Finite Group Databasebeta

← #13169149

Subgroups — #13169149

Order 1728.

1204 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723696C211yesmaximal, characteristic, complemented
2#11723515C211yesmaximal, characteristic, complemented
3#11723454C211yesmaximal, characteristic, complemented
4#11723404C211yesmaximal, characteristic, complemented
5C3×C4×#626C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic, complemented
7C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8#11723025C212yesmaximal, complemented
9#11722995C212yesmaximal, complemented
10#11722960C212yesmaximal, complemented
11#11722930C212yesmaximal, complemented
12#10594843—31nomaximal
13#10594561—31nomaximal
14#10593923—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6295C2212yes—
19C2×#6290C2212yes—
20C2×C3×#626C2211yescharacteristic
21C2×C3×#624C2212yes—
22C2×C3×D3×Dic3C2212yes—
23C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4×Dic3C2211yescharacteristic
27#88814C2212yes—
28#88807C2212yes—
29#88806C2212yes—
30#88803C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2211yescharacteristic
34C3×Dic3⋊Dic3C2212yes—
35C3×#3722C2212yes—
36C3×#3722C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38#64139—31no—
39#64101—31no—
40#64079—31no—
41C3×C4×#67—31no—
42C2×C3×C4⋊Dic3—31no—
43C3×#893—31no—
44C3×D3×C4⋊C4—31no—
45C3×C4×D12—31no—
46C3×C4×D12—31no—
47#63978—32no—
48#63952—32no—
49#63916—31no—
50#63909—31no—
51#63908—31no—
52#63908—31no—
53#63908—31no—
54#63908—61no—
55#63906—32no—
56#63905—32no—
57C4×#626D311yescharacteristic, complemented
58C4×#625—32no—
59#63894D311yescharacteristic, complemented
60D3×C4⋊Dic3D311yescharacteristic, complemented
61#63885—32no—
62#63879—32no—
63#63869—31no—
64#63869—31no—
65#63869—61no—
66#63862—32no—
67#63858—32no—
68#63854—32no—
69#63850—32no—
70#63848—32no—
71#63841—31no—
72#63841—31no—
73#63841—61no—
74C22×C3×C3⋊D3C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C32×D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4⋊(C3⋊D3)—22no—
82C3×C4×C3⋊D3—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88#6295—42no—
89#6290—24no—
90C3×#626—22no—
91C3×#624—42no—
92C3×D3×Dic3—42no—
93#5565—91no—
94#5558—91no—
95#5514—91no—
96C22×C32×C4—31no—
97C2×#638—32no—
98C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
99C2×C4×C3⋊D3C2×D311yescharacteristic
100C2×C3×#67—31no—
101C22×C3×Dic3—32no—
102C2×C3×D12—31no—
103C2×C3×D12—31no—
104C2×C3×D12—31no—
105C2×C3×D12—61no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—61no—
113C2×C3×C4×D3C2×D311yescharacteristic
114C2×C3×C4×D3C2×D311yescharacteristic
115C2×#626—32no—
116C2×#626—32no—
117C2×#626C2×D311yescharacteristic
118C2×#625—32no—
119C2×#625—32no—
120C2×#625—32no—
121C2×#625—62no—
122C2×#624C2×D312yes—
123C2×D3×Dic3C2×D312yes—
124C32×C4⋊C4—31no—
125C32×C42—31no—
126#3752—32no—
127#3752—32no—
128C4⋊(C3⋊Dic3)—31no—
129C4⋊(C3⋊Dic3)—31no—
130C4⋊(C3⋊Dic3)—31no—
131C4⋊(C3⋊Dic3)—61no—
132C4⋊(C3⋊Dic3)—61no—
133C4⋊(C3⋊Dic3)—61no—
134C4⋊(C3⋊Dic3)—121no—
135C4⋊(C3⋊Dic3)C2×D311yescharacteristic
136#3750—32no—
137#3750—32no—
138C4×C3⋊Dic3—32no—
139C3×#217—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—31no—
145C3×C4⋊Dic3—21no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—32no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—61no—
151C3×C4⋊Dic3C2×D311yescharacteristic
152C3×C4⋊Dic3C2×D311yescharacteristic
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—31no—
155C3×C4×Dic3—21no—
156C3×C4×Dic3C2×D311yescharacteristic
157C3×C4×Dic3C2×D311yescharacteristic
158#3724—32no—
159#3724—32no—
160#3724—62no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—62no—
164Dic3⋊Dic3C2×D312yes—
165Dic3⋊Dic3C2×D311yescharacteristic
166#3722—32no—
167#3722C2×D312yes—
168#3722C2×D311yescharacteristic
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—62no—
176(C2×D3)⋊Dic3—62no—
177(C2×D3)⋊Dic3C2×D311yescharacteristic
178Dic32—32no—
179Dic32—32no—
180Dic32—62no—
181C22×C33C2411yescharacteristic
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3—22no—
185C2×C3×C3⋊D3—22no—
186C2×C3×C3⋊D3—22no—
187C2×C3×C3⋊D3—21no—
188C2×C32×D3—21no—
189C2×C32×D3—21no—
190C2×C32×D3#4112yes—
191C33×C4#4112yes—
192C3⋊(C3⋊Dic3)—22no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—22no—
195C32×Dic3—21no—
196C32×Dic3—21no—
197C32×Dic3—22no—
198C32×Dic3—21no—
199C3×C4×D4—91no—
200C3×C4×D4—91no—
201C2×C3×C4⋊C4—91no—
202#939—92no—
203#938—91no—
204#938—91no—
205#930—91no—
206#930—92no—
207#930—91no—
208#930—91no—
209#930—181no—
210#929—92no—
211C4×#67—31no—
212C4×#67—92no—
213C4×#67—92no—
214#926—91no—
215C2×C4⋊Dic3—31no—
216#898—92no—
217#898—92no—
218#895—91no—
219#894—92no—
220#893—31no—
221#892—91no—
222#892—91no—
223#892—181no—
224D3×C4⋊C4—31no—
225#890—91no—
226#884—92no—
227#883—92no—
228#67⋊C4—92no—
229#879—92no—
230C4×D12—31no—
231C4×D12—31no—
232#870—91no—
233#870—91no—
234#870—181no—
235C23×C32—31no—
236C22×C3⋊D3C22×D312yes—
237C22×C3⋊D3C22×D311yescharacteristic
238C22×C3×D3—21no—
239C22×C3×D3—31no—
240C22×C3×D3—32no—
241C22×C3×D3—32no—
242C22×C3×D3—31no—
243C22×C3×D3—61no—
244C22×C3×D3—62no—
245C22×C3×D3C22×D311yescharacteristic
246C22×C3×D3C22×D311yescharacteristic
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—31no—
251C2×C32×C4—32no—
252C2×C32×C4—31no—
253C2×C32×C4—31no—
254C2×C32×C4—41no—
255C2×C32×C4—62no—
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259#638—64no—
260C2×C3⋊Dic3—32no—
261C2×C3⋊Dic3—32no—
262C2×C3⋊Dic3—32no—
263C2×C3⋊Dic3—62no—
264C2×C3⋊Dic3—62no—
265C2×C3⋊Dic3—62no—
266C2×C3⋊Dic3—122no—
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D312yes—
269C4⋊(C3⋊D3)—22no—
270C4×C3⋊D3—22no—
271C3×#67—62no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—122no—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C3×D12—62no—
292C3×D12—62no—
293C3×D12—62no—
294C3×D12—122no—
295C3×C4×D3—22no—
296C3×C4×D3—22no—
297C3×C4×D3—42no—
298C3×C4×D3—64no—
299C3×C4×D3—62no—
300C3×C4×D3—62no—
301C3×C4×D3—122no—
302C3×C4×D3—122no—
303C3×C4×D3—122no—
304#626—22no—
305#626—122no—
306#626—122no—
307#625—64no—
308#625—64no—
309#625—124no—
310#625—122no—
311#624—42no—
312D3×Dic3—42no—
313#553—271noSylow
314C2×C33C2×#4111yescharacteristic
315C2×C33C2×#4111yescharacteristic
316C2×C33H(5,𝔽2)11yescharacteristic
317C3×C3⋊D3—41no—
318C3×C3⋊D3—42no—
319C32×D3—22no—
320C2×C3×D4—91no—
321C2×C3×D4—91no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—61no—
325C22×C3×C4—92no—
326C22×C3×C4—92no—
327C22×C3×C4—91no—
328C2×#67—31no—
329C2×#67—92no—
330C2×#67—92no—
331C2×#67—92no—
332C2×#67—92no—
333C2×#67—92no—
334C2×#67—182no—
335C22×Dic3—32no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—92no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—32no—
344C2×C4×D3—32no—
345C2×C4×D3—32no—
346C2×C4×D3—61no—
347C2×C4×D3D3211yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—92no—
352C3×C4⋊C4—91no—
353C3×C4⋊C4—91no—
354C3×C22⋊C4—92no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4—91no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360#217—31no—
361#217—92no—
362#217—92no—
363#217—92no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—32no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—32no—
368(C2×D3)⋊C4—31no—
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—92no—
375(C2×D3)⋊C4—182no—
376(C2×D3)⋊C4—182no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—32no—
381C4⋊Dic3—61no—
382C4⋊Dic3—91no—
383C4⋊Dic3—91no—
384C4⋊Dic3—91no—
385C4⋊Dic3—92no—
386C4⋊Dic3—181no—
387C4⋊Dic3—181no—
388C4⋊Dic3—181no—
389C4⋊Dic3—361no—
390C4⋊Dic3D3211yescharacteristic
391Dic3⋊C4—32no—
392Dic3⋊C4—31no—
393Dic3⋊C4—92no—
394Dic3⋊C4—92no—
395Dic3⋊C4—92no—
396Dic3⋊C4—92no—
397Dic3⋊C4—92no—
398Dic3⋊C4—182no—
399Dic3⋊C4—182no—
400C4×Dic3—92no—
401C4×Dic3—92no—
402C4×Dic3—92no—
403C4×Dic3—182no—
404C4×Dic3D3211yescharacteristic
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—32no—
409C22×C32—41no—
410C22×C32—61no—
411C22×C32—61no—
412C22×C32C23×D311yescharacteristic
413C22×C32C23×D311yescharacteristic
414C22×C32C23×D311yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—62no—
429C2×C3×D3—62no—
430C2×C3×D3—61no—
431C2×C3×D3—61no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—61no—
435C2×C3×D3—62no—
436C2×C3×D3—61no—
437C2×C3×D3—62no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—62no—
441C2×C3×D3—121no—
442C2×C3×D3—121no—
443C2×C3×D3—122no—
444C2×C3×D3—122no—
445C2×C3×D3—122no—
446C2×C3×D3#23512yes—
447C2×C3×D3#23912yes—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—22no—
451C32×C4—42no—
452C32×C4—61no—
453C32×C4—61no—
454C32×C4—61no—
455C32×C4—62no—
456C32×C4#23512yes—
457C32×C4#23512yes—
458C32×C4#23712yes—
459C3⋊Dic3—21no—
460C3⋊Dic3—22no—
461C3⋊Dic3—62no—
462C3⋊Dic3—62no—
463C3⋊Dic3—62no—
464C3⋊Dic3—122no—
465C3⋊Dic3—122no—
466C3⋊Dic3—122no—
467C3⋊Dic3—242no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—22no—
472C3×Dic3—21no—
473C3×Dic3—22no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—42no—
480C3×Dic3—62no—
481C3×Dic3—61no—
482C3×Dic3—61no—
483C3×Dic3—62no—
484C3×Dic3—62no—
485C3×Dic3—122no—
486#126—272no—
487#125—271no—
488#123—272no—
489#121—272no—
490#121—271no—
491#121—271no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—272no—
495#117—271no—
496C2×C4⋊C4—91no—
497C33#55311yescharacteristic, complemented, Sylow
498C23×C3—31no—
499C23×C3—31no—
500C23×C3—61no—
501C23×C3—91no—
502C23×C3—92no—
503C22×D3—32no—
504C22×D3—32no—
505C22×D3—31no—
506C22×D3—31no—
507C22×D3—61no—
508C22×D3—62no—
509C22×D3C2×D3211yescharacteristic
510C3×D4—182no—
511C3×D4—182no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—62no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—62no—
529C2×C3×C4—62no—
530C2×C3×C4—91no—
531C2×C3×C4—92no—
532C2×C3×C4—122no—
533C2×C3×C4—182no—
534C2×C3×C4—362no—
535C2×C3×C4—362no—
536C2×C3×C4C2×D3211yescharacteristic
537C2×C3×C4C2×D3211yescharacteristic
538C2×C3×C4C2×D3211yescharacteristic
539#67—62no—
540#67—184no—
541#67—184no—
542#67—184no—
543#67—364no—
544#67—362no—
545#67—362no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—61no—
551C2×Dic3—62no—
552C2×Dic3—92no—
553C2×Dic3—92no—
554C2×Dic3—92no—
555C2×Dic3—122no—
556C2×Dic3—182no—
557C2×Dic3—182no—
558C2×Dic3—182no—
559C2×Dic3—362no—
560C2×Dic3C2×D3212yes—
561C2×Dic3C2×D3211yescharacteristic
562C2×Dic3C2×D3211yescharacteristic
563C2×Dic3C2×D3211yescharacteristic
564D12—62no—
565D12—62no—
566D12—62no—
567D12—122no—
568D12—362no—
569C4×D3—22no—
570C4×D3—64no—
571C4×D3—62no—
572C4×D3—62no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32—41no—
588C2×C32—62no—
589C2×C32C2×#23511yescharacteristic
590C2×C32C2×#23511yescharacteristic
591C2×C32C2×#23511yescharacteristic
592C2×C32C2×#23711yescharacteristic
593C2×C32#100411yescharacteristic
594C2×C32#100411yescharacteristic
595C2×C32C2×#23911yescharacteristic
596C2×C32D3×#4111yescharacteristic
597C2×C32#100911yescharacteristic
598C3⋊D3—41no—
599C3⋊D3—42no—
600C3×D3—22no—
601C3×D3—22no—
602C3×D3—42no—
603C3×D3—122no—
604C3×D3—122no—
605C3×D3—121no—
606C3×D3—121no—
607C3×D3—122no—
608C3×D3—242no—
609C2×D4—91no—
610C2×D4—91no—
611C2×D4—272no—
612C2×D4—272no—
613C22×C4—31no—
614C22×C4—92no—
615C22×C4—92no—
616C22×C4—91no—
617C4⋊C4—31no—
618C4⋊C4—92no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—272no—
622C4⋊C4—272no—
623C4⋊C4—271no—
624C22⋊C4—92no—
625C22⋊C4—91no—
626C22⋊C4—91no—
627C22⋊C4—272no—
628C22⋊C4—272no—
629C22⋊C4—272no—
630C42—31no—
631C42—272no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—32no—
637C22×C3—41no—
638C22×C3—62no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—181no—
646C22×C3—182no—
647C22×C3—182no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—182no—
651C22×C3C22×D3211yescharacteristic
652C22×C3C22×D3211yescharacteristic
653C22×C3C22×D3211yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—62no—
657C2×D3—61no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—61no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—122no—
672C2×D3—122no—
673C2×D3—122no—
674C2×D3#379912yes—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—42no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—62no—
683C3×C4—62no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—122no—
690C3×C4—121no—
691C3×C4—181no—
692C3×C4—182no—
693C3×C4#379512yes—
694C3×C4#379812yes—
695C3×C4#380412yes—
696Dic3—21no—
697Dic3—21no—
698Dic3—22no—
699Dic3—21no—
700Dic3—62no—
701Dic3—61no—
702Dic3—62no—
703Dic3—62no—
704Dic3—61no—
705Dic3—122no—
706Dic3—182no—
707Dic3—182no—
708Dic3—182no—
709Dic3—362no—
710Dic3—362no—
711Dic3—362no—
712Dic3—722no—
713C32—21no—
714C32—21no—
715C32—21no—
716C32—41no—
717C32#551411yescharacteristic, complemented
718C32#555811yescharacteristic, complemented
719C32#556511yescharacteristic, complemented
720C23—31no—
721C23—92no—
722C23—91no—
723D4—182no—
724D4—182no—
725D4—544no—
726D4—1082no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—32no—
730C2×C4—31no—
731C2×C4—62no—
732C2×C4—91no—
733C2×C4—92no—
734C2×C4—182no—
735C2×C4—272no—
736C2×C4—362no—
737C2×C4—362no—
738C2×C4D3311yescharacteristic
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—41no—
751C2×C3—62no—
752C2×C3—62no—
753C2×C3—122no—
754C2×C3—361no—
755C2×C3—362no—
756C2×C3C2×#379511yescharacteristic
757C2×C3C2×#379811yescharacteristic
758C2×C3C2×#379911yescharacteristic
759C2×C3D3×#23511yescharacteristic
760C2×C3#6430711yescharacteristic
761C2×C3#6430711yescharacteristic
762C2×C3#6431311yescharacteristic
763C2×C3D3×#23911yescharacteristic
764C2×C3C2×#380411yescharacteristic
765D3—22no—
766D3—122no—
767D3—122no—
768D3—121no—
769D3—121no—
770D3—122no—
771D3—242no—
772C22—32no—
773C22—61no—
774C22—61no—
775C22—182no—
776C22—181no—
777C22—181no—
778C22—182no—
779C22—181no—
780C22—182no—
781C22C2×D3311yescharacteristic
782C4—61no—
783C4—62no—
784C4—61no—
785C4—61no—
786C4—182no—
787C4—181no—
788C4—542no—
789C4#8896012yes—
790C3—21no—
791C3—21no—
792C3—21no—
793C3—41no—
794C3#1059392311yescharacteristic, complemented
795C3#1059456111yescharacteristic, complemented
796C3#1059484311yescharacteristic, complemented
797C2—62no—
798C2—361no—
799C2—362no—
800C2#1172438011yescharacteristic
801C2D3×#379911yescharacteristic
802C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723696C2semidirect
2. #11723515C2semidirect
3. #11723454C2semidirect
4. #11723404C2semidirect
5. C3×C4×#626C2semidirect
6. C3×#63894C2semidirect
7. C3×D3×C4⋊Dic3C2semidirect
8. #11723025C2semidirect
9. #11722995C2semidirect
10. #11722960C2semidirect
11. #11722930C2semidirect
57. C4×#626D3semidirect
59. #63894D3semidirect
60. D3×C4⋊Dic3D3semidirect
497. C33#553semidirect
717. C32#5514semidirect
718. C32#5558semidirect
719. C32#5565semidirect
794. C3#10593923semidirect
795. C3#10594561semidirect
796. C3#10594843semidirect

Maximal subgroups

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

subgroupindex
#117236962
#117235152
#117234542
#117234042
C3×C4×#6262
C3×#638942
C3×D3×C4⋊Dic32
#117230252
#117229952
#117229602
#117229302
#105948433
#105945613
#105939233