Finite Group Databasebeta

← #13150999

Subgroups — #13150999

Order 1728.

1040 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88742C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3C3×#63501C211yesmaximal, characteristic, complemented
4C9×#935C211yesmaximal, characteristic, complemented
5#11721275C211yesmaximal, characteristic, complemented
6#611⋊Dic3C211yesmaximal, characteristic, complemented
7#11721267C211yesmaximal, characteristic, complemented
8#11721260C211yesmaximal, characteristic, complemented
9#11721256C211yesmaximal, characteristic, complemented
10C2×Dic9⋊Dic3C211yesmaximal, characteristic, complemented
11#11721241C211yesmaximal, characteristic, complemented
12#11720996C211yesmaximal, characteristic, complemented
13#11720980C211yesmaximal, characteristic, complemented
14#11720941C211yesmaximal, characteristic, complemented
15#11720905C211yesmaximal, characteristic, complemented
16#10595162—31nomaximal
17#10589757—31nomaximal
18C2×C3×D4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic
22C22×C3⋊Dic9C2211yescharacteristic
23#88742—24no—
24C2×C4×C3⋊D9C2211yescharacteristic
25C2×#6226C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C22×C9×Dic3C2211yescharacteristic
29C22×C3×Dic9C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33#88658—24no—
34C2×Dic3×D9C2211yescharacteristic
35C2×#6189C2211yescharacteristic
36C9×#217C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C9×#217C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C9×Dic3⋊C4C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49#88442C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3830—31no—
56C2×#3804—31no—
57C3×#939—31no—
58C3×#935D311yescharacteristic
59#63982—31no—
60#63975—31no—
61#67⋊Dic3—31no—
62C2×Dic3⋊Dic3—31no—
63#63962—31no—
64#63958—31no—
65#63952—31no—
66#63896—31no—
67#63883—31no—
68#63853—31no—
69#63840—31no—
70C2×#3699—31no—
71C2×#3699—61no—
72C2×#3697—31no—
73C9×#123—31no—
74#63501D311yescharacteristic, complemented
75C2×Dic9⋊C4—31no—
76#63458—31no—
77#63456—31no—
78C4⋊C4×D9—31no—
79#63450—31no—
80#63448—31no—
81#63446—31no—
82#63445—31no—
83#611⋊C4—31no—
84#611⋊C4—31no—
85#63440—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C3×D4×C9—22no—
91C2×C3×C4×C9C2311yescharacteristic
92#6233—22no—
93#6233D414yescomplemented
94C2×C3⋊Dic9—22no—
95C2×C3⋊Dic9—22no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C4×C3⋊D9—22no—
100#6226—22no—
101C3×#611—22no—
102C3×#611—22no—
103C2×C9×Dic3—22no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9—22no—
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112#6192—22no—
113(C3⋊D9)⋊C4—22no—
114(C3⋊D9)⋊C4—22no—
115Dic3×D9—22no—
116#6189—22no—
117#5655—91no—
118#5611—91no—
119C2×C32×D4C2×D311yescharacteristic
120C2×#638—31no—
121C2×#638—31no—
122C22×C3⋊Dic3—31no—
123C22×C3⋊Dic3—31no—
124#3830—64no—
125C2×C4×C3⋊D3—31no—
126C2×#634—31no—
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3C2×D311yescharacteristic
131C2×#627—31no—
132C2×#626—31no—
133C2×#624—31no—
134C2×#624—31no—
135#3804—64no—
136C2×D3×Dic3—31no—
137C3×#217—31no—
138C3×#217C2×D311yescharacteristic
139C3×#217C2×D311yescharacteristic
140C3×#217C2×D311yescharacteristic
141C3×(C2×D3)⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4C2×D311yescharacteristic
144C3×Dic3⋊C4C2×D311yescharacteristic
145#3724—31no—
146Dic3⋊Dic3—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150Dic3⋊Dic3—31no—
151Dic3⋊Dic3—31no—
152#3722—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C2×D4×C9—21no—
157C2×D4×C9C2×D311yescharacteristic
158C22×C4×C9—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—61no—
162C2×#611—61no—
163C2×#611C2×D311yescharacteristic
164C2×#611C2×D311yescharacteristic
165C22×Dic9—31no—
166C22×Dic9—31no—
167C22×Dic9—61no—
168C22×Dic9—61no—
169C22×Dic9C2×D311yescharacteristic
170#3699—64no—
171#3699—68no—
172#3697—64no—
173C2×D36—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—61no—
179C2×Dic18—31no—
180C2×Dic18—31no—
181C2×Dic18—61no—
182C9×C4⋊C4—31no—
183C9×C4⋊C4—31no—
184C9×C22⋊C4—31no—
185C9×C22⋊C4—31no—
186C9×C22⋊C4—31no—
187#3676C2×D311yescharacteristic
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4C2×D311yescharacteristic
192C4⋊Dic9—31no—
193C4⋊Dic9—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4C2×D311yescharacteristic
200C4×Dic9—31no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9C2×D412yes—
207C22×C3×C9C2411yescharacteristic
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9C2×D412yes—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C3×C4×C9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9C2×D412yes—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9#4112yescomplemented
225C2×#237—91no—
226C2×#237—91no—
227C2×#237—91no—
228C2×#237—181no—
229C2×#235—91no—
230C3×#123—31no—
231C3×#121—91no—
232#939—31no—
233#938—91no—
234#935—91no—
235#935D911yescharacteristic, complemented
236D4×Dic3—91no—
237C4×#67—91no—
238C2×C4⋊Dic3—91no—
239C2×Dic3⋊C4—91no—
240#896—91no—
241#894—91no—
242D3×C4⋊C4—91no—
243D3×C4⋊C4—91no—
244#888—91no—
245#888—91no—
246#886—91no—
247#884—91no—
248#883—91no—
249#883—91no—
250#883—91no—
251#67⋊C4—91no—
252#67⋊C4—91no—
253#878—91no—
254#878—91no—
255#878—91no—
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—31no—
259C22×C3×D3—31no—
260C32×D4—22no—
261C2×C32×C4C22×D311yescharacteristic
262#638—34no—
263#638—62no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—31no—
267C2×C3⋊Dic3—62no—
268C2×C3⋊Dic3—62no—
269C4×C3⋊D3—62no—
270#634—62no—
271C3×#67—62no—
272C3×#67—62no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—62no—
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282#627—62no—
283#626—62no—
284#624—62no—
285#624—62no—
286D3×Dic3—62no—
287C23×C9—21no—
288C23×C9—21no—
289C23×C9C22×D311yescharacteristic
290C23×C9C22×D311yescharacteristic
291C22×D9—31no—
292C22×D9—61no—
293C22×D9C22×D311yescharacteristic
294D4×C9—24no—
295D4×C9—22no—
296C2×C4×C9—21no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301C2×C4×C9—62no—
302C2×C4×C9C22×D311yescharacteristic
303#611—22no—
304#611—22no—
305#611—34no—
306#611—64no—
307#611—62no—
308#611—64no—
309C2×Dic9—22no—
310C2×Dic9—31no—
311C2×Dic9—31no—
312C2×Dic9—31no—
313C2×Dic9—61no—
314C2×Dic9—61no—
315C2×Dic9—61no—
316C2×Dic9—62no—
317C2×Dic9—64no—
318C2×Dic9—64no—
319C2×Dic9—62no—
320C2×Dic9C22×D311yescharacteristic
321C2×Dic9C22×D311yescharacteristic
322C2×Dic9C22×D311yescharacteristic
323D36—62no—
324C4×D9—62no—
325C4×D9—62no—
326C4×D9—62no—
327C4×D9—64no—
328C4×D9—62no—
329Dic18—62no—
330Dic18—62no—
331Dic18—64no—
332#547—271noSylow
333C2×C3×C9—22no—
334C2×C3×C9—41no—
335C2×C3×C9C22×D411yescharacteristic
336C2×C3×C9C2×#4111yescharacteristic
337C2×C3×C92−1+411yescharacteristic
338C3⋊D9—22no—
339C3×D9—41no—
340C2×C3×D4—21no—
341C2×C3×D4—91no—
342C2×C3×D4—91no—
343C2×C3×D4C2×D911yescharacteristic
344C2×C3×D4D3211yescharacteristic
345C22×C3×C4—31no—
346C22×C3×C4—91no—
347C2×#67—31no—
348C2×#67—31no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—91no—
353C2×#67—91no—
354C2×#67—181no—
355C2×#67—181no—
356C22×Dic3—31no—
357C22×Dic3—91no—
358C22×Dic3—91no—
359C22×Dic3—91no—
360C22×Dic3—91no—
361C22×Dic3—91no—
362C22×Dic3—181no—
363C22×Dic3—181no—
364C22×Dic3C2×D911yescharacteristic
365#237—184no—
366#237—184no—
367#237—184no—
368#237—188no—
369#235—184no—
370C2×D12—91no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—181no—
379C2×Dic6—91no—
380C2×Dic6—91no—
381C2×Dic6—91no—
382C2×Dic6—91no—
383C2×Dic6—181no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—91no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392#217—31no—
393#217—91no—
394#217—91no—
395#217C2×D911yescharacteristic
396#217C2×D911yescharacteristic
397#217C2×D911yescharacteristic
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403C4⋊Dic3—91no—
404C4⋊Dic3—91no—
405C4⋊Dic3—91no—
406C4⋊Dic3—91no—
407C4⋊Dic3—91no—
408C4⋊Dic3—91no—
409Dic3⋊C4—31no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4C2×D911yescharacteristic
419Dic3⋊C4C2×D911yescharacteristic
420C4×Dic3—91no—
421C4×Dic3—91no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32D3×D412yes—
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—32no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C32×C4—21no—
436C3⋊Dic3—32no—
437C3⋊Dic3—61no—
438C3⋊Dic3—61no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—32no—
444C3×Dic3—61no—
445C3×Dic3—61no—
446C22×C9—21no—
447C22×C9—21no—
448C22×C9—22no—
449C22×C9—21no—
450C22×C9—21no—
451C22×C9—21no—
452C22×C9—21no—
453C22×C9—22no—
454C22×C9—41no—
455C22×C9—41no—
456C22×C9—41no—
457C22×C9—41no—
458C22×C9D3×D412yes—
459C22×C9C23×D311yescharacteristic
460C2×D9—21no—
461C2×D9—21no—
462C2×D9—21no—
463C2×D9—32no—
464C2×D9—62no—
465C2×D9—61no—
466C2×D9—61no—
467C2×D9—121no—
468C2×D9—121no—
469C4×C9—22no—
470C4×C9—21no—
471C4×C9—61no—
472C4×C9—61no—
473C4×C9—61no—
474C4×C9—61no—
475Dic9—21no—
476Dic9—21no—
477Dic9—32no—
478Dic9—62no—
479Dic9—62no—
480Dic9—62no—
481Dic9—61no—
482Dic9—61no—
483Dic9#23712yescomplemented
484C2×#41—271no—
485C2×#41—271no—
486C4⋊Q8—271no—
487#123—31no—
488#123—271no—
489#123—271no—
490#123—271no—
491C22⋊Q8—271no—
492C22⋊Q8—271no—
493#121—91no—
494#121—271no—
495C4×D4—271no—
496C4×D4—271no—
497C2×C4⋊C4—271no—
498C2×C4⋊C4—271no—
499C3×C9#54711yescharacteristic, complemented, Sylow
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—91no—
503C23×C3C22×D911yescharacteristic
504C23×C3C22×D911yescharacteristic
505C23×C3C2×D3211yescharacteristic
506C23×C3C2×D3211yescharacteristic
507C22×D3—31no—
508C22×D3—91no—
509C22×D3—91no—
510C22×D3—181no—
511C3×D4—24no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—182no—
515C3×D4—182no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—62no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—182no—
526C2×C3×C4C22×D911yescharacteristic
527C2×C3×C4C2×D3211yescharacteristic
528#67—62no—
529#67—62no—
530#67—94no—
531#67—94no—
532#67—184no—
533#67—182no—
534#67—182no—
535#67—182no—
536#67—184no—
537C2×Dic3—22no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—62no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—181no—
549C2×Dic3—181no—
550C2×Dic3—181no—
551C2×Dic3—182no—
552C2×Dic3—182no—
553C2×Dic3—182no—
554C2×Dic3—184no—
555C2×Dic3—184no—
556C2×Dic3—182no—
557C2×Dic3—182no—
558C2×Dic3C22×D911yescharacteristic
559C2×Dic3C22×D911yescharacteristic
560C2×Dic3C22×D911yescharacteristic
561C2×Dic3C22×D911yescharacteristic
562D12—182no—
563C4×D3—182no—
564C4×D3—182no—
565C4×D3—182no—
566C4×D3—182no—
567C4×D3—182no—
568C4×D3—182no—
569C4×D3—182no—
570C4×D3—184no—
571Dic6—182no—
572Dic6—182no—
573Dic6—182no—
574Dic6—182no—
575Dic6—184no—
576C2×C32—22no—
577C2×C32—41no—
578C2×C32C2×D3×D411yescharacteristic
579C2×C32D3×#4111yescharacteristic
580C2×C32#101011yescharacteristic
581C3⋊D3—62no—
582C3×D3—121no—
583C2×C9—22no—
584C2×C9—21no—
585C2×C9—21no—
586C2×C9—21no—
587C2×C9—42no—
588C2×C9—42no—
589C2×C9—41no—
590C2×C9C2×D3×D411yescharacteristic
591C2×C9C2×#23711yescharacteristic
592C2×C9#101011yescharacteristic
593D9—41no—
594D9—62no—
595D9—122no—
596#41—544no—
597#41—544no—
598C2×Q8—271no—
599C2×Q8—271no—
600C2×D4—91no—
601C2×D4—91no—
602C2×D4—271no—
603C2×D4—271no—
604C2×D4—271no—
605C2×D4D3×D911yescharacteristic
606C22×C4—31no—
607C22×C4—91no—
608C22×C4—271no—
609C22×C4—271no—
610C22×C4—271no—
611C22×C4—271no—
612C22×C4—271no—
613C22×C4—271no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—91no—
617C4⋊C4—271no—
618C4⋊C4—271no—
619C4⋊C4—271no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C4⋊C4—271no—
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—31no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C42—271no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—22no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3D4×D912yes—
654C22×C3C23×D911yescharacteristic
655C22×C3#381112yes—
656C22×C3C22×D3211yescharacteristic
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—92no—
661C2×D3—92no—
662C2×D3—182no—
663C2×D3—181no—
664C2×D3—181no—
665C2×D3—181no—
666C2×D3—181no—
667C2×D3—361no—
668C2×D3—361no—
669C3×C4—22no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—92no—
677C3×C4—181no—
678C3×C4—181no—
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—21no—
683Dic3—32no—
684Dic3—61no—
685Dic3—61no—
686Dic3—92no—
687Dic3—92no—
688Dic3—182no—
689Dic3—182no—
690Dic3—182no—
691Dic3—181no—
692Dic3—181no—
693Dic3—181no—
694Dic3—181no—
695C32#565511yescharacteristic
696C9—21no—
697C9#561111yescharacteristic, complemented
698C23—91no—
699C23—271no—
700C23C2×D3×D911yescharacteristic
701C23C2×D3×D911yescharacteristic
702Q8—542no—
703Q8—542no—
704D4—22no—
705D4—182no—
706D4—182no—
707D4—274no—
708D4—542no—
709D4—542no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—62no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—182no—
719C2×C4—271no—
720C2×C4—271no—
721C2×C4—271no—
722C2×C4—542no—
723C2×C4—542no—
724C2×C4—542no—
725C2×C4—542no—
726C2×C4—542no—
727C2×C4—542no—
728C2×C4C2×D3×D911yescharacteristic
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—42no—
735C2×C3—42no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—361no—
739C2×C3C2×D4×D911yescharacteristic
740C2×C3#41×D911yescharacteristic
741C2×C3#6371611yescharacteristic
742C2×C3#6430911yescharacteristic
743C2×C3D3×#23711yescharacteristic
744C2×C3C2×#381111yescharacteristic
745D3—121no—
746D3—182no—
747D3—182no—
748D3—362no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—181no—
755C22—181no—
756C22—181no—
757C22—272no—
758C22—541no—
759C22—541no—
760C22#8866812yes—
761C22C22×D3×D911yescharacteristic
762C4—21no—
763C4—61no—
764C4—61no—
765C4—61no—
766C4—61no—
767C4—92no—
768C4—181no—
769C4—181no—
770C4—272no—
771C4—541no—
772C4—541no—
773C3—21no—
774C3#1058975711yescharacteristic, complemented
775C3#1059516211yescharacteristic
776C2—22no—
777C2—41no—
778C2—361no—
779C2—542no—
780C2#1172249411yescharacteristic
781C2D9×#23711yescharacteristic
782C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#547
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#88742C2semidirect
2. C2×#88658C2semidirect
3. C3×#63501C2semidirect
4. C9×#935C2semidirect
5. #11721275C2semidirect
6. #611⋊Dic3C2semidirect
7. #11721267C2semidirect
8. #11721260C2semidirect
9. #11721256C2semidirect
10. C2×Dic9⋊Dic3C2semidirect
11. #11721241C2semidirect
12. #11720996C2semidirect
13. #11720980C2semidirect
14. #11720941C2semidirect
15. #11720905C2semidirect
74. #63501D3semidirect
93. #6233D4semidirect
224. C3×Dic9#41semidirect
235. #935D9semidirect
483. Dic9#237semidirect
499. C3×C9#547semidirect
697. C9#5611semidirect
774. C3#10589757semidirect

Maximal subgroups

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

subgroupindex
C2×#887422
C2×#886582
C3×#635012
C9×#9352
#117212752
#611⋊Dic32
#117212672
#117212602
#117212562
C2×Dic9⋊Dic32
#117212412
#117209962
#117209802
#117209412
#117209052
#105951623
#105897573