Finite Group Databasebeta

← #13178671

Subgroups — #13178671

Order 1728.

1288 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64147C211yesmaximal, characteristic, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723726C212yesmaximal, complemented
5#11723725C212yesmaximal, complemented
6#11723720C212yesmaximal, complemented
7#11723716C212yesmaximal, complemented
8C4×#6295C211yesmaximal, characteristic, complemented
9#11723689C211yesmaximal, characteristic, complemented
10#11723680C211yesmaximal, characteristic, complemented
11#11723667C211yesmaximal, characteristic, complemented
12#10595245—31nomaximal
13#10595182—31nomaximal
14#10595122—31nomaximal
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yes—
18C22×C3×C3⋊Dic3C2212yes—
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2212yes—
23C3×#3757C2212yes—
24C3×#3757C2212yes—
25C3×#3757C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30#88815C2212yes—
31#88815C2212yes—
32#88815C2212yes—
33#88815C2211yescharacteristic
34#88814C2212yes—
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37#88813C2212yes—
38#64147D311yescharacteristic, complemented
39#64147D311yescharacteristic, complemented
40D4×C3⋊Dic3D311yescharacteristic, complemented
41C3×#938—31no—
42C3×#938—31no—
43C3×#938—31no—
44C3×#938—31no—
45C3×#938—61no—
46C3×#938—61no—
47C3×D4×Dic3—31no—
48C3×D4×Dic3—31no—
49C3×D4×Dic3—61no—
50#67⋊Dic3—32no—
51Dic3×#67—32no—
52#63971—32no—
53#63970—32no—
54#63966—32no—
55#63962—32no—
56#63961—32no—
57#63958—32no—
58#63956—32no—
59#63956—32no—
60#63956—32no—
61#63952—32no—
62C4×#626—31no—
63C4×#626—31no—
64C4×#625—31no—
65#63900—31no—
66D3×C4⋊Dic3—31no—
67D3×C4⋊Dic3—31no—
68#63872—31no—
69#63869—31no—
70#63869—31no—
71#63849—31no—
72#63841—31no—
73#63841—31no—
74C23×C33C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C3×C3⋊D3C2311yescharacteristic
77C33×D4—22no—
78C2×C33×C4C2311yescharacteristic
79C3×#638—24no—
80C3×#638—42no—
81C2×C3×C3⋊Dic3—42no—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C3×C4×C3⋊D3—22no—
90C3×C4×C3⋊D3—22no—
91#6295—22no—
92#6294—42no—
93#5618—91no—
94#5614—91no—
95#5558—91no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4—21no—
99C2×C32×D4—41no—
100C2×C32×D4C2×D311yescharacteristic
101C2×C32×D4C2×D311yescharacteristic
102C2×C32×D4C2×D311yescharacteristic
103C2×#638C2×D312yes—
104C2×#638C2×D312yes—
105C22×C3⋊Dic3C2×D312yes—
106C2×C4×C3⋊D3C2×D311yescharacteristic
107C2×C4×C3⋊D3C2×D311yescharacteristic
108C2×C3×#67—32no—
109C2×C3×#67—32no—
110C2×C3×#67—32no—
111C2×C3×#67—32no—
112C2×C3×#67—62no—
113C2×C3×#67—62no—
114C22×C3×Dic3—32no—
115C22×C3×Dic3—32no—
116C22×C3×Dic3—62no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—61no—
122C2×C3×C4×D3—61no—
123C2×#626—31no—
124C2×#626—31no—
125C2×#625—31no—
126C2×#624—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—32no—
129#3757C2×D312yes—
130#3757C2×D312yes—
131#3757C2×D312yes—
132C4⋊(C3⋊Dic3)C2×D311yescharacteristic
133C4⋊(C3⋊Dic3)C2×D311yescharacteristic
134C4⋊(C3⋊Dic3)C2×D311yescharacteristic
135C4×C3⋊Dic3C2×D311yescharacteristic
136C3×#217—32no—
137C3×#217—32no—
138C3×#217—32no—
139C3×#217—32no—
140C3×#217—32no—
141C3×#217—32no—
142C3×#217—62no—
143C3×#217—62no—
144C3×#217—62no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—61no—
152C3×C4⋊Dic3—61no—
153C3×C4⋊Dic3—61no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—31no—
156C3×C4×Dic3—61no—
157#3724—32no—
158#3724—32no—
159#3724—32no—
160#3724—31no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169#3722—32no—
170#3722—31no—
171#3722—31no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178Dic32—32no—
179Dic32—32no—
180Dic32—32no—
181C22×C33—22no—
182C22×C33—22no—
183C22×C33—22no—
184C22×C33C2411yescharacteristic
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—21no—
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—21no—
190C2×C3×C3⋊D3#4112yes—
191C33×C4#4112yes—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3—21no—
197C3×C3⋊Dic3—22no—
198C3×C3⋊Dic3—22no—
199C3×#121—91no—
200C3×#121—91no—
201C3×C4×D4—91no—
202#939—92no—
203#938—31no—
204#938—31no—
205#938—31no—
206#938—31no—
207#938—61no—
208#938—61no—
209#938—92no—
210#935—92no—
211D4×Dic3—31no—
212D4×Dic3—31no—
213D4×Dic3—61no—
214D4×Dic3—92no—
215#929—92no—
216C4×#67—91no—
217C4×#67—91no—
218C4×#67—92no—
219#926—91no—
220C2×C4⋊Dic3—91no—
221#892—91no—
222#892—91no—
223D3×C4⋊C4—91no—
224D3×C4⋊C4—91no—
225#890—91no—
226#890—91no—
227#886—92no—
228#884—92no—
229#67⋊C4—92no—
230#879—92no—
231#879—92no—
232#879—92no—
233C4×D12—91no—
234#870—91no—
235C23×C32—22no—
236C23×C32—22no—
237C23×C32—22no—
238C23×C32—42no—
239C23×C32C22×D312yes—
240C23×C32C22×D312yes—
241C23×C32C22×D312yes—
242C22×C3⋊D3C22×D311yescharacteristic
243C22×C3⋊D3C22×D311yescharacteristic
244C22×C3×D3—31no—
245C22×C3×D3—31no—
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—61no—
249C22×C3×D3—61no—
250C32×D4—22no—
251C32×D4—24no—
252C32×D4—22no—
253C32×D4—22no—
254C32×D4—42no—
255C32×D4—42no—
256C32×D4—44no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—41no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264#638—24no—
265#638—42no—
266C2×C3⋊Dic3—42no—
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D312yes—
269C2×C3⋊Dic3C22×D312yes—
270C2×C3⋊Dic3C22×D311yescharacteristic
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D312yes—
274C4×C3⋊D3—22no—
275C4×C3⋊D3—22no—
276C3×#67—64no—
277C3×#67—64no—
278C3×#67—124no—
279C3×#67—122no—
280C3×#67—122no—
281C3×#67—124no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—32no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—62no—
301C2×C3×Dic3—61no—
302C2×C3×Dic3—61no—
303C2×C3×Dic3—122no—
304C2×C3×Dic3—122no—
305C2×C3×Dic3—124no—
306C3×C4×D3—62no—
307C3×C4×D3—62no—
308C3×C4×D3—62no—
309C3×C4×D3—62no—
310C3×C4×D3—122no—
311C3×C4×D3—122no—
312#626—62no—
313#626—62no—
314#625—62no—
315#624—122no—
316D3×Dic3—122no—
317D3×Dic3—122no—
318#553—271noSylow
319C2×C33—42no—
320C2×C33C2×#4111yescharacteristic
321C2×C33C2×#4111yescharacteristic
322C2×C33H(5,𝔽2)11yescharacteristic
323C3×C3⋊D3—22no—
324C3×C3⋊D3—41no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—41no—
329C2×C3×D4—92no—
330C2×C3×D4—92no—
331C2×C3×D4D3211yescharacteristic
332C2×C3×D4D3211yescharacteristic
333C2×C3×D4D3211yescharacteristic
334C22×C3×C4—92no—
335C22×C3×C4—91no—
336C22×C3×C4—91no—
337C2×#67—32no—
338C2×#67—32no—
339C2×#67—32no—
340C2×#67—32no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—91no—
344C2×#67—91no—
345C22×Dic3—32no—
346C22×Dic3—32no—
347C22×Dic3—62no—
348C22×Dic3—92no—
349C2×D12—91no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—92no—
357C2×C4×D3—92no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
361C3×C22⋊C4—92no—
362C3×C22⋊C4—92no—
363C3×C22⋊C4—92no—
364C3×C42—91no—
365#217—32no—
366#217—32no—
367#217—32no—
368#217—32no—
369#217—32no—
370#217—32no—
371#217—62no—
372#217—62no—
373#217—62no—
374#217—92no—
375#217—91no—
376#217—91no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—92no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—92no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—91no—
393C4⋊Dic3—92no—
394C4⋊Dic3—92no—
395C4⋊Dic3—92no—
396Dic3⋊C4—92no—
397Dic3⋊C4—92no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—92no—
401Dic3⋊C4—92no—
402Dic3⋊C4—92no—
403Dic3⋊C4—92no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—61no—
407C4×Dic3—92no—
408C4×Dic3—92no—
409C4×Dic3—92no—
410C22×C32—22no—
411C22×C32—24no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—22no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—41no—
424C22×C32—42no—
425C22×C32—42no—
426C22×C32—44no—
427C22×C32—42no—
428C22×C32—42no—
429C22×C32—42no—
430C22×C32—42no—
431C22×C32—42no—
432C22×C32—42no—
433C22×C32—82no—
434C22×C32—82no—
435C22×C32C23×D311yescharacteristic
436C22×C32C23×D311yescharacteristic
437C22×C32C23×D311yescharacteristic
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C2×C3⋊D3#23712yes—
444C2×C3×D3—32no—
445C2×C3×D3—32no—
446C2×C3×D3—62no—
447C2×C3×D3—61no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C2×C3×D3—61no—
451C2×C3×D3—62no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—121no—
459C2×C3×D3—121no—
460C2×C3×D3—121no—
461C2×C3×D3—121no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—42no—
466C32×C4#23512yes—
467C32×C4#23712yes—
468C32×C4#23712yes—
469C3⋊Dic3—21no—
470C3⋊Dic3—21no—
471C3⋊Dic3—21no—
472C3⋊Dic3—22no—
473C3⋊Dic3—22no—
474C3⋊Dic3—22no—
475C3⋊Dic3—21no—
476C3×Dic3—62no—
477C3×Dic3—61no—
478C3×Dic3—61no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C3×Dic3—62no—
483C3×Dic3—62no—
484C3×Dic3—61no—
485C3×Dic3—61no—
486C3×Dic3—62no—
487C3×Dic3—62no—
488C3×Dic3—62no—
489C3×Dic3—62no—
490C3×Dic3—61no—
491C3×Dic3—121no—
492C3×Dic3—121no—
493C3×Dic3—121no—
494C3×Dic3—122no—
495C3×Dic3—122no—
496C3×Dic3—122no—
497#126—272no—
498#125—271no—
499#123—272no—
500#121—91no—
501#121—91no—
502#121—272no—
503C4×D4—91no—
504C4×D4—271no—
505C4×D4—272no—
506#117—271no—
507C2×C4⋊C4—271no—
508C33#55311yescharacteristic, complemented, Sylow
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—42no—
513C23×C3—91no—
514C23×C3—91no—
515C23×C3C2×D3212yes—
516C23×C3C2×D3212yes—
517C23×C3C2×D3212yes—
518C22×D3—31no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—61no—
523C22×D3—61no—
524C3×D4—24no—
525C3×D4—22no—
526C3×D4—22no—
527C3×D4—22no—
528C3×D4—42no—
529C3×D4—42no—
530C3×D4—44no—
531C3×D4—184no—
532C3×D4—362no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—41no—
537C2×C3×C4—91no—
538C2×C3×C4—92no—
539C2×C3×C4—92no—
540C2×C3×C4—91no—
541C2×C3×C4—92no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—182no—
545C2×C3×C4—182no—
546C2×C3×C4—362no—
547C2×C3×C4C2×D3211yescharacteristic
548C2×C3×C4C2×D3211yescharacteristic
549C2×C3×C4C2×D3211yescharacteristic
550#67—64no—
551#67—64no—
552#67—124no—
553#67—122no—
554#67—122no—
555#67—124no—
556#67—182no—
557#67—182no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—32no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—62no—
575C2×Dic3—62no—
576C2×Dic3—62no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—122no—
580C2×Dic3—122no—
581C2×Dic3—124no—
582C2×Dic3—362no—
583D12—182no—
584C4×D3—62no—
585C4×D3—62no—
586C4×D3—62no—
587C4×D3—62no—
588C4×D3—122no—
589C4×D3—122no—
590C4×D3—362no—
591C4×D3—362no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—41no—
602C2×C32—41no—
603C2×C32—41no—
604C2×C32—42no—
605C2×C32—44no—
606C2×C32—42no—
607C2×C32—42no—
608C2×C32—82no—
609C2×C32—82no—
610C2×C32—84no—
611C2×C32C2×#23511yescharacteristic
612C2×C32C2×#23711yescharacteristic
613C2×C32C2×#23711yescharacteristic
614C2×C32C2×#23711yescharacteristic
615C2×C32#100411yescharacteristic
616C2×C32#100411yescharacteristic
617C2×C32D3×#4111yescharacteristic
618C2×C32D3×#4111yescharacteristic
619C2×C32#100911yescharacteristic
620C3⋊D3—22no—
621C3⋊D3—41no—
622C3×D3—62no—
623C3×D3—62no—
624C3×D3—122no—
625C3×D3—122no—
626C3×D3—121no—
627C3×D3—121no—
628C2×D4—92no—
629C2×D4—92no—
630C2×D4—271no—
631C2×D4#111311yescharacteristic
632C22×C4—92no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4—272no—
636C4⋊C4—91no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—272no—
640C4⋊C4—272no—
641C4⋊C4—271no—
642C4⋊C4—272no—
643C22⋊C4—92no—
644C22⋊C4—92no—
645C22⋊C4—92no—
646C22⋊C4—272no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C42—91no—
650C42—272no—
651C22×C3—24no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—44no—
673C22×C3—41no—
674C22×C3—82no—
675C22×C3—82no—
676C22×C3—92no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3—181no—
682C22×C3C22×D3211yescharacteristic
683C22×C3C22×D3211yescharacteristic
684C22×C3C22×D3211yescharacteristic
685C2×D3—32no—
686C2×D3—32no—
687C2×D3—62no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—62no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—42no—
707C3×C4—181no—
708C3×C4—182no—
709C3×C4—182no—
710C3×C4—182no—
711C3×C4—181no—
712C3×C4—181no—
713C3×C4—181no—
714C3×C4#380412yes—
715C3×C4#380412yes—
716C3×C4#380512yes—
717Dic3—62no—
718Dic3—62no—
719Dic3—62no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—62no—
727Dic3—61no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—61no—
732Dic3—121no—
733Dic3—121no—
734Dic3—122no—
735Dic3—122no—
736Dic3—122no—
737Dic3—121no—
738C32—21no—
739C32—21no—
740C32—21no—
741C32—41no—
742C32#555811yescharacteristic, complemented
743C32#561411yescharacteristic, complemented
744C32#561811yescharacteristic, complemented
745C23—91no—
746C23—91no—
747C23C2×#111312yes—
748D4—22no—
749D4—184no—
750D4—362no—
751D4—542no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—92no—
756C2×C4—92no—
757C2×C4—91no—
758C2×C4—92no—
759C2×C4—182no—
760C2×C4—182no—
761C2×C4—362no—
762C2×C4—1082no—
763C2×C4C2×#111311yescharacteristic
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—44no—
774C2×C3—42no—
775C2×C3—42no—
776C2×C3—42no—
777C2×C3—41no—
778C2×C3—41no—
779C2×C3—41no—
780C2×C3—82no—
781C2×C3—82no—
782C2×C3—84no—
783C2×C3—182no—
784C2×C3—361no—
785C2×C3D3×#23711yescharacteristic
786C2×C3D3×#23711yescharacteristic
787C2×C3#6431211yescharacteristic
788C2×C3#6431311yescharacteristic
789C2×C3#6431411yescharacteristic
790C2×C3#6431411yescharacteristic
791C2×C3C2×#380411yescharacteristic
792C2×C3C2×#380411yescharacteristic
793C2×C3C2×#380511yescharacteristic
794D3—62no—
795D3—62no—
796D3—122no—
797D3—122no—
798D3—121no—
799D3—121no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—92no—
804C22—181no—
805C22—181no—
806C22—181no—
807C22—181no—
808C22—181no—
809C22C22×#111311yescharacteristic
810C4—182no—
811C4—181no—
812C4—181no—
813C4—182no—
814C4—182no—
815C4—181no—
816C4—181no—
817C4#8904612yes—
818C3—21no—
819C3—21no—
820C3—21no—
821C3—41no—
822C3#1059512211yescharacteristic, complemented
823C3#1059518211yescharacteristic, complemented
824C3#1059524511yescharacteristic, complemented
825C2—42no—
826C2—182no—
827C2—361no—
828C2#1172462211yescharacteristic
829C2#1172462311yescharacteristic
830C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64147C2semidirect
2. C3×#64147C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. #11723726C2semidirect
5. #11723725C2semidirect
6. #11723720C2semidirect
7. #11723716C2semidirect
8. C4×#6295C2semidirect
9. #11723689C2semidirect
10. #11723680C2semidirect
11. #11723667C2semidirect
38. #64147D3semidirect
39. #64147D3semidirect
40. D4×C3⋊Dic3D3semidirect
508. C33#553semidirect
742. C32#5558semidirect
743. C32#5614semidirect
744. C32#5618semidirect
822. C3#10595122semidirect
823. C3#10595182semidirect
824. C3#10595245semidirect

Maximal subgroups

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

subgroupindex
C3×#641472
C3×D4×C3⋊Dic32
#117237262
#117237252
#117237202
#117237162
C4×#62952
#117236892
#117236802
#117236672
#105952453
#105951823
#105951223