Finite Group Databasebeta

← #13150453

Subgroups — #13150453

Order 1728.

1024 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
1C2×C3×#3697C211yesmaximal, characteristic, complemented
2C2×#88640C211yesmaximal, characteristic, complemented
3C4×#6233C211yesmaximal, characteristic, complemented
4C4×C9×#67C211yesmaximal, characteristic, complemented
5#11721289C211yesmaximal, characteristic, complemented
6#11721271C211yesmaximal, characteristic, complemented
7#11721270C211yesmaximal, characteristic, complemented
8#11721257C211yesmaximal, characteristic, complemented
9#11721035C211yesmaximal, characteristic, complemented
10C4×#6194C211yesmaximal, characteristic, complemented
11C4×#6192C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720982C211yesmaximal, characteristic, complemented
14C4×Dic3×D9C211yesmaximal, characteristic, complemented
15#11720904C211yesmaximal, characteristic, complemented
16#10595003—31nomaximal
17#10589650—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C3×#3697—24no—
26C2×C3×D36C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28C2×C3×C4×D9C2211yescharacteristic
29C2×C3×Dic18C2211yescharacteristic
30C2×#6195C2211yescharacteristic
31C2×#6194C2211yescharacteristic
32C2×#6194C2211yescharacteristic
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic
35C2×Dic3×D9C2211yescharacteristic
36C2×Dic3×D9C2211yescharacteristic
37C2×#6189C2211yescharacteristic
38#88640—24no—
39#88551C2211yescharacteristic
40#88536C2211yescharacteristic
41#88534C2211yescharacteristic
42C4×C3⋊Dic9C2211yescharacteristic
43C9×#217C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C9×Dic3⋊C4C2211yescharacteristic
46C4×C9×Dic3C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48#88445C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52#88442C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×C3×#235—31no—
56C2×#3798—31no—
57C4×#638—31no—
58C3×C4×#67D311yescharacteristic
59#63979—31no—
60#63971—31no—
61#63970—31no—
62#63959—31no—
63#63907—31no—
64C4×#626—31no—
65C4×#625—31no—
66#63886—31no—
67#63885—31no—
68C4×D3×Dic3—31no—
69#63839—31no—
70C2×#3697—31no—
71C2×#3697D311yescharacteristic, complemented
72C4×D4×C9—31no—
73#63502—31no—
74#63500—31no—
75C4×#611—31no—
76C4×#611—31no—
77C4×#611—61no—
78#63457—31no—
79#63450—31no—
80#63447—31no—
81#63447—31no—
82#63446—31no—
83#63446—31no—
84C4×D36—31no—
85C42×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9—22no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—22no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C4×C3⋊D9—22no—
99C9×#67—22no—
100C3×#611—22no—
101C3×#611—22no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C4×D3×C9—22no—
108C3×D36—22no—
109C3×C4×D9—22no—
110C3×C4×D9D414yescomplemented
111C3×Dic18—22no—
112#6195—22no—
113#6194—22no—
114#6194—22no—
115#6192—22no—
116#6192—22no—
117Dic3×D9—22no—
118Dic3×D9—22no—
119#6189—22no—
120#5832—91no—
121#5548—91no—
122C22×C32×C4C2×D311yescharacteristic
123C2×#638—31no—
124C2×C4×C3⋊D3—31no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67C2×D311yescharacteristic
128C3×#235—64no—
129C2×C3×D12—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×Dic6—31no—
134C2×#627—31no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#625—31no—
139C2×#625—31no—
140C2×D3×Dic3—31no—
141C2×D3×Dic3—31no—
142#3798—64no—
143#3757—31no—
144#3752—31no—
145#3750—31no—
146C4×C3⋊Dic3—31no—
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4C2×D311yescharacteristic
149C3×Dic3⋊C4C2×D311yescharacteristic
150C3×C4×Dic3C2×D311yescharacteristic
151#3724—31no—
152Dic3⋊Dic3—31no—
153#3722—31no—
154(C2×D3)⋊Dic3—31no—
155(C2×D3)⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157Dic32—31no—
158Dic32—31no—
159C2×D4×C9—31no—
160C22×C4×C9—21no—
161C22×C4×C9—31no—
162C22×C4×C9C2×D311yescharacteristic
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—31no—
167C2×#611—61no—
168C2×#611C2×D311yescharacteristic
169C2×#611C2×D311yescharacteristic
170#3697—24no—
171#3697—64no—
172C2×D36—31no—
173C2×D36—31no—
174C2×D36C2×D311yescharacteristic
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—61no—
179C2×C4×D9C2×D311yescharacteristic
180C2×C4×D9C2×D311yescharacteristic
181C2×Dic18—31no—
182C2×Dic18C2×D311yescharacteristic
183C9×C4⋊C4—31no—
184C9×C22⋊C4—31no—
185C9×C22⋊C4—31no—
186C42×C9—31no—
187#3676—31no—
188#3676—31no—
189#3676—61no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—61no—
195C4⋊Dic9—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—61no—
199C4×Dic9—31no—
200C4×Dic9—31no—
201C4×Dic9—31no—
202C4×Dic9—61no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9C2×D412yes—
219C3×C4×C9—21no—
220C3×C4×C9C2×D412yes—
221C3⋊Dic9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9#4112yescomplemented
224C9×Dic3—21no—
225C9×Dic3—21no—
226C9×Dic3#4112yescomplemented
227C3×Dic9—21no—
228C3×Dic9C2×D412yes—
229C2×C3×#41—91no—
230C2×#235—31no—
231C2×#235—91no—
232C2×#235—91no—
233C3×C4×D4—31no—
234#947—91no—
235#944—91no—
236#940—91no—
237#940—91no—
238#939—91no—
239#939—91no—
240#939—91no—
241#939—91no—
242#938—91no—
243#936—91no—
244C4×#67—91no—
245C4×#67—91no—
246C4×#67—91no—
247C4×#67—91no—
248C4×#67—91no—
249C4×#67—181no—
250C4×#67D911yescharacteristic, complemented
251C2×C4×Dic3—91no—
252#895—91no—
253#888—91no—
254#885—91no—
255#885—91no—
256#884—91no—
257#884—91no—
258C4×D12—91no—
259C42×D3—91no—
260C23×C32C22×D311yescharacteristic
261C22×C3⋊D3—31no—
262C22×C3×D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3C22×D311yescharacteristic
265C2×C32×C4—22no—
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268#638—62no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C4×C3⋊D3—62no—
273C3×#67—22no—
274C3×#67—62no—
275C3×#67—62no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C3×D12—62no—
282C3×C4×D3—22no—
283C3×C4×D3—34no—
284C3×C4×D3—62no—
285C3×Dic6—62no—
286#627—62no—
287#626—62no—
288#626—62no—
289#626—62no—
290#625—62no—
291#625—62no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294C23×C9—21no—
295C23×C9—31no—
296C23×C9C22×D311yescharacteristic
297C22×D9—31no—
298C22×D9—61no—
299C22×D9C22×D311yescharacteristic
300C22×D9C22×D311yescharacteristic
301D4×C9—62no—
302C2×C4×C9—22no—
303C2×C4×C9—21no—
304C2×C4×C9—21no—
305C2×C4×C9—31no—
306C2×C4×C9—31no—
307C2×C4×C9—31no—
308C2×C4×C9—42no—
309C2×C4×C9—62no—
310C2×C4×C9C22×D311yescharacteristic
311C2×C4×C9C22×D311yescharacteristic
312#611—22no—
313#611—22no—
314#611—62no—
315#611—62no—
316#611—64no—
317#611—62no—
318#611—62no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9C22×D311yescharacteristic
326C2×Dic9C22×D311yescharacteristic
327D36—22no—
328D36—62no—
329D36—62no—
330C4×D9—22no—
331C4×D9—62no—
332C4×D9—62no—
333C4×D9—62no—
334C4×D9—122no—
335C4×D9#6714yescomplemented
336Dic18—22no—
337Dic18—62no—
338#532—271noSylow
339C2×C3×C9—41no—
340C2×C3×C9C22×D411yescharacteristic
341C2×C3×C9C2×#4111yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343C3⋊D9—41no—
344D3×C9—41no—
345C3×D9—22no—
346C3×D9—41no—
347C3×#41—184no—
348C2×C3×Q8—91no—
349C2×C3×D4—31no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—91no—
356C22×C3×C4—91no—
357C22×C3×C4C2×D911yescharacteristic
358C22×C3×C4D3211yescharacteristic
359C2×#67—31no—
360C2×#67—31no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—181no—
371C2×#67C2×D911yescharacteristic
372C22×Dic3—91no—
373C22×Dic3—91no—
374#235—64no—
375#235—184no—
376#235—184no—
377C2×D12—31no—
378C2×D12—91no—
379C2×D12—91no—
380C2×D12—91no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—181no—
388C2×C4×D3C2×D911yescharacteristic
389C2×Dic6—31no—
390C2×Dic6—91no—
391C2×Dic6—91no—
392C3×C4⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—31no—
395C3×C42—31no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—181no—
402#217C2×D911yescharacteristic
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—181no—
411(C2×D3)⋊C4C2×D911yescharacteristic
412C4⋊Dic3—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—181no—
419Dic3⋊C4C2×D911yescharacteristic
420C4×Dic3—91no—
421C4×Dic3—91no—
422C4×Dic3—91no—
423C4×Dic3—91no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3—181no—
427C4×Dic3C2×D911yescharacteristic
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32C23×D311yescharacteristic
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—32no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C32×C4—21no—
445C32×C4D3×D412yes—
446C3⋊Dic3—32no—
447C3⋊Dic3—61no—
448C3⋊Dic3—61no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—32no—
452C3×Dic3—61no—
453C3×Dic3#23512yes—
454C22×C9—22no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—41no—
460C22×C9—41no—
461C22×C9—61no—
462C22×C9—61no—
463C22×C9—61no—
464C22×C9C23×D311yescharacteristic
465C2×D9—21no—
466C2×D9—21no—
467C2×D9—21no—
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—62no—
471C2×D9—61no—
472C2×D9—61no—
473C2×D9—61no—
474C2×D9—121no—
475C2×D9—121no—
476C2×D9C2×#6712yes—
477C4×C9—21no—
478C4×C9—22no—
479C4×C9—32no—
480C4×C9—41no—
481C4×C9—61no—
482C4×C9—61no—
483C4×C9C2×#6712yes—
484Dic9—21no—
485Dic9—32no—
486Dic9—62no—
487Dic9—61no—
488Dic9—61no—
489Dic9—121no—
490Dic9—121no—
491Dic9C2×#6712yes—
492C2×#41—91no—
493C2×#41—271no—
494C4⋊Q8—271no—
495#127—271no—
496#124—271no—
497#124—271no—
498#121—271no—
499#121—271no—
500#121—271no—
501#121—271no—
502C4×D4—31no—
503C4×D4—271no—
504C4×D4—271no—
505C4×D4—271no—
506C2×C42—271no—
507C3×C9#53211yescharacteristic, complemented, Sylow
508C23×C3—21no—
509C23×C3—31no—
510C23×C3—91no—
511C23×C3—91no—
512C23×C3C22×D911yescharacteristic
513C23×C3C2×D3211yescharacteristic
514C22×D3—31no—
515C22×D3—31no—
516C22×D3—91no—
517C22×D3—91no—
518C22×D3—181no—
519C22×D3C22×D911yescharacteristic
520C3×Q8—182no—
521C3×D4—62no—
522C3×D4—182no—
523C3×D4—182no—
524C3×D4—182no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—42no—
533C2×C3×C4—62no—
534C2×C3×C4—91no—
535C2×C3×C4—94no—
536C2×C3×C4—91no—
537C2×C3×C4—182no—
538C2×C3×C4C22×D911yescharacteristic
539C2×C3×C4C22×D911yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541C2×C3×C4C2×D3211yescharacteristic
542#67—22no—
543#67—62no—
544#67—62no—
545#67—182no—
546#67—182no—
547#67—182no—
548#67—182no—
549#67—182no—
550#67—182no—
551#67—182no—
552#67—182no—
553#67—184no—
554#67—182no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—91no—
560C2×Dic3—91no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—181no—
564C2×Dic3—181no—
565C2×Dic3—181no—
566C2×Dic3—182no—
567C2×Dic3—182no—
568C2×Dic3C22×D911yescharacteristic
569C2×Dic3C22×D911yescharacteristic
570C2×Dic3C22×D911yescharacteristic
571D12—62no—
572D12—182no—
573D12—182no—
574D12—182no—
575C4×D3—22no—
576C4×D3—34no—
577C4×D3—62no—
578C4×D3—182no—
579C4×D3—182no—
580C4×D3—182no—
581C4×D3—182no—
582C4×D3—362no—
583Dic6—62no—
584Dic6—182no—
585Dic6—182no—
586C2×C32—41no—
587C2×C32C2×#23511yescharacteristic
588C2×C32C2×D3×D411yescharacteristic
589C2×C32D3×#4111yescharacteristic
590C3⋊D3—121no—
591C3×D3—41no—
592C3×D3—62no—
593C3×D3—121no—
594C2×C9—21no—
595C2×C9—21no—
596C2×C9—21no—
597C2×C9—42no—
598C2×C9—41no—
599C2×C9—121no—
600C2×C9D3×#4111yescharacteristic
601C2×C9D3×#4111yescharacteristic
602C2×C9C22×#6711yescharacteristic
603D9—22no—
604D9—41no—
605D9—122no—
606D9—121no—
607#41—184no—
608#41—544no—
609C2×Q8—91no—
610C2×Q8—271no—
611C2×D4—31no—
612C2×D4—91no—
613C2×D4—91no—
614C2×D4—91no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C2×D4—271no—
621C22×C4—31no—
622C22×C4—91no—
623C22×C4—91no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4D3×D911yescharacteristic
628C4⋊C4—31no—
629C4⋊C4—271no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C42—31no—
641C42—271no—
642C42—271no—
643C42—271no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—92no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3—181no—
663C22×C3C23×D911yescharacteristic
664C22×C3C22×D3211yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—32no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—182no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—361no—
682C2×D3—361no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—22no—
686C3×C4—32no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—92no—
691C3×C4—181no—
692C3×C4D4×D912yes—
693C3×C4D3×#6712yes—
694Dic3—21no—
695Dic3—21no—
696Dic3—32no—
697Dic3—61no—
698Dic3—92no—
699Dic3—92no—
700Dic3—182no—
701Dic3—181no—
702Dic3—181no—
703Dic3—181no—
704Dic3—181no—
705Dic3—361no—
706Dic3—361no—
707Dic3#369712yescomplemented
708C32#554811yescharacteristic
709C9—21no—
710C9#583211yescharacteristic, complemented
711C23—31no—
712C23—91no—
713C23—91no—
714C23—271no—
715C23C2×D3×D911yescharacteristic
716Q8—182no—
717Q8—542no—
718D4—62no—
719D4—182no—
720D4—182no—
721D4—182no—
722D4—542no—
723D4—542no—
724D4—542no—
725D4—542no—
726D4—542no—
727D4—542no—
728C2×C4—22no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—62no—
733C2×C4—91no—
734C2×C4—94no—
735C2×C4—91no—
736C2×C4—182no—
737C2×C4—271no—
738C2×C4—271no—
739C2×C4—271no—
740C2×C4—542no—
741C2×C4—542no—
742C2×C4—542no—
743C2×C4C2×D3×D911yescharacteristic
744C2×C4C2×D3×D911yescharacteristic
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—42no—
749C2×C3—41no—
750C2×C3—41no—
751C2×C3—121no—
752C2×C3—182no—
753C2×C3—361no—
754C2×C3C2×#369711yescharacteristic
755C2×C3C2×D4×D911yescharacteristic
756C2×C3#41×D911yescharacteristic
757C2×C3D3×#23511yescharacteristic
758C2×C3#6430611yescharacteristic
759C2×C3C2×D3×#6711yescharacteristic
760D3—41no—
761D3—62no—
762D3—121no—
763D3—362no—
764D3—361no—
765D3—361no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—92no—
773C22—181no—
774C22—181no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—541no—
779C22—541no—
780C22—541no—
781C22C22×D3×D911yescharacteristic
782C4—21no—
783C4—32no—
784C4—61no—
785C4—61no—
786C4—92no—
787C4—181no—
788C4—272no—
789C4—541no—
790C4—541no—
791C4D9×#6712yes—
792C3—21no—
793C3#1058965011yescharacteristic, complemented
794C3#1059500311yescharacteristic
795C2—41no—
796C2—121no—
797C2—182no—
798C2—361no—
799C2—1081no—
800C2D3×#369711yescharacteristic
801C2#1172247511yescharacteristic
802C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#532
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3697C2semidirect
2. C2×#88640C2semidirect
3. C4×#6233C2semidirect
4. C4×C9×#67C2semidirect
5. #11721289C2semidirect
6. #11721271C2semidirect
7. #11721270C2semidirect
8. #11721257C2semidirect
9. #11721035C2semidirect
10. C4×#6194C2semidirect
11. C4×#6192C2semidirect
12. #11720983C2semidirect
13. #11720982C2semidirect
14. C4×Dic3×D9C2semidirect
15. #11720904C2semidirect
71. C2×#3697D3semidirect
110. C3×C4×D9D4semidirect
223. C3⋊Dic9#41semidirect
226. C9×Dic3#41semidirect
250. C4×#67D9semidirect
335. C4×D9#67semidirect
507. C3×C9#532semidirect
707. Dic3#3697semidirect
710. C9#5832semidirect
793. C3#10589650semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#36972
C2×#886402
C4×#62332
C4×C9×#672
#117212892
#117212712
#117212702
#117212572
#117210352
C4×#61942
C4×#61922
#117209832
#117209822
C4×Dic3×D92
#117209042
#105950033
#105896503