Finite Group Databasebeta

← #13172164

Subgroups — #13172164

Order 1728.

1830 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic
2C2×#88814C211yesmaximal, characteristic, complemented
3#11723622C212yesmaximal, complemented
4C3×#63974C211yesmaximal, characteristic, complemented
5C3×#67⋊Dic3C212yesmaximal, complemented
6#11722933C212yesmaximal, complemented
7#11722930C212yesmaximal, complemented
8#11722921C211yesmaximal, characteristic, complemented
9#11722919C211yesmaximal, characteristic, complemented
10#11722906C211yesmaximal, characteristic, complemented
11D3×#3722C211yesmaximal, characteristic, complemented
12#10595223—31nomaximal
13#10594254—32nomaximal
14C23×C3×C3⋊D3C2211yescharacteristic
15C22×D3×C3⋊D3C2211yescharacteristic
16C2×#6312C2211yescharacteristic
17C22×C3×C3⋊Dic3C2212yescomplemented
18C2×C32×#67C2211yescharacteristic
19C3⋊D3×#67C418yescomplemented
20C2×#6292C2211yescharacteristic
21C2×#6290C2211yescharacteristic
22C2×#6289C2212yescomplemented
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×C3×#624C2212yescomplemented
25C2×C3×D3×Dic3C2212yescomplemented
26C32×#217C2212yescomplemented
27#88814C2211yescharacteristic
28#88814C2211yescharacteristic
29#88814C2212yescomplemented
30#88806C2212yescomplemented
31#88804C2212yescomplemented
32Dic3×C3⋊Dic3C2212yescomplemented
33C3×Dic3⋊Dic3C2212yescomplemented
34C3×#3722C2211yescharacteristic
35C3×#3722C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2212yescomplemented
37C3×Dic32C2212yescomplemented
38C2×D4×C3⋊D3—31no—
39C2×D3×#67—32no—
40C2×D3×#67—61no—
41#64090—32no—
42C3×D4×Dic3—32no—
43C3×#67⋊C4—32no—
44C3×D3×C22⋊C4—32no—
45#63974—31no—
46#63974D311yescharacteristic, complemented
47#67⋊Dic3D312yescomplemented
48C2×#3722—31no—
49C2×#3722—31no—
50C2×(C2×D3)⋊Dic3—32no—
51#63952—32no—
52#63952—32no—
53#63952—32no—
54#63952—62no—
55#63921—32no—
56D3×(C2×D3)⋊C4—32no—
57#63904—32no—
58C4×#626—32no—
59C4×#625—32no—
60#63894—32no—
61#63879—32no—
62#63878—32no—
63#63877—32no—
64#63874—31no—
65#63849—31no—
66C23×C33C2311yescharacteristic
67C22×C3⋊(C3⋊D3)C2311yescharacteristic
68C22×C3×C3⋊D3—42no—
69C22×C3×C3⋊D3C2×C414yescomplemented
70C22×C3×C3⋊D3C2311yescharacteristic
71C22×C3×C3⋊D3C2311yescharacteristic
72C22×C32×D3C2311yescharacteristic
73C2×D3×C3⋊D3—42no—
74C2×D3×C3⋊D3C2×C414yescomplemented
75#6312C2×C414yescomplemented
76C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
77C2×C3×C3⋊Dic3—42no—
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C32×#67C2×C414yescomplemented
81C2×C32×Dic3C2312yes—
82C2×C32×Dic3C2312yes—
83C2×C32×Dic3C2311yescharacteristic
84#6292C2×C414yescomplemented
85#6290C2×C414yescomplemented
86#6289—42no—
87Dic3×C3⋊D3C2×C414yescomplemented
88C3×#624—42no—
89C3×D3×Dic3—42no—
90#5545—92no—
91#5486—91no—
92C23×C3⋊D3—31no—
93C23×C3⋊D3C2×D311yescharacteristic
94C23×C3×D3—32no—
95C23×C3×D3—61no—
96C22×D32—32no—
97C22×D32—61no—
98C2×C32×D4—31no—
99C2×#638—32no—
100C2×#638—31no—
101C2×#638—31no—
102C2×#638—61no—
103C2×#638—62no—
104C2×#638—121no—
105C22×C3⋊Dic3C2×D312yescomplemented
106D4×C3⋊D3—38no—
107C2×C4⋊(C3⋊D3)—31no—
108C2×C4×C3⋊D3—31no—
109C2×C4×C3⋊D3—32no—
110C2×C3×#67—21no—
111C2×C3×#67C2×D312yes—
112C22×C3×Dic3—32no—
113C22×C3×Dic3—32no—
114C22×C3×Dic3—32no—
115C22×C3×Dic3—62no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—32no—
119D3×#67—316no—
120D3×#67—68no—
121C2×#626—32no—
122C2×#626—61no—
123C2×#625—32no—
124C2×#625—61no—
125C2×#624—32no—
126C2×#624—32no—
127C2×#624—62no—
128C2×#624C2×D312yescomplemented
129C2×D3×Dic3—32no—
130C2×D3×Dic3—61no—
131C2×D3×Dic3C2×D312yescomplemented
132C32×C22⋊C4—32no—
133#3752—32no—
134#3750—32no—
135C4×C3⋊Dic3—32no—
136C3×#217—22no—
137C3×#217—32no—
138C3×#217C2×D312yescomplemented
139C3×#217C2×D312yescomplemented
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×C4⋊Dic3—32no—
144C3×Dic3⋊C4—32no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3—32no—
147#3724—32no—
148#3724—32no—
149#3724—62no—
150Dic3⋊Dic3C2×D312yescomplemented
151#3722—31no—
152#3722—31no—
153#3722—32no—
154#3722—32no—
155#3722—32no—
156#3722—62no—
157#3722C2×D311yescharacteristic
158#3722C2×D311yescharacteristic
159(C2×D3)⋊Dic3—32no—
160(C2×D3)⋊Dic3—32no—
161(C2×D3)⋊Dic3—32no—
162(C2×D3)⋊Dic3—32no—
163(C2×D3)⋊Dic3C2×D312yescomplemented
164Dic32—32no—
165Dic32—32no—
166Dic32—62no—
167Dic32C2×D312yescomplemented
168C22×C33—22no—
169C22×C33C22×C412yes—
170C22×C33C2411yescharacteristic
171C2×C3⋊(C3⋊D3)—22no—
172C2×C3⋊(C3⋊D3)C22×C412yes—
173C2×C3×C3⋊D3—22no—
174C2×C3×C3⋊D3—22no—
175C2×C3×C3⋊D3—44no—
176C2×C3×C3⋊D3C22×C412yes—
177C2×C3×C3⋊D3C22×C412yes—
178C2×C32×D3—22no—
179C2×C32×D3C22×C412yes—
180D3×C3⋊D3—44no—
181C3⋊(C3⋊Dic3)C22×C412yes—
182C3×C3⋊Dic3—22no—
183C3×C3⋊Dic3—22no—
184C32×Dic3—22no—
185C32×Dic3—22no—
186C32×Dic3C22×C412yes—
187C22×#67—91no—
188C2×D3×D4—92no—
189C2×D3×D4—181no—
190C3×C4×D4—92no—
191C2×C3×C22⋊C4—91no—
192C2×#217—91no—
193D4×Dic3—32no—
194C4×#67—92no—
195C4×#67—92no—
196C4×#67—92no—
197C4×#67—92no—
198C2×(C2×D3)⋊C4—92no—
199C2×(C2×D3)⋊C4—92no—
200#893—92no—
201#892—92no—
202#67⋊C4—32no—
203#67⋊C4—92no—
204#67⋊C4—92no—
205#67⋊C4—92no—
206#67⋊C4—182no—
207D3×C22⋊C4—32no—
208D3×C22⋊C4—91no—
209D3×C22⋊C4—92no—
210D3×C22⋊C4—91no—
211#877—91no—
212#877—91no—
213C4×D12—92no—
214#872—92no—
215C23×C32—21no—
216C23×C32—22no—
217C23×C32—31no—
218C23×C32—41no—
219C23×C32C22×D312yes—
220C23×C32C22×D311yescharacteristic
221C22×C3⋊D3—32no—
222C22×C3⋊D3—31no—
223C22×C3⋊D3—34no—
224C22×C3⋊D3—42no—
225C22×C3⋊D3—61no—
226C22×C3⋊D3—62no—
227C22×C3⋊D3—121no—
228C22×C3⋊D3—122no—
229C22×C3⋊D3C4×D314yescomplemented
230C22×C3⋊D3C22×D311yescharacteristic
231C22×C3⋊D3C22×D311yescharacteristic
232C22×C3×D3—21no—
233C22×C3×D3—32no—
234C22×C3×D3—32no—
235C22×C3×D3—38no—
236C22×C3×D3—61no—
237C22×C3×D3—64no—
238C22×C3×D3—61no—
239C22×C3×D3—122no—
240C22×C3×D3—122no—
241C22×C3×D3—124no—
242C22×C3×D3C22×D312yes—
243C2×D32—38no—
244C2×D32—64no—
245C2×D32—122no—
246C2×D32—122no—
247C2×D32—124no—
248C32×D4—34no—
249C2×C32×C4—31no—
250C2×C32×C4—32no—
251C2×C32×C4—32no—
252#638—38no—
253#638—34no—
254#638—34no—
255#638—64no—
256#638—68no—
257#638—124no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—32no—
260C2×C3⋊Dic3—42no—
261C2×C3⋊Dic3—62no—
262C2×C3⋊Dic3—61no—
263C2×C3⋊Dic3—121no—
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D312yes—
266C4⋊(C3⋊D3)—34no—
267C4×C3⋊D3—34no—
268C4×C3⋊D3—122no—
269C3×#67—24no—
270C3×#67C4×D318yescomplemented
271C2×C3×Dic3—21no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—62no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—122no—
281C2×C3×Dic3—122no—
282C2×C3×Dic3—122no—
283C2×C3×Dic3—124no—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D312yes—
289C3×C4×D3—122no—
290C3×C4×D3—122no—
291C3×C4×D3—122no—
292#626—38no—
293#626—64no—
294#625—38no—
295#625—64no—
296#624—42no—
297#624—122no—
298#624—122no—
299#624—124no—
300D3×Dic3—38no—
301D3×Dic3—42no—
302D3×Dic3—64no—
303#518—271noSylow
304C2×C33—22no—
305C2×C33C23×C411yescharacteristic
306C2×C33H(5,𝔽2)12yes—
307C3⋊(C3⋊D3)—22no—
308C3×C3⋊D3—22no—
309C3×C3⋊D3—22no—
310C32×D3—22no—
311C24×C3—91no—
312C23×D3—32no—
313C23×D3—61no—
314C23×D3—92no—
315C23×D3—91no—
316C23×D3—181no—
317C2×C3×D4—32no—
318C2×C3×D4—61no—
319C22×C3×C4—92no—
320C22×C3×C4—92no—
321C22×C3×C4—92no—
322C2×#67—92no—
323C2×#67—91no—
324C2×#67—92no—
325C2×#67—91no—
326C2×#67—98no—
327C2×#67—91no—
328C2×#67—181no—
329C2×#67—182no—
330C2×#67—181no—
331C2×#67—361no—
332C2×#67D3211yescharacteristic
333C22×Dic3—32no—
334C22×Dic3—32no—
335C22×Dic3—32no—
336C22×Dic3—62no—
337C22×Dic3—91no—
338D3×D4—916no—
339D3×D4—188no—
340C2×D12—92no—
341C2×D12—181no—
342C2×C4×D3—32no—
343C2×C4×D3—32no—
344C2×C4×D3—32no—
345C2×C4×D3—92no—
346C2×C4×D3—92no—
347C2×C4×D3—92no—
348C2×C4×D3—92no—
349C2×C4×D3—181no—
350C2×C4×D3—182no—
351C3×C4⋊C4—92no—
352C3×C22⋊C4—32no—
353C3×C22⋊C4—32no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4—91no—
357C3×C22⋊C4—92no—
358C3×C42—92no—
359#217—32no—
360#217—91no—
361#217—91no—
362#217—92no—
363#217D3212yescomplemented
364(C2×D3)⋊C4—32no—
365(C2×D3)⋊C4—32no—
366(C2×D3)⋊C4—32no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—92no—
370(C2×D3)⋊C4—92no—
371(C2×D3)⋊C4—92no—
372(C2×D3)⋊C4—92no—
373(C2×D3)⋊C4—92no—
374(C2×D3)⋊C4—182no—
375C4⋊Dic3—32no—
376Dic3⋊C4—32no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—182no—
381C4×Dic3—32no—
382C4×Dic3—32no—
383C4×Dic3—92no—
384C4×Dic3—92no—
385C4×Dic3—92no—
386C4×Dic3—182no—
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—21no—
392C22×C32—24no—
393C22×C32—22no—
394C22×C32—32no—
395C22×C32—41no—
396C22×C32—42no—
397C22×C32—42no—
398C22×C32—42no—
399C22×C32—42no—
400C22×C32—62no—
401C22×C32—82no—
402C22×C32C2×C4×D312yes—
403C22×C32C2×C4×D314yes—
404C22×C32C23×D311yescharacteristic
405C22×C32C23×D312yes—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—22no—
408C2×C3⋊D3—34no—
409C2×C3⋊D3—32no—
410C2×C3⋊D3—44no—
411C2×C3⋊D3—62no—
412C2×C3⋊D3—64no—
413C2×C3⋊D3—62no—
414C2×C3⋊D3—62no—
415C2×C3⋊D3—62no—
416C2×C3⋊D3—122no—
417C2×C3⋊D3—122no—
418C2×C3⋊D3—122no—
419C2×C3⋊D3—122no—
420C2×C3⋊D3—124no—
421C2×C3⋊D3—242no—
422C2×C3⋊D3C2×C4×D312yes—
423C2×C3⋊D3C2×C4×D312yes—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—34no—
428C2×C3×D3—34no—
429C2×C3×D3—42no—
430C2×C3×D3—62no—
431C2×C3×D3—62no—
432C2×C3×D3—64no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—122no—
438C2×C3×D3—128no—
439C2×C3×D3—128no—
440C2×C3×D3C2×C4×D314yes—
441D32—128no—
442D32—128no—
443C32×C4—32no—
444C32×C4—62no—
445C32×C4—62no—
446C3⋊Dic3—22no—
447C3⋊Dic3—22no—
448C3⋊Dic3—34no—
449C3⋊Dic3—32no—
450C3⋊Dic3—62no—
451C3⋊Dic3—64no—
452C3⋊Dic3—122no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—42no—
459C3×Dic3—42no—
460C3×Dic3—64no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—62no—
465C3×Dic3—122no—
466C3×Dic3C2×C4×D314yes—
467C22×D4—271no—
468C4×D4—92no—
469C4×D4—272no—
470C4×D4—272no—
471C4×D4—272no—
472#117—271no—
473#117—271no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—271no—
476C2×C22⋊C4—271no—
477C2×C22⋊C4—271no—
478C33#51811yescharacteristic, complemented, Sylow
479C23×C3—22no—
480C23×C3—21no—
481C23×C3—32no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—91no—
485C23×C3—91no—
486C23×C3—94no—
487C23×C3—362no—
488C23×C3C2×D3212yes—
489C23×C3C2×D3211yescharacteristic
490C22×D3—32no—
491C22×D3—32no—
492C22×D3—38no—
493C22×D3—61no—
494C22×D3—64no—
495C22×D3—61no—
496C22×D3—98no—
497C22×D3—92no—
498C22×D3—91no—
499C22×D3—94no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—124no—
503C22×D3—184no—
504C22×D3—182no—
505C22×D3—181no—
506C22×D3—361no—
507C22×D3—362no—
508C22×D3—362no—
509C22×D3—362no—
510C22×D3—364no—
511C22×D3C2×D3211yescharacteristic
512C3×D4—38no—
513C3×D4—64no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—61no—
520C2×C3×C4—62no—
521C2×C3×C4—62no—
522C2×C3×C4—92no—
523C2×C3×C4—92no—
524C2×C3×C4—362no—
525C2×C3×C4—362no—
526C2×C3×C4—362no—
527#67—98no—
528#67—98no—
529#67—94no—
530#67—94no—
531#67—94no—
532#67—184no—
533#67—184no—
534#67—188no—
535#67—364no—
536#67#62414yescomplemented
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—92no—
544C2×Dic3—91no—
545C2×Dic3—94no—
546C2×Dic3—122no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3—124no—
550C2×Dic3—182no—
551C2×Dic3—181no—
552C2×Dic3—361no—
553C2×Dic3C2×D3212yes—
554C2×Dic3C2×D3212yes—
555C2×Dic3C2×D3211yescharacteristic
556D12—98no—
557D12—184no—
558C4×D3—98no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—184no—
563C4×D3—362no—
564C4×D3—362no—
565C4×D3—362no—
566C4×D3—364no—
567C2×C32—22no—
568C2×C32—24no—
569C2×C32—22no—
570C2×C32—22no—
571C2×C32—22no—
572C2×C32—22no—
573C2×C32—21no—
574C2×C32—41no—
575C2×C32—42no—
576C2×C32—42no—
577C2×C32—44no—
578C2×C32—62no—
579C2×C32—82no—
580C2×C32C22×C4×D311yescharacteristic
581C2×C32C22×C4×D312yes—
582C2×C32#100412yes—
583C2×C32#100412yes—
584C2×C32#100912yes—
585C3⋊D3—22no—
586C3⋊D3—22no—
587C3⋊D3—62no—
588C3⋊D3—64no—
589C3⋊D3—122no—
590C3⋊D3—124no—
591C3⋊D3—242no—
592C3×D3—24no—
593C3×D3—42no—
594C3×D3—64no—
595C3×D3—64no—
596C3×D3—64no—
597C3×D3—122no—
598C24—91no—
599C24—271no—
600C2×D4—31no—
601C2×D4—271no—
602C2×D4—278no—
603C2×D4—271no—
604C2×D4—271no—
605C22×C4—92no—
606C22×C4—92no—
607C22×C4—92no—
608C22×C4—272no—
609C22×C4—271no—
610C4⋊C4—92no—
611C4⋊C4—272no—
612C22⋊C4—32no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—92no—
616C22⋊C4—272no—
617C22⋊C4—271no—
618C22⋊C4—271no—
619C22⋊C4—272no—
620C42—92no—
621C42—272no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—21no—
627C22×C3—22no—
628C22×C3—24no—
629C22×C3—34no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—41no—
634C22×C3—42no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—82no—
639C22×C3—92no—
640C22×C3—92no—
641C22×C3—122no—
642C22×C3—182no—
643C22×C3—182no—
644C22×C3—364no—
645C22×C3C4×D3214yes—
646C22×C3C2×#62412yes—
647C22×C3C22×D3212yes—
648C22×C3C22×D3211yescharacteristic
649C2×D3—22no—
650C2×D3—34no—
651C2×D3—34no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—64no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—94no—
660C2×D3—92no—
661C2×D3—122no—
662C2×D3—128no—
663C2×D3—128no—
664C2×D3—182no—
665C2×D3—184no—
666C2×D3—182no—
667C2×D3—182no—
668C2×D3—182no—
669C2×D3—362no—
670C2×D3—362no—
671C2×D3—362no—
672C2×D3—362no—
673C2×D3—364no—
674C2×D3—368no—
675C2×D3—368no—
676C2×D3—722no—
677C2×D3C2×#62412yes—
678C3×C4—34no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—62no—
682C3×C4—62no—
683C3×C4—62no—
684C3×C4—122no—
685C3×C4—122no—
686C3×C4—182no—
687C3×C4—182no—
688Dic3—22no—
689Dic3—22no—
690Dic3—64no—
691Dic3—62no—
692Dic3—62no—
693Dic3—62no—
694Dic3—62no—
695Dic3—94no—
696Dic3—92no—
697Dic3—122no—
698Dic3—182no—
699Dic3—184no—
700Dic3—362no—
701Dic3C2×#62412yes—
702C32—21no—
703C32—22no—
704C32—41no—
705C32#548611yescharacteristic, complemented
706C32#554512yescomplemented
707C23—31no—
708C23—91no—
709C23—91no—
710C23—94no—
711C23—274no—
712C23—271no—
713C23—362no—
714C23—1082no—
715C23D3311yescharacteristic
716D4—34no—
717D4—274no—
718D4—274no—
719D4—274no—
720C2×C4—31no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—92no—
724C2×C4—92no—
725C2×C4—274no—
726C2×C4—271no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4—1082no—
731C2×C3—22no—
732C2×C3—24no—
733C2×C3—21no—
734C2×C3—22no—
735C2×C3—22no—
736C2×C3—22no—
737C2×C3—22no—
738C2×C3—42no—
739C2×C3—44no—
740C2×C3—41no—
741C2×C3—42no—
742C2×C3—64no—
743C2×C3—82no—
744C2×C3—122no—
745C2×C3—182no—
746C2×C3—182no—
747C2×C3C2×C4×D3212yes—
748C2×C3#6431312yes—
749C2×C3#6431412yes—
750C2×C3#6431412yes—
751C2×C3C22×#62411yescharacteristic
752D3—22no—
753D3—64no—
754D3—64no—
755D3—64no—
756D3—122no—
757D3—182no—
758D3—184no—
759D3—362no—
760D3—364no—
761D3—722no—
762C22—22no—
763C22—32no—
764C22—62no—
765C22—92no—
766C22—92no—
767C22—182no—
768C22—182no—
769C22—272no—
770C22—364no—
771C22—542no—
772C22—1084no—
773C22D3×#62412yes—
774C22C2×D3311yescharacteristic
775C4—32no—
776C4—62no—
777C4—62no—
778C4—182no—
779C4—182no—
780C4—272no—
781C3—21no—
782C3—22no—
783C3—41no—
784C3#1059425412yescomplemented
785C3#1059522311yescharacteristic, complemented
786C2—22no—
787C2—62no—
788C2—182no—
789C2—182no—
790C2—542no—
791C2C2×D3×#62411yescharacteristic
792C2#1172441612yes—
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC23×C33C23
socle, cosocleC22×C33C24
prime radicalC2×C3⋊D3×#67C2
hypercenterC23D33
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#88814C2semidirect
3. #11723622C2semidirect
4. C3×#63974C2semidirect
5. C3×#67⋊Dic3C2semidirect
6. #11722933C2semidirect
7. #11722930C2semidirect
8. #11722921C2semidirect
9. #11722919C2semidirect
10. #11722906C2semidirect
11. D3×#3722C2semidirect
17. C22×C3×C3⋊Dic3C22semidirect
19. C3⋊D3×#67C4semidirect
22. C2×#6289C22semidirect
24. C2×C3×#624C22semidirect
25. C2×C3×D3×Dic3C22semidirect
26. C32×#217C22semidirect
29. #88814C22semidirect
30. #88806C22semidirect
31. #88804C22semidirect
32. Dic3×C3⋊Dic3C22semidirect
33. C3×Dic3⋊Dic3C22semidirect
36. C3×(C2×D3)⋊Dic3C22semidirect
37. C3×Dic32C22semidirect
46. #63974D3semidirect
47. #67⋊Dic3D3semidirect
69. C22×C3×C3⋊D3C2×C4semidirect
74. C2×D3×C3⋊D3C2×C4semidirect
75. #6312C2×C4semidirect
80. C32×#67C2×C4semidirect
84. #6292C2×C4semidirect
85. #6290C2×C4semidirect
87. Dic3×C3⋊D3C2×C4semidirect
105. C22×C3⋊Dic3C2×D3semidirect
128. C2×#624C2×D3semidirect
131. C2×D3×Dic3C2×D3semidirect
138. C3×#217C2×D3semidirect
139. C3×#217C2×D3semidirect
150. Dic3⋊Dic3C2×D3semidirect
163. (C2×D3)⋊Dic3C2×D3semidirect
167. Dic32C2×D3semidirect
229. C22×C3⋊D3C4×D3semidirect
270. C3×#67C4×D3semidirect
363. #217D32semidirect
478. C33#518semidirect
536. #67#624semidirect
705. C32#5486semidirect
706. C32#5545semidirect
784. C3#10594254semidirect
785. C3#10595223semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#888142
#117236222
C3×#639742
C3×#67⋊Dic32
#117229332
#117229302
#117229212
#117229192
#117229062
D3×#37222
#105952233
#105942543