—
242C23×C32—42no—
243C23×C32—42no—
244C23×C32D1212yes—
245C23×C32#6712yes—
246C23×C32#6712yes—
247C23×C32C22×D311yescharacteristic
248C23×C32C22×D311yescharacteristic
249C23×C32C22×D311yescharacteristic
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3#6712yes—
257C22×C3×D3—32no—
258C22×C3×D3—32no—
259C22×C3×D3—62no—
260C22×C3×D3—62no—
261C22×C3×D3—62no—
262C22×C3×D3—61no—
263C22×C3×D3—61no—
264C22×C3×D3—61no—
265C22×C3×D3—61no—
266C22×C3×D3—61no—
267C22×C3×D3—61no—
268C22×C3×D3—61no—
269C22×C3×D3—61no—
270C22×C3×D3—61no—
271C22×C3×D3—61no—
272C22×C3×D3—61no—
273C22×C3×D3—61no—
274C22×C3×D3—121no—
275C22×C3×D3—121no—
276C22×C3×D3—121no—
277C22×C3×D3—121no—
278#638—28no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3—21no—
292C2×C3⋊Dic3#6712yes—
293C2×C3⋊Dic3#6712yescomplemented
294C3×#67—616no—
295C3×#67—68no—
296C3×#67—68no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—32no—
300C2×C3×Dic3—32no—
301C2×C3×Dic3—62no—
302C2×C3×Dic3—62no—
303C2×C3×Dic3—62no—
304C2×C3×Dic3—62no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—61no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—62no—
315C2×C3×Dic3—62no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—61no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—61no—
326C2×C3×Dic3—61no—
327C2×C3×Dic3—61no—
328C2×C3×Dic3—61no—
329C2×C3×Dic3—61no—
330C2×C3×Dic3—61no—
331C2×C3×Dic3—61no—
332C2×C3×Dic3—61no—
333C2×C3×Dic3—61no—
334C2×C3×Dic3—121no—
335C2×C3×Dic3—121no—
336C2×C3×Dic3—121no—
337C2×C3×Dic3—121no—
338C2×C3×Dic3—121no—
339C2×C3×Dic3—121no—
340C2×C3×Dic3—121no—
341C2×C3×Dic3—121no—
342#394—271noSylow
343C2×C33—42no—
344C2×C33#12011yescharacteristic
345C2×C33#12111yescharacteristic
346C2×C33#12111yescharacteristic
347C2×C33#12111yescharacteristic
348C2×C33#12311yescharacteristic
349C2×C33#12311yescharacteristic
350C2×C33#12411yescharacteristic
351C3×C3⋊D3—42no—
352C24×C3—21no—
353C24×C3—21no—
354C24×C3—21no—
355C24×C3—41no—
356C24×C3—91no—
357C24×C3D3211yescharacteristic
358C24×C3D3211yescharacteristic
359C24×C3D3211yescharacteristic
360C23×D3—31no—
361C23×D3—31no—
362C23×D3—61no—
363C2×C3×D4—182no—
364C2×C3×D4—182no—
365C2×C3×D4—182no—
366C22×C3×C4—91no—
367C22×C3×C4—91no—
368C22×C3×C4—91no—
369C22×C3×C4—91no—
370C22×C3×C4—91no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—64no—
376C2×#67—64no—
377C2×#67—64no—
378C2×#67—62no—
379C2×#67—62no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C3×C22⋊C4—182no—
396C3×C22⋊C4—182no—
397#217—62no—
398#217—62no—
399#217—64no—
400#217—64no—
401#217—62no—
402#217—62no—
403#217—182no—
404#217—182no—
405(C2×D3)⋊C4—182no—
406(C2×D3)⋊C4—182no—
407(C2×D3)⋊C4—182no—
408(C2×D3)⋊C4—182no—
409C4⋊Dic3—182no—
410Dic3⋊C4—182no—
411Dic3⋊C4—182no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—42no—
453C22×C32—42no—
454C22×C32—42no—
455C22×C32—42no—
456C22×C32—42no—
457C22×C32—42no—
458C22×C32—44no—
459C22×C32—44no—
460C22×C32—44no—
461C22×C32—42no—
462C22×C32—42no—
463C22×C32—42no—
464C22×C32—42no—
465C22×C32—42no—
466C22×C32—42no—
467C22×C32—42no—
468C22×C32—42no—
469C22×C32—42no—
470C22×C32—42no—
471C22×C32—42no—
472C22×C32—42no—
473C22×C32—44no—
474C22×C32—44no—
475C22×C32—44no—
476C22×C32—44no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32C2×D1211yescharacteristic
490C22×C32#23511yescharacteristic
491C22×C32#23511yescharacteristic
492C22×C32#23511yescharacteristic
493C22×C32D3×D411yescharacteristic
494C22×C32D3×D411yescharacteristic
495C22×C32D3×D411yescharacteristic
496C22×C32D3×D411yescharacteristic
497C22×C32D3×D411yescharacteristic
498C22×C32D3×D411yescharacteristic
499C22×C32#23711yescharacteristic
500C22×C32#23711yescharacteristic
501C22×C32#23711yescharacteristic
502C22×C32#23711yescharacteristic
503C22×C32#23711yescharacteristic
504C22×C32#23711yescharacteristic
505C22×C32C2×#6711yescharacteristic
506C22×C32C2×#6711yescharacteristic
507C22×C32C2×#6711yescharacteristic
508C22×C32C2×#6711yescharacteristic
509C22×C32C2×#6711yescharacteristic
510C2×C3⋊D3—22no—
511C2×C3⋊D3—22no—
512C2×C3⋊D3—22no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3×D3—64no—
518C2×C3×D3—62no—
519C2×C3×D3—62no—
520C2×C3×D3—62no—
521C2×C3×D3—62no—
522C2×C3×D3—62no—
523C2×C3×D3—62no—
524C2×C3×D3—122no—
525C2×C3×D3—122no—
526C2×C3×D3—122no—
527C2×C3×D3—122no—
528C2×C3×D3—122no—
529C2×C3×D3—122no—
530C2×C3×D3—121no—
531C2×C3×D3—121no—
532C2×C3×D3—121no—
533C2×C3×D3—121no—
534C2×C3×D3—121no—
535C2×C3×D3—121no—
536C2×C3×D3—121no—
537C2×C3×D3—121no—
538C3⋊Dic3—22no—
539C3⋊Dic3—22no—
540C3⋊Dic3—41no—
541C3⋊Dic3—41no—
542C3⋊Dic3—41no—
543C3×Dic3—64no—
544C3×Dic3—62no—
545C3×Dic3—62no—
546C3×Dic3—62no—
547C3×Dic3—62no—
548C3×Dic3—122no—
549C3×Dic3—122no—
550C3×Dic3—122no—
551C3×Dic3—122no—
552C3×Dic3—121no—
553C3×Dic3—121no—
554C3×Dic3—121no—
555C3×Dic3—121no—
556C3×Dic3—121no—
557C3×Dic3—121no—
558C22×D4—91no—
559C2×C4⋊C4—271no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—271no—
563C2×C22⋊C4—271no—
564#95—271no—
565C33#39411yescharacteristic, complemented, Sylow
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—42no—
609C23×C3—42no—
610C23×C3—42no—
611C23×C3—42no—
612C23×C3—42no—
613C23×C3—42no—
614C23×C3—42no—
615C23×C3—41no—
616C23×C3—92no—
617C23×C3—181no—
618C23×C3—181no—
619C23×C3—181no—
620C23×C3—181no—
621C23×C3—181no—
622C23×C3—181no—
623C23×C3#62512yes—
624C23×C3#62612yes—
625C23×C3#62612yes—
626C23×C3C2×D3211yescharacteristic
627C23×C3C2×D3211yescharacteristic
628C23×C3C2×D3211yescharacteristic
629C22×D3—32no—
630C22×D3—32no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—62no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—61no—
642C22×D3—61no—
643C22×D3—61no—
644C22×D3—61no—
645C22×D3—61no—
646C22×D3—121no—
647C22×D3—121no—
648C22×D3—121no—
649C22×D3—121no—
650C3×D4—188no—
651C2×C3×C4—92no—
652C2×C3×C4—92no—
653C2×C3×C4—181no—
654C2×C3×C4—181no—
655C2×C3×C4—181no—
656C2×C3×C4—181no—
657C2×C3×C4—181no—
658C2×C3×C4—181no—
659C2×C3×C4—181no—
660C2×C3×C4—181no—
661C2×C3×C4—181no—
662C2×C3×C4—181no—
663C2×C3×C4—181no—
664C2×C3×C4—181no—
665C2×C3×C4—181no—
666#67—616no—
667#67—68no—
668#67—68no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—21no—
721C2×C32—21no—
722C2×C32—21no—
723C2×C32—21no—
724C2×C32—21no—
725C2×C32—21no—
726C2×C32—21no—
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—21no—
730C2×C32—21no—
731C2×C32—21no—
732C2×C32—21no—
733C2×C32—21no—
734C2×C32—21no—
735C2×C32—41no—
736C2×C32—41no—
737C2×C32—41no—
738C2×C32—41no—
739C2×C32—41no—
740C2×C32—41no—
741C2×C32—41no—
742C2×C32—44no—
743C2×C32—44no—
744C2×C32—44no—
745C2×C32—48no—
746C2×C32—42no—
747C2×C32—42no—
748C2×C32—42no—
749C2×C32#88211yescharacteristic
750C2×C32#88311yescharacteristic
751C2×C32#88311yescharacteristic
752C2×C32#88411yescharacteristic
753C2×C32#88411yescharacteristic
754C2×C32#88511yescharacteristic
755C2×C32#88511yescharacteristic
756C2×C32#88611yescharacteristic
757C2×C32#92911yescharacteristic
758C2×C32#93011yescharacteristic
759C2×C32#93511yescharacteristic
760C2×C32#93511yescharacteristic
761C2×C32#93611yescharacteristic
762C2×C32#93711yescharacteristic
763C2×C32#93811yescharacteristic
764C2×C32#93811yescharacteristic
765C2×C32#93911yescharacteristic
766C2×C32#93911yescharacteristic
767C2×C32#93911yescharacteristic
768C2×C32#93911yescharacteristic
769C2×C32#95311yescharacteristic
770C3⋊D3—42no—
771C3×D3—124no—
772C3×D3—122no—
773C3×D3—122no—
774C24—91no—
775C24#111311yescharacteristic
776C2×D4—182no—
777C2×D4—182no—
778C2×D4—182no—
779C22×C4—91no—
780C22×C4—91no—
781C22×C4—91no—
782C22×C4—91no—
783C22×C4—91no—
784C4⋊C4—542no—
785C22⋊C4—182no—
786C22⋊C4—182no—
787C22⋊C4—542no—
788C22⋊C4—542no—
789C22×C3—24no—
790C22×C3—24no—
791C22×C3—24no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—44no—
829C22×C3—44no—
830C22×C3—44no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—44no—
844C22×C3—44no—
845C22×C3—44no—
846C22×C3—44no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—41no—
860C22×C3—41no—
861C22×C3—41no—
862C22×C3—41no—
863C22×C3—41no—
864C22×C3—41no—
865C22×C3—41no—
866C22×C3—182no—
867C22×C3—182no—
868C22×C3—182no—
869C22×C3—361no—
870C22×C3—361no—
871C22×C3—361no—
872C22×C3—361no—
873C22×C3#380411yescharacteristic
874C22×C3#380411yescharacteristic
875C22×C3#380411yescharacteristic
876C22×C3#380411yescharacteristic
877C22×C3#380411yescharacteristic
878C22×C3#380411yescharacteristic
879C22×C3#380511yescharacteristic
880C22×C3#380511yescharacteristic
881C22×C3#380511yescharacteristic
882C22×C3C2×#62511yescharacteristic
883C22×C3C2×#62611yescharacteristic
884C22×C3C2×#62611yescharacteristic
885C22×C3D3×#6711yescharacteristic
886C22×C3D3×#6711yescharacteristic
887C22×C3D3×#6711yescharacteristic
888C22×C3D3×#6711yescharacteristic
889C22×C3D3×#6711yescharacteristic
890C22×C3D3×#6711yescharacteristic
891C22×C3#381111yescharacteristic
892C22×C3#381111yescharacteristic
893C22×C3#381111yescharacteristic
894C2×D3—64no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—122no—
902C2×D3—122no—
903C2×D3—122no—
904C2×D3—122no—
905C2×D3—122no—
906C2×D3—122no—
907C2×D3—121no—
908C2×D3—121no—
909C2×D3—121no—
910C2×D3—121no—
911C2×D3—121no—
912C2×D3—121no—
913C2×D3—121no—
914C2×D3—121no—
915C3×C4—182no—
916C3×C4—182no—
917C3×C4—361no—
918C3×C4—361no—
919C3×C4—361no—
920Dic3—64no—
921Dic3—62no—
922Dic3—62no—
923Dic3—62no—
924Dic3—62no—
925Dic3—122no—
926Dic3—122no—
927Dic3—122no—
928Dic3—122no—
929Dic3—121no—
930Dic3—121no—
931Dic3—121no—
932Dic3—121no—
933Dic3—121no—
934Dic3—121no—
935C32—21no—
936C32—21no—
937C32—21no—
938C32—41no—
939C32#495911yescharacteristic, complemented
940C32#496111yescharacteristic, complemented
941C32#522211yescharacteristic, complemented
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—92no—
949C23—181no—
950C23—181no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23#629512yes—
956C23C2×#111311yescharacteristic
957D4—188no—
958C2×C4—92no—
959C2×C4—92no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—181no—
966C2×C4—181no—
967C2×C4—181no—
968C2×C4—181no—
969C2×C4—181no—
970C2×C4—181no—
971C2×C4—181no—
972C2×C4—181no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—44no—
995C2×C3—44no—
996C2×C3—44no—
997C2×C3—48no—
998C2×C3—42no—
999C2×C3—42no—
1000C2×C3—42no—
1001C2×C3—41no—
1002C2×C3—41no—
1003C2×C3—41no—
1004C2×C3—41no—
1005C2×C3—41no—
1006C2×C3—41no—
1007C2×C3—41no—
1008C2×C3—362no—
1009C2×C3#6395311yescharacteristic
1010C2×C3#6395811yescharacteristic
1011C2×C3#6395811yescharacteristic
1012C2×C3#6395911yescharacteristic
1013C2×C3#6395911yescharacteristic
1014C2×C3#6396111yescharacteristic
1015C2×C3#6396211yescharacteristic
1016C2×C3#6396611yescharacteristic
1017C2×C3#6396911yescharacteristic
1018C2×C3#6396911yescharacteristic
1019C2×C3#6397011yescharacteristic
1020C2×C3#6397011yescharacteristic
1021C2×C3#6397111yescharacteristic
1022C2×C3#6397111yescharacteristic
1023C2×C3#6397511yescharacteristic
1024C2×C3#6397611yescharacteristic
1025C2×C3#6397711yescharacteristic
1026C2×C3#6397811yescharacteristic
1027C2×C3#6397811yescharacteristic
1028C2×C3#6398011yescharacteristic
1029C2×C3#6398111yescharacteristic
1030D3—124no—
1031D3—122no—
1032D3—122no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—182no—
1041C22—182no—
1042C22—182no—
1043C22—361no—
1044C22—361no—
1045C22—361no—
1046C22—361no—
1047C22#8904611yescharacteristic
1048C22#8904611yescharacteristic
1049C22#8904611yescharacteristic
1050C22C2×#629511yescharacteristic
1051C22#8904911yescharacteristic
1052C22#8904911yescharacteristic
1053C22#8904911yescharacteristic
1054C4—182no—
1055C4—182no—
1056C4—361no—
1057C4—361no—
1058C4—361no—
1059C3—21no—
1060C3—21no—
1061C3—21no—
1062C3—41no—
1063C3#1059170811yescharacteristic, complemented
1064C3#1059170911yescharacteristic, complemented
1065C3#1059171211yescharacteristic, complemented
1066C2—42no—
1067C2—362no—
1068C2#1172371711yescharacteristic
1069C2#1172371811yescharacteristic
1070C2#1172372011yescharacteristic
1071C2#1172372411yescharacteristic
1072C2#1172372511yescharacteristic
1073C2#1172372511yescharacteristic
1074C2#1172372711yescharacteristic
subgroupG/H
center, FrattiniC23C2×#1113
commutator, socle, cosocleC23×C33C23
FittingC24×C33C22
prime radicalC22×C3×#638C2
hypercenterC24#1113
hypocenterC33#394
LCSG ▷ C23×C33 ▷ C33
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3757C2semidirect
3. C2×C3×#3757C2semidirect
4. C2×#88815C2semidirect
5. C2×#88814C2semidirect
6. C2×#88814C2semidirect
7. #11722082C2semidirect
30. C2×#3757D3semidirect
31. C2×#3757D3semidirect
80. C2×C3×C3⋊Dic3D4semidirect
293. C2×C3⋊Dic3#67semidirect
565. C33#394semidirect
939. C32#4959semidirect
940. C32#4961semidirect
941. C32#5222semidirect
1063. C3#10591708semidirect
1064. C3#10591709semidirect
1065. C3#10591712semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C2×C3×#37572
C2×#888152
C2×#888142
#117220822
#105917123
#105917093
#105917083