Finite Group Databasebeta

← #13149375

Subgroups — #13149375

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721750C211yesmaximal, characteristic, complemented
2C9×#895C211yesmaximal, characteristic, complemented
3C3×#63460C211yesmaximal, characteristic, complemented
4#11721051C211yesmaximal, characteristic, complemented
5#11721050C211yesmaximal, characteristic, complemented
6#11721050C211yesmaximal, characteristic, complemented
7#11721045C211yesmaximal, characteristic, complemented
8#11721041C211yesmaximal, characteristic, complemented
9#11721040C211yesmaximal, characteristic, complemented
10#11721034C211yesmaximal, characteristic, complemented
11#11721020C211yesmaximal, characteristic, complemented
12#11721017C211yesmaximal, characteristic, complemented
13#11721016C211yesmaximal, characteristic, complemented
14#11720963C211yesmaximal, characteristic, complemented
15#11720954C211yesmaximal, characteristic, complemented
16#10594661—31nomaximal
17#10589722—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic, complemented
21C2×C9×D12C2211yescharacteristic
22C2×C9×D12C2211yescharacteristic
23C2×C9×D12C2211yescharacteristic, complemented
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic, complemented
29C2×#6195C2211yescharacteristic, complemented
30C2×#6194C2211yescharacteristic
31C2×#6194C2211yescharacteristic
32C2×D3×Dic9C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic
34C3×C9×C4⋊C4C2211yescharacteristic, complemented
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37#88536C2211yescharacteristic, complemented
38#88534C2211yescharacteristic, complemented
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46C3×C4×Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53#64103—31no—
54C3×#898—31no—
55C3×#895D311yescharacteristic
56#63923—31no—
57#63922—31no—
58#63922—31no—
59#63916—31no—
60#63912—31no—
61#63911—31no—
62#63906—31no—
63#63890—31no—
64#63886—31no—
65#63885—31no—
66#63859—31no—
67#63850—31no—
68C9×#121—31no—
69#63502—31no—
70#63501—31no—
71#63501—31no—
72#63500—31no—
73#63499—31no—
74#63499—31no—
75#63492—31no—
76#63491—31no—
77#63460D311yescharacteristic, complemented
78#63456—31no—
79#63456—61no—
80#63448—31no—
81#63446—31no—
82#63444—31no—
83#63441—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×D3×D9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C4⋊(C3⋊D9)—41no—
99C4×C3⋊D9—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C9×D12—41no—
105C9×D12—41no—
106C9×D12—41no—
107C4×D3×C9—41no—
108#6195—41no—
109#6195—41no—
110#6195—41no—
111#6195—41no—
112#6195—41no—
113#6194—41no—
114#6194—41no—
115D3×Dic9—41no—
116#6192—41no—
117#5711—91no—
118#5620—91no—
119C22×D32—31no—
120C2×C4⋊(C3⋊D3)—31no—
121C2×C4×C3⋊D3—31no—
122C2×C3×D12C2×D311yescharacteristic
123C2×C3×D12C2×D311yescharacteristic
124C2×C3×D12C2×D311yescharacteristic
125C2×C3×C4×D3C2×D311yescharacteristic
126C2×#626—31no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#625—31no—
133C2×#625—31no—
134C2×D3×Dic3—31no—
135C23×D9—31no—
136C32×C4⋊C4C2×D311yescharacteristic
137#3752—31no—
138#3752—31no—
139#3752—31no—
140#3750—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×C4⋊Dic3—31no—
147C3×Dic3⋊C4—31no—
148C3×C4×Dic3—31no—
149#3724—31no—
150Dic3⋊Dic3—31no—
151#3722—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155C2×D4×C9—31no—
156C2×D4×C9—31no—
157C2×D4×C9—31no—
158C22×C4×C9—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C22×Dic9—31no—
167C2×D36—31no—
168C2×D36—31no—
169C2×D36—61no—
170C2×C4×D9—31no—
171C2×C4×D9—61no—
172C9×C4⋊C4—21no—
173C9×C4⋊C4C2×D311yescharacteristic, complemented
174C9×C22⋊C4—31no—
175C9×C22⋊C4—31no—
176#3676—31no—
177#3676—31no—
178#3676—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—61no—
184(C2×D9)⋊C4—61no—
185(C2×D9)⋊C4—61no—
186(C2×D9)⋊C4C2×D311yescharacteristic
187(C2×D9)⋊C4C2×D311yescharacteristic
188(C2×D9)⋊C4C2×D311yescharacteristic
189C4⋊Dic9—31no—
190C4⋊Dic9C2×D311yescharacteristic, complemented
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—61no—
194Dic9⋊C4C2×D311yescharacteristic, complemented
195C4×Dic9C2×D311yescharacteristic, complemented
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215D3×D9—44no—
216C3×C4×C9—21no—
217C3×C4×C9—21no—
218C3×C4×C9—21no—
219C3⋊Dic9—21no—
220C3⋊Dic9—21no—
221C9×Dic3—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#126—91no—
226C3×#121—31no—
227#940—91no—
228#939—91no—
229#939—91no—
230#938—91no—
231#937—91no—
232#937—91no—
233#930—91no—
234#929—91no—
235#898—31no—
236#895—91no—
237#895—91no—
238#895D911yescharacteristic, complemented
239#894—91no—
240#894—91no—
241#894—91no—
242#894—91no—
243#894—181no—
244#886—91no—
245#884—91no—
246#884—91no—
247#884—91no—
248#884—91no—
249#882—91no—
250#882—91no—
251#882—91no—
252#882—91no—
253#879—91no—
254#876—91no—
255#874—91no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—31no—
258C22×C3×D3—31no—
259C22×C3×D3C22×D311yescharacteristic
260C22×C3×D3C22×D311yescharacteristic
261C22×C3×D3C22×D311yescharacteristic
262C2×D32—121no—
263C2×D32—121no—
264C2×D32—121no—
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—31no—
270C4⋊(C3⋊D3)—121no—
271C4×C3⋊D3—121no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3C22×D311yescharacteristic
276C3×D12—41no—
277C3×D12—41no—
278C3×D12—41no—
279C3×C4×D3—41no—
280#626—121no—
281#626—121no—
282#626—121no—
283#626—121no—
284#626—121no—
285#626—121no—
286#625—121no—
287#625—121no—
288D3×Dic3—121no—
289C23×C9—31no—
290C23×C9—31no—
291C23×C9—31no—
292C22×D9—31no—
293C22×D9—31no—
294C22×D9—61no—
295C22×D9—61no—
296C22×D9—121no—
297C22×D9—121no—
298C22×D9—121no—
299C22×D9C22×D311yescharacteristic
300D4×C9—121no—
301D4×C9—121no—
302D4×C9—121no—
303C2×C4×C9—21no—
304C2×C4×C9—21no—
305C2×C4×C9—21no—
306C2×C4×C9—31no—
307C2×C4×C9—121no—
308C2×C4×C9C22×D311yescharacteristic
309C2×C4×C9C22×D311yescharacteristic
310C2×C4×C9C22×D311yescharacteristic
311#611—121no—
312#611—121no—
313#611—121no—
314#611—121no—
315#611—121no—
316#611—121no—
317#611—121no—
318C2×Dic9—31no—
319C2×Dic9—31no—
320C2×Dic9—61no—
321C2×Dic9—61no—
322C2×Dic9—121no—
323C2×Dic9C22×D311yescharacteristic
324C2×Dic9C22×D311yescharacteristic
325C2×Dic9C22×D311yescharacteristic
326D36—121no—
327D36—122no—
328D36—121no—
329C4×D9—121no—
330C4×D9—122no—
331#560—271noSylow
332C2×C3×C9H(5,𝔽2)11yescharacteristic
333C2×C3×C9H(5,𝔽2)11yescharacteristic
334C2×C3×C9H(5,𝔽2)11yescharacteristic
335C3⋊D9—41no—
336C3⋊D9—41no—
337D3×C9—41no—
338D3×C9—41no—
339D3×C9—41no—
340C3×D9—41no—
341C23×D3—91no—
342C23×D3—91no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C22×C3×C4—31no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—91no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C22×Dic3—91no—
358C2×D12—91no—
359C2×D12—91no—
360C2×D12—91no—
361C2×D12—91no—
362C2×D12—91no—
363C2×D12—91no—
364C2×D12—91no—
365C2×D12—91no—
366C2×D12—181no—
367C2×D12C2×D911yescharacteristic
368C2×D12C2×D911yescharacteristic
369C2×D12C2×D911yescharacteristic, complemented
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—181no—
374C2×C4×D3C2×D911yescharacteristic, complemented
375C3×C4⋊C4—21no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4C2×D911yescharacteristic, complemented
379C3×C4⋊C4D3211yescharacteristic
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C42—91no—
386#217—91no—
387#217—91no—
388#217—91no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—181no—
404(C2×D3)⋊C4—181no—
405(C2×D3)⋊C4—181no—
406(C2×D3)⋊C4C2×D911yescharacteristic
407(C2×D3)⋊C4C2×D911yescharacteristic, complemented
408C4⋊Dic3—31no—
409C4⋊Dic3—91no—
410Dic3⋊C4—31no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—181no—
417C4×Dic3—31no—
418C22×C32C23×D311yescharacteristic
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
424C2×C3⋊D3—61no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437D32—124no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—21no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3×Dic3—21no—
444C3×Dic3—61no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C22×C9—21no—
448C22×C9—61no—
449C22×C9—61no—
450C22×C9—61no—
451C22×C9—61no—
452C22×C9—61no—
453C22×C9—61no—
454C22×C9—61no—
455C22×C9—61no—
456C22×C9—61no—
457C22×C9C23×D311yescharacteristic
458C2×D9—21no—
459C2×D9—21no—
460C2×D9—21no—
461C2×D9—62no—
462C2×D9—61no—
463C2×D9—61no—
464C2×D9—61no—
465C2×D9—61no—
466C2×D9—61no—
467C2×D9—61no—
468C2×D9—121no—
469C2×D9—121no—
470C2×D9—121no—
471C2×D9—121no—
472C2×D9—121no—
473C2×D9—124no—
474C4×C9—21no—
475C4×C9—21no—
476C4×C9—21no—
477C4×C9—41no—
478C4×C9—41no—
479C4×C9—41no—
480C4×C9—61no—
481Dic9—21no—
482Dic9—21no—
483Dic9—21no—
484Dic9—61no—
485Dic9—61no—
486Dic9—121no—
487Dic9—121no—
488#127—271no—
489#126—91no—
490#126—271no—
491#123—271no—
492#123—271no—
493#123—271no—
494#121—31no—
495#121—271no—
496#121—271no—
497#121—271no—
498#121—271no—
499#121—271no—
500#120—271no—
501#120—271no—
502#120—271no—
503C3×C9#56011yescharacteristic, complemented, Sylow
504C23×C3—31no—
505C23×C3—31no—
506C23×C3—31no—
507C23×C3—91no—
508C22×D3—31no—
509C22×D3—91no—
510C22×D3—91no—
511C22×D3—91no—
512C22×D3—91no—
513C22×D3—181no—
514C22×D3—181no—
515C22×D3—361no—
516C22×D3—361no—
517C22×D3—361no—
518C22×D3—361no—
519C22×D3—361no—
520C22×D3—361no—
521C22×D3C22×D911yescharacteristic
522C22×D3C22×D911yescharacteristic
523C22×D3C22×D911yescharacteristic
524C3×D4—121no—
525C3×D4—121no—
526C3×D4—121no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—91no—
532C2×C3×C4—91no—
533C2×C3×C4—91no—
534C2×C3×C4—121no—
535C2×C3×C4C22×D911yescharacteristic
536C2×C3×C4C22×D911yescharacteristic
537C2×C3×C4C22×D911yescharacteristic
538C2×C3×C4C2×D3211yescharacteristic
539C2×C3×C4C2×D3211yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541#67—361no—
542#67—361no—
543#67—361no—
544#67—361no—
545#67—361no—
546#67—361no—
547#67—361no—
548#67—361no—
549#67—361no—
550#67—361no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—181no—
559C2×Dic3—181no—
560C2×Dic3—361no—
561C2×Dic3C22×D911yescharacteristic
562D12—41no—
563D12—41no—
564D12—41no—
565D12—361no—
566D12—361no—
567D12—362no—
568D12—361no—
569D12—361no—
570D12—361no—
571D12—361no—
572D12—361no—
573D12—361no—
574C4×D3—41no—
575C4×D3—361no—
576C4×D3—361no—
577C4×D3—361no—
578C4×D3—362no—
579C2×C32#100411yescharacteristic
580C2×C32#100411yescharacteristic
581C2×C32#100911yescharacteristic
582C3⋊D3—121no—
583C3⋊D3—121no—
584C3×D3—41no—
585C3×D3—41no—
586C3×D3—41no—
587C3×D3—121no—
588C2×C9—21no—
589C2×C9—21no—
590C2×C9—21no—
591C2×C9—121no—
592C2×C9—121no—
593C2×C9—121no—
594C2×C9#100911yescharacteristic
595C2×C9#100911yescharacteristic
596C2×C9#100911yescharacteristic
597D9—41no—
598D9—122no—
599D9—121no—
600D9—121no—
601D9—241no—
602C24—271no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—271no—
607C2×D4—271no—
608C2×D4—271no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—31no—
616C22×C4—271no—
617C22×C4—271no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C4⋊C4D3×D911yescharacteristic, complemented
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C42—91no—
637C22×C3—21no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3C23×D911yescharacteristic
651C22×C3C22×D3211yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—182no—
665C2×D3—181no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—181no—
670C2×D3—181no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—361no—
678C2×D3—361no—
679C2×D3—361no—
680C2×D3—361no—
681C2×D3—361no—
682C2×D3—364no—
683C2×D3—364no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—181no—
695C3×C4—181no—
696C3×C4—181no—
697Dic3—21no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—181no—
702Dic3—181no—
703Dic3—181no—
704Dic3—181no—
705Dic3—361no—
706Dic3—361no—
707C32#562011yescharacteristic
708C9—21no—
709C9#571111yescharacteristic, complemented
710C23—31no—
711C23—31no—
712C23—31no—
713C23—91no—
714C23—271no—
715C23—271no—
716C23—1081no—
717C23—1081no—
718C23—1081no—
719D4—121no—
720D4—121no—
721D4—121no—
722D4—1081no—
723D4—1081no—
724D4—1081no—
725D4—1081no—
726D4—1081no—
727D4—1081no—
728D4—1081no—
729D4—1081no—
730D4—1081no—
731C2×C4—31no—
732C2×C4—91no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—121no—
736C2×C4—271no—
737C2×C4—271no—
738C2×C4—1081no—
739C2×C4—1081no—
740C2×C4C2×D3×D911yescharacteristic
741C2×C4C2×D3×D911yescharacteristic
742C2×C4C2×D3×D911yescharacteristic
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—121no—
747C2×C3—121no—
748C2×C3—121no—
749C2×C3—361no—
750C2×C3#6371011yescharacteristic
751C2×C3#6371011yescharacteristic
752C2×C3#6371511yescharacteristic
753C2×C3#6430711yescharacteristic
754C2×C3#6431411yescharacteristic
755C2×C3#6432011yescharacteristic
756D3—41no—
757D3—41no—
758D3—41no—
759D3—121no—
760D3—362no—
761D3—361no—
762D3—361no—
763D3—361no—
764D3—361no—
765D3—721no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—541no—
779C22—541no—
780C22—541no—
781C22—541no—
782C22—541no—
783C22—541no—
784C22—1084no—
785C22C22×D3×D911yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—61no—
790C4—181no—
791C4—181no—
792C4—181no—
793C4—541no—
794C4—541no—
795C3—21no—
796C3#1058972211yescharacteristic, complemented
797C3#1059466111yescharacteristic
798C2—121no—
799C2—121no—
800C2—121no—
801C2—361no—
802C2—1081no—
803C2—1081no—
804C2#1172247611yescharacteristic
805C2#1172250011yescharacteristic
806C2#1172251511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#560
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721750C2semidirect
2. C9×#895C2semidirect
3. C3×#63460C2semidirect
4. #11721051C2semidirect
5. #11721050C2semidirect
6. #11721050C2semidirect
7. #11721045C2semidirect
8. #11721041C2semidirect
9. #11721040C2semidirect
10. #11721034C2semidirect
11. #11721020C2semidirect
12. #11721017C2semidirect
13. #11721016C2semidirect
14. #11720963C2semidirect
15. #11720954C2semidirect
20. C2×C4×C3⋊D9C22semidirect
23. C2×C9×D12C22semidirect
24. C2×C4×D3×C9C22semidirect
28. C2×#6195C22semidirect
29. C2×#6195C22semidirect
32. C2×D3×Dic9C22semidirect
34. C3×C9×C4⋊C4C22semidirect
37. #88536C22semidirect
38. #88534C22semidirect
40. C9×(C2×D3)⋊C4C22semidirect
44. C3×C4⋊Dic9C22semidirect
45. C3×Dic9⋊C4C22semidirect
46. C3×C4×Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
77. #63460D3semidirect
173. C9×C4⋊C4C2×D3semidirect
190. C4⋊Dic9C2×D3semidirect
194. Dic9⋊C4C2×D3semidirect
195. C4×Dic9C2×D3semidirect
238. #895D9semidirect
369. C2×D12C2×D9semidirect
374. C2×C4×D3C2×D9semidirect
378. C3×C4⋊C4C2×D9semidirect
407. (C2×D3)⋊C4C2×D9semidirect
503. C3×C9#560semidirect
623. C4⋊C4D3×D9semidirect
709. C9#5711semidirect
796. C3#10589722semidirect

Maximal subgroups

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

subgroupindex
#117217502
C9×#8952
C3×#634602
#117210512
#117210502
#117210452
#117210412
#117210402
#117210342
#117210202
#117210172
#117210162
#117209632
#117209542
#105946613
#105897223