Finite Group Databasebeta

← #13178341

Subgroups — #13178341

Order 1728.

1208 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64104C211yesmaximal, characteristic, complemented
2C3×#64101C211yesmaximal, characteristic, complemented
3C3×#64097C211yesmaximal, characteristic, complemented
4#11723696C211yesmaximal, characteristic, complemented
5C4×#6295C211yesmaximal, characteristic, complemented
6#11723691C211yesmaximal, characteristic, complemented
7#11723687C212yesmaximal, complemented
8#11723683C212yesmaximal, complemented
9#11723677C212yesmaximal, complemented
10#11723670C212yesmaximal, complemented
11#11723667C211yesmaximal, characteristic, complemented
12#10594564—31nomaximal
13#10594486—31nomaximal
14#10594463—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#634C2212yes—
20C2×#6295C2211yescharacteristic
21C2×#6295C2212yes—
22C2×#6294C2212yes—
23C33×C4⋊C4C2211yescharacteristic
24C3×#3752C2212yes—
25C3×#3752C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2212yes—
29C3×C4×C3⋊Dic3C2211yescharacteristic
30C3×C4×C3⋊Dic3C2212yes—
31#88815C2211yescharacteristic
32#88814C2212yes—
33#88814C2211yescharacteristic
34#88814C2212yes—
35#88814C2211yescharacteristic
36#88814C2212yes—
37#88813C2212yes—
38#64104D311yescharacteristic, complemented
39#64101D311yescharacteristic, complemented
40#64097D311yescharacteristic, complemented
41C3×#895—31no—
42C3×#895—31no—
43C3×#895—61no—
44C3×#892—31no—
45C3×#892—31no—
46C3×#892—61no—
47C3×#888—31no—
48C3×#888—31no—
49C3×#888—61no—
50#63916—31no—
51#63913—32no—
52#63910—32no—
53#63909—31no—
54#63908—31no—
55#63907—32no—
56#63907—32no—
57C4×#626—31no—
58C4×#626—31no—
59C4×#625—31no—
60#63898—31no—
61#63894—31no—
62Dic3×D12—31no—
63#63886—32no—
64#63885—32no—
65#63878—32no—
66#63877—32no—
67#63864—32no—
68#63863—32no—
69#63860—32no—
70#63849—31no—
71#63841—31no—
72#63841—31no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2312yes—
76C22×C3×C3⋊D3C2311yescharacteristic
77C2×C33×C4C2312yes—
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4⋊(C3⋊D3)—22no—
86C3×C4⋊(C3⋊D3)—42no—
87C3×C4×C3⋊D3—22no—
88C3×C4×C3⋊D3—22no—
89C3×#634—42no—
90#6295—22no—
91#6295—42no—
92#6294—24no—
93#5734—91no—
94#5616—91no—
95#5532—91no—
96C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
97C2×C4⋊(C3⋊D3)C2×D312yes—
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×C4×C3⋊D3C2×D311yescharacteristic
100C2×#634C2×D312yes—
101C2×C3×D12—31no—
102C2×C3×D12—31no—
103C2×C3×D12—32no—
104C2×C3×D12—32no—
105C2×C3×D12—61no—
106C2×C3×D12—62no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3—61no—
113C2×C3×Dic6—32no—
114C2×C3×Dic6—32no—
115C2×C3×Dic6—62no—
116C2×#626—31no—
117C2×#626—31no—
118C2×#626—32no—
119C2×#626—32no—
120C2×#625—31no—
121C2×#625—32no—
122C2×#624—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—32no—
125C32×C4⋊C4—21no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4—21no—
128C32×C4⋊C4—41no—
129C32×C4⋊C4C2×D311yescharacteristic
130C32×C4⋊C4C2×D311yescharacteristic
131C32×C4⋊C4C2×D311yescharacteristic
132#3752C2×D312yes—
133#3752C2×D312yes—
134C4⋊(C3⋊Dic3)C2×D311yescharacteristic
135C4⋊(C3⋊Dic3)C2×D311yescharacteristic
136#3750C2×D312yes—
137C4×C3⋊Dic3C2×D311yescharacteristic
138C4×C3⋊Dic3C2×D312yes—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4—62no—
144C3×(C2×D3)⋊C4—62no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—61no—
150C3×C4⋊Dic3—61no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—62no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—31no—
156C3×C4×Dic3—32no—
157C3×C4×Dic3—32no—
158C3×C4×Dic3—61no—
159C3×C4×Dic3—62no—
160#3724—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163#3722—32no—
164#3722—32no—
165#3722—31no—
166#3722—32no—
167#3722—31no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178Dic32—32no—
179Dic32—32no—
180Dic32—32no—
181C22×C33C2411yescharacteristic
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—21no—
190C2×C3×C3⋊D3—22no—
191C33×C4—22no—
192C33×C4#4112yes—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—22no—
195C3×C3⋊Dic3—21no—
196C3×C3⋊Dic3—21no—
197C3×C3⋊Dic3—22no—
198C3×C3⋊Dic3#4112yes—
199C3×C4⋊Q8—91no—
200C3×#121—91no—
201C3×#117—91no—
202#947—92no—
203#947—92no—
204#939—92no—
205#938—91no—
206#936—92no—
207D4×Dic3—91no—
208#930—91no—
209C4×#67—91no—
210C4×#67—91no—
211#926—91no—
212#895—31no—
213#895—31no—
214#895—61no—
215#895—92no—
216#895—91no—
217#893—91no—
218#892—31no—
219#892—31no—
220#892—61no—
221#892—92no—
222#892—91no—
223#892—91no—
224#888—31no—
225#888—31no—
226#888—61no—
227#885—92no—
228#885—92no—
229#884—92no—
230#877—92no—
231#875—92no—
232C4×D12—91no—
233C4×D12—91no—
234#872—92no—
235C22×C3⋊D3C22×D311yescharacteristic
236C22×C3⋊D3C22×D312yes—
237C22×C3⋊D3C22×D311yescharacteristic
238C22×C3×D3—31no—
239C22×C3×D3—31no—
240C22×C3×D3—32no—
241C22×C3×D3—32no—
242C22×C3×D3—31no—
243C22×C3×D3—31no—
244C22×C3×D3—61no—
245C22×C3×D3—61no—
246C22×C3×D3—62no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—22no—
251C2×C32×C4—22no—
252C2×C32×C4—22no—
253C2×C32×C4—41no—
254C2×C32×C4—42no—
255C2×C32×C4C22×D312yes—
256C2×C32×C4C22×D312yes—
257C2×C32×C4C22×D312yes—
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D312yes—
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D311yescharacteristic
267C4⋊(C3⋊D3)—22no—
268C4⋊(C3⋊D3)—42no—
269C4×C3⋊D3—22no—
270C4×C3⋊D3—22no—
271#634—42no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—62no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—61no—
290C3×D12—62no—
291C3×D12—62no—
292C3×D12—122no—
293C3×D12—122no—
294C3×D12—122no—
295C3×D12—124no—
296C3×C4×D3—64no—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×C4×D3—62no—
301C3×C4×D3—122no—
302C3×Dic6—122no—
303C3×Dic6—122no—
304C3×Dic6—124no—
305#626—62no—
306#626—62no—
307#626—122no—
308#626—122no—
309#625—62no—
310#625—122no—
311#624—64no—
312D3×Dic3—64no—
313D3×Dic3—64no—
314#555—271noSylow
315C2×C33C2×#4111yescharacteristic
316C2×C33C2×#4111yescharacteristic
317C2×C33H(5,𝔽2)11yescharacteristic
318C3×C3⋊D3—41no—
319C3×C3⋊D3—41no—
320C3×C3⋊D3—42no—
321C2×C3×Q8—92no—
322C2×C3×D4—91no—
323C2×C3×D4—92no—
324C22×C3×C4—91no—
325C22×C3×C4—91no—
326C2×#67—91no—
327C2×#67—91no—
328C2×#67—92no—
329C2×#67—92no—
330C22×Dic3—92no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—32no—
334C2×D12—32no—
335C2×D12—61no—
336C2×D12—62no—
337C2×D12—91no—
338C2×D12—92no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—92no—
346C2×C4×D3—92no—
347C2×Dic6—32no—
348C2×Dic6—32no—
349C2×Dic6—62no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—91no—
355C3×C4⋊C4—92no—
356C3×C4⋊C4—91no—
357C3×C4⋊C4D3211yescharacteristic
358C3×C4⋊C4D3211yescharacteristic
359C3×C4⋊C4D3211yescharacteristic
360C3×C22⋊C4—92no—
361C3×C22⋊C4—92no—
362C3×C42—92no—
363C3×C42—91no—
364#217—92no—
365#217—91no—
366#217—92no—
367#217—92no—
368#217—91no—
369(C2×D3)⋊C4—32no—
370(C2×D3)⋊C4—32no—
371(C2×D3)⋊C4—32no—
372(C2×D3)⋊C4—32no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—92no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—92no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—92no—
381(C2×D3)⋊C4—92no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—92no—
384(C2×D3)⋊C4—92no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—91no—
392Dic3⋊C4—32no—
393Dic3⋊C4—32no—
394Dic3⋊C4—62no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397C4×Dic3—32no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—32no—
401C4×Dic3—61no—
402C4×Dic3—62no—
403C4×Dic3—92no—
404C4×Dic3—92no—
405C4×Dic3—92no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—41no—
410C22×C32C23×D311yescharacteristic
411C22×C32C23×D311yescharacteristic
412C22×C32C23×D311yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3×D3—62no—
423C2×C3×D3—62no—
424C2×C3×D3—61no—
425C2×C3×D3—62no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3—62no—
429C2×C3×D3—61no—
430C2×C3×D3—61no—
431C2×C3×D3—62no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—62no—
437C2×C3×D3—62no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—62no—
441C2×C3×D3—61no—
442C2×C3×D3—121no—
443C2×C3×D3—121no—
444C2×C3×D3—121no—
445C2×C3×D3—121no—
446C2×C3×D3—122no—
447C2×C3×D3—122no—
448C2×C3×D3—122no—
449C32×C4—22no—
450C32×C4—22no—
451C32×C4—22no—
452C32×C4—22no—
453C32×C4—22no—
454C32×C4—22no—
455C32×C4—42no—
456C32×C4—42no—
457C32×C4—42no—
458C32×C4—42no—
459C32×C4—82no—
460C32×C4#23512yes—
461C32×C4#23712yes—
462C32×C4#23912yes—
463C3⋊Dic3—21no—
464C3⋊Dic3—21no—
465C3⋊Dic3—21no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3⋊Dic3#23912yes—
469C3×Dic3—32no—
470C3×Dic3—32no—
471C3×Dic3—62no—
472C3×Dic3—62no—
473C3×Dic3—62no—
474C3×Dic3—61no—
475C3×Dic3—61no—
476C3×Dic3—62no—
477C3×Dic3—61no—
478C3×Dic3—62no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—62no—
482C3×Dic3—62no—
483C3×Dic3—61no—
484C3×Dic3—122no—
485C3×Dic3—121no—
486C3×Dic3—122no—
487C4⋊Q8—91no—
488#124—272no—
489#124—272no—
490#121—91no—
491#121—272no—
492#121—271no—
493C4×D4—271no—
494C4×D4—271no—
495#117—91no—
496#117—272no—
497#117—271no—
498C33#55511yescharacteristic, complemented, Sylow
499C23×C3—91no—
500C23×C3—92no—
501C23×C3—91no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—32no—
505C22×D3—32no—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—62no—
511C3×Q8—362no—
512C3×D4—182no—
513C3×D4—362no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—41no—
521C2×C3×C4—42no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4—92no—
525C2×C3×C4—92no—
526C2×C3×C4—91no—
527C2×C3×C4—91no—
528C2×C3×C4—182no—
529C2×C3×C4—182no—
530C2×C3×C4C2×D3212yes—
531C2×C3×C4C2×D3212yes—
532C2×C3×C4C2×D3212yes—
533C2×C3×C4C2×D3211yescharacteristic
534C2×C3×C4C2×D3211yescharacteristic
535C2×C3×C4C2×D3211yescharacteristic
536#67—182no—
537#67—182no—
538#67—362no—
539#67—362no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—62no—
556C2×Dic3—62no—
557C2×Dic3—61no—
558C2×Dic3—184no—
559D12—62no—
560D12—62no—
561D12—122no—
562D12—122no—
563D12—122no—
564D12—124no—
565D12—182no—
566D12—362no—
567C4×D3—64no—
568C4×D3—62no—
569C4×D3—62no—
570C4×D3—62no—
571C4×D3—62no—
572C4×D3—122no—
573C4×D3—184no—
574C4×D3—184no—
575Dic6—122no—
576Dic6—122no—
577Dic6—124no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—41no—
588C2×C32—41no—
589C2×C32—41no—
590C2×C32C2×#23511yescharacteristic
591C2×C32C2×#23711yescharacteristic
592C2×C32#100411yescharacteristic
593C2×C32#100411yescharacteristic
594C2×C32C2×#23911yescharacteristic
595C2×C32C2×#23911yescharacteristic
596C2×C32D3×#4111yescharacteristic
597C2×C32D3×#4111yescharacteristic
598C2×C32#100911yescharacteristic
599C3⋊D3—41no—
600C3⋊D3—41no—
601C3⋊D3—42no—
602C3×D3—122no—
603C3×D3—122no—
604C3×D3—121no—
605C3×D3—121no—
606C3×D3—122no—
607C3×D3—121no—
608C3×D3—122no—
609C3×D3—121no—
610C3×D3—242no—
611C2×Q8—92no—
612C2×D4—91no—
613C2×D4—92no—
614C2×D4—271no—
615C2×D4—272no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—272no—
619C4⋊C4—91no—
620C4⋊C4—92no—
621C4⋊C4—91no—
622C4⋊C4—271no—
623C4⋊C4#111311yescharacteristic
624C22⋊C4—92no—
625C22⋊C4—92no—
626C22⋊C4—272no—
627C22⋊C4—272no—
628C22⋊C4—271no—
629C22⋊C4—272no—
630C22⋊C4—271no—
631C42—92no—
632C42—91no—
633C42—272no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—181no—
639C22×C3—181no—
640C22×C3—182no—
641C22×C3—181no—
642C22×C3—182no—
643C22×C3—181no—
644C22×C3—182no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3C22×D3211yescharacteristic
648C22×C3C22×D3211yescharacteristic
649C22×C3C22×D3211yescharacteristic
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—62no—
655C2×D3—61no—
656C2×D3—62no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—62no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—62no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—62no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—122no—
675C2×D3—122no—
676C2×D3—122no—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—82no—
688C3×C4—92no—
689C3×C4—181no—
690C3×C4—181no—
691C3×C4—182no—
692C3×C4—181no—
693C3×C4—182no—
694C3×C4#379512yes—
695C3×C4#379612yes—
696C3×C4#379912yes—
697Dic3—32no—
698Dic3—32no—
699Dic3—62no—
700Dic3—62no—
701Dic3—62no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—61no—
706Dic3—61no—
707Dic3—62no—
708Dic3—61no—
709Dic3—62no—
710Dic3—62no—
711Dic3—62no—
712Dic3—122no—
713Dic3—121no—
714Dic3—122no—
715C32—21no—
716C32—21no—
717C32—21no—
718C32—41no—
719C32#553211yescharacteristic, complemented
720C32#561611yescharacteristic, complemented
721C32#573411yescharacteristic, complemented
722C23—91no—
723C23—92no—
724C23—91no—
725Q8—362no—
726D4—182no—
727D4—362no—
728D4—542no—
729D4—1082no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—92no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—92no—
736C2×C4—182no—
737C2×C4—182no—
738C2×C4—544no—
739C2×C4C2×#111312yes—
740C2×C4C2×#111311yescharacteristic
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—361no—
754C2×C3—362no—
755C2×C3—361no—
756C2×C3C2×#379511yescharacteristic
757C2×C3C2×#379611yescharacteristic
758C2×C3C2×#379911yescharacteristic
759C2×C3#6431311yescharacteristic
760C2×C3#6431411yescharacteristic
761C2×C3#6431411yescharacteristic
762C2×C3D3×#23911yescharacteristic
763C2×C3D3×#23911yescharacteristic
764C2×C3#6431911yescharacteristic
765D3—122no—
766D3—122no—
767D3—121no—
768D3—121no—
769D3—122no—
770D3—121no—
771D3—121no—
772D3—122no—
773D3—242no—
774C22—181no—
775C22—181no—
776C22—182no—
777C22—181no—
778C22—182no—
779C22—181no—
780C22—182no—
781C22—181no—
782C22—181no—
783C22C22×#111311yescharacteristic
784C4—22no—
785C4—92no—
786C4—181no—
787C4—181no—
788C4—182no—
789C4—181no—
790C4—182no—
791C4#8904112yes—
792C3—21no—
793C3—21no—
794C3—21no—
795C3—41no—
796C3#1059446311yescharacteristic, complemented
797C3#1059448611yescharacteristic, complemented
798C3#1059456411yescharacteristic, complemented
799C2—361no—
800C2—361no—
801C2—362no—
802C2C2×#8904111yescharacteristic
803C2#1172462311yescharacteristic
804C2#1172462611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4#1113
hypocenterC33#555
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64104C2semidirect
2. C3×#64101C2semidirect
3. C3×#64097C2semidirect
4. #11723696C2semidirect
5. C4×#6295C2semidirect
6. #11723691C2semidirect
7. #11723687C2semidirect
8. #11723683C2semidirect
9. #11723677C2semidirect
10. #11723670C2semidirect
11. #11723667C2semidirect
38. #64104D3semidirect
39. #64101D3semidirect
40. #64097D3semidirect
498. C33#555semidirect
719. C32#5532semidirect
720. C32#5616semidirect
721. C32#5734semidirect
796. C3#10594463semidirect
797. C3#10594486semidirect
798. C3#10594564semidirect

Maximal subgroups

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

subgroupindex
C3×#641042
C3×#641012
C3×#640972
#117236962
C4×#62952
#117236912
#117236872
#117236832
#117236772
#117236702
#117236672
#105945643
#105944863
#105944633