Finite Group Databasebeta

← #13177391

Subgroups — #13177391

Order 1728.

2064 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3#11723976C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5#11723641C211yesmaximal, characteristic, complemented
6#11723631C211yesmaximal, characteristic, complemented
7#11723621C211yesmaximal, characteristic, complemented
8#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
9Dic3×#638C211yesmaximal, characteristic, complemented
10C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
11#11723602C211yesmaximal, characteristic, complemented
12#11723518C211yesmaximal, characteristic, complemented
13#11723487C211yesmaximal, characteristic, complemented
14C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#11723394C211yesmaximal, characteristic, complemented
16#10596082—31nomaximal
17#10595151—34nomaximal
18C2×C33×D4C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C3×#3830—24no—
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×#634C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic
28C2×C32×#67C2211yescharacteristic
29C22×C32×Dic3C2211yescharacteristic
30C2×#6293C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×Dic3×C3⋊D3C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic
34#89029—24no—
35C2×D3×C3⋊Dic3C2211yescharacteristic
36#88864C2211yescharacteristic
37#88864C2211yescharacteristic
38#88864C2211yescharacteristic
39#88857C2211yescharacteristic
40#88857C2211yescharacteristic
41C32×#217C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44#88807C2211yescharacteristic
45#88806C2211yescharacteristic
46#88806C2211yescharacteristic
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49Dic3⋊(C3⋊Dic3)C2211yescharacteristic
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic
51#88803C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×#3830—31no—
56C2×#3830D311yescharacteristic, complemented
57C2×C3×#237—34no—
58C2×#3805—34no—
59C32×#121—31no—
60#64147—31no—
61#64144—31no—
62#64144—31no—
63#64144—34no—
64#64144—64no—
65D4×C3⋊Dic3—31no—
66C4×#638—31no—
67C2×C4⋊(C3⋊Dic3)—31no—
68C4⋊C4×C3⋊D3—31no—
69#64097—31no—
70#64092—31no—
71#64092—31no—
72#64087—31no—
73#64087—31no—
74C3×#939D314yescomplemented
75Dic3×#67—34no—
76Dic3×#67—34no—
77#63970—34no—
78#63969—34no—
79C2×Dic3⋊Dic3—34no—
80#63964—34no—
81#63961—34no—
82#63905—34no—
83#63887—34no—
84D3×Dic3⋊C4—34no—
85#63839—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C33×D4—22no—
91C2×C33×C4C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)—22no—
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C3×#638—22no—
98C3×#638D414yescomplemented
99C2×C3×C3⋊Dic3—22no—
100C2×C3×C3⋊Dic3—22no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C3×C4×C3⋊D3—22no—
105C3×#634—22no—
106C32×#67—22no—
107C32×#67—22no—
108C2×C32×Dic3—22no—
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112#6293—22no—
113#6290—22no—
114Dic3×C3⋊D3—22no—
115Dic3×C3⋊D3—22no—
116D3×C3⋊Dic3—22no—
117#5824—91no—
118#5611—94no—
119C2×C32×D4—24no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C2×C32×D4C2×D314yes—
123C2×C32×D4C2×D311yescharacteristic
124C22×C32×C4—31no—
125C2×#638—31no—
126C2×#638C2×D311yescharacteristic
127C2×#638C2×D311yescharacteristic
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—34no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—64no—
132C22×C3⋊Dic3C2×D311yescharacteristic
133C22×C3⋊Dic3C2×D311yescharacteristic
134#3830—24no—
135#3830—64no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3C2×D311yescharacteristic
139C2×#634—31no—
140C2×#634C2×D311yescharacteristic
141C2×C3×#67—34no—
142C2×C3×#67—34no—
143C2×C3×#67C2×D314yes—
144C2×C3×#67C2×D314yes—
145C22×C3×Dic3—34no—
146C22×C3×Dic3—34no—
147C22×C3×Dic3C2×D314yes—
148C3×#237—616no—
149C2×C3×C4×D3—34no—
150C2×C3×Dic6—34no—
151C2×#627—34no—
152C2×#625—34no—
153#3805—616no—
154C2×D3×Dic3—34no—
155C2×D3×Dic3—34no—
156C2×D3×Dic3—34no—
157C32×C4⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160#3757—31no—
161#3757—31no—
162#3757—31no—
163#3757—34no—
164#3757—34no—
165#3757—34no—
166#3757—31no—
167#3757—31no—
168#3757—64no—
169#3757—64no—
170#3757—64no—
171#3752—31no—
172C4⋊(C3⋊Dic3)—31no—
173C4⋊(C3⋊Dic3)—31no—
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—31no—
176#3750—31no—
177#3750—31no—
178#3750—34no—
179#3750—34no—
180#3750—31no—
181#3750—31no—
182#3750—31no—
183#3750—64no—
184#3750—64no—
185C4×C3⋊Dic3—31no—
186C3×#217C2×D314yes—
187C3×(C2×D3)⋊C4C2×D314yes—
188C3×Dic3⋊C4C2×D314yes—
189#3724—34no—
190#3724—34no—
191Dic3⋊Dic3—34no—
192Dic3⋊Dic3—34no—
193Dic3⋊Dic3—34no—
194Dic3⋊Dic3—34no—
195Dic3⋊Dic3—34no—
196(C2×D3)⋊Dic3—34no—
197(C2×D3)⋊Dic3—34no—
198(C2×D3)⋊Dic3—34no—
199Dic32—34no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33—21no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33C2×D412yes—
206C22×C33C2411yescharacteristic
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3C2×D412yes—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C33×C4—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3⋊(C3⋊Dic3)—21no—
216C3⋊(C3⋊Dic3)—21no—
217C3⋊(C3⋊Dic3)—21no—
218C3×C3⋊Dic3—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3C2×D412yes—
221C32×Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3#4112yescomplemented
224C2×C3×#41—91no—
225C2×#237—34no—
226C2×#237—94no—
227C2×#237—91no—
228C3×#121—34no—
229#946—91no—
230#944—91no—
231#939—91no—
232#939C3⋊D311yescharacteristic, complemented
233#938—94no—
234#935—94no—
235#935—94no—
236#935—91no—
237#935—91no—
238#935—184no—
239D4×Dic3—94no—
240D4×Dic3—91no—
241#929—91no—
242#929—91no—
243C4×#67—94no—
244C4×#67—91no—
245C2×C4⋊Dic3—94no—
246#924—91no—
247C2×Dic3⋊C4—91no—
248C2×Dic3⋊C4—91no—
249D3×C4⋊C4—94no—
250#888—94no—
251#883—94no—
252#883—94no—
253#878—94no—
254#878—94no—
255C23×C32—24no—
256C23×C32—24no—
257C23×C32—31no—
258C23×C32C22×D314yes—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—34no—
264C22×C3×D3C22×D314yes—
265C32×D4—22no—
266C32×D4—28no—
267C32×D4—48no—
268C32×D4—62no—
269C32×D4—62no—
270C2×C32×C4—24no—
271C2×C32×C4—31no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—62no—
275C2×C32×C4C22×D314yes—
276C2×C32×C4C22×D311yescharacteristic
277#638—22no—
278#638—62no—
279#638#6714yescomplemented
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—34no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3—64no—
294C2×C3⋊Dic3—62no—
295C2×C3⋊Dic3—62no—
296C2×C3⋊Dic3—68no—
297C2×C3⋊Dic3—128no—
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C4×C3⋊D3—22no—
302C4×C3⋊D3—62no—
303C4×C3⋊D3—62no—
304#634—22no—
305#634—62no—
306C3×#67—28no—
307C3×#67—28no—
308C3×#67—316no—
309C3×#67—68no—
310C2×C3×Dic3—28no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3—34no—
314C2×C3×Dic3—68no—
315C2×C3×Dic3—68no—
316C2×C3×Dic3C22×D314yes—
317C2×C3×Dic3C22×D314yes—
318C2×C3×Dic3C22×D314yes—
319C3×C4×D3—68no—
320C3×Dic6—68no—
321#627—68no—
322#625—68no—
323D3×Dic3—68no—
324D3×Dic3—68no—
325D3×Dic3—68no—
326#547—271noSylow
327C2×C33—22no—
328C2×C33—41no—
329C2×C33C22×D411yescharacteristic
330C2×C33C2×#4111yescharacteristic
331C2×C332−1+411yescharacteristic
332C3×C3⋊D3—22no—
333C32×D3—41no—
334C3×#41—184no—
335C2×C3×Q8—91no—
336C2×C3×D4—24no—
337C2×C3×D4—34no—
338C2×C3×D4—34no—
339C2×C3×D4—91no—
340C2×C3×D4—91no—
341C2×C3×D4D3214yes—
342C2×C3×D4C2×C3⋊D311yescharacteristic
343C22×C3×C4—34no—
344C22×C3×C4—91no—
345C22×C3×C4—91no—
346C22×C3×C4—91no—
347C2×#67—34no—
348C2×#67—34no—
349C2×#67—94no—
350C2×#67—91no—
351C2×#67C2×C3⋊D311yescharacteristic
352C2×#67C2×C3⋊D311yescharacteristic
353C22×Dic3—34no—
354C22×Dic3—34no—
355C22×Dic3—94no—
356C22×Dic3—94no—
357C22×Dic3—91no—
358C22×Dic3—91no—
359C22×Dic3—91no—
360C22×Dic3—184no—
361C22×Dic3C2×C3⋊D311yescharacteristic
362#237—616no—
363#237—184no—
364#237—1816no—
365C2×C4×D3—34no—
366C2×C4×D3—94no—
367C2×C4×D3—94no—
368C2×C4×D3—91no—
369C2×Dic6—34no—
370C2×Dic6—94no—
371C2×Dic6—91no—
372C3×C4⋊C4—34no—
373C3×C22⋊C4—34no—
374C3×C22⋊C4—34no—
375#217—94no—
376#217—94no—
377#217—94no—
378#217—94no—
379#217—94no—
380#217—91no—
381#217—91no—
382#217—91no—
383#217—91no—
384#217—184no—
385#217—184no—
386#217—184no—
387#217C2×C3⋊D311yescharacteristic
388(C2×D3)⋊C4—94no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
392C4⋊Dic3—94no—
393C4⋊Dic3—94no—
394C4⋊Dic3—94no—
395C4⋊Dic3—94no—
396C4⋊Dic3—91no—
397Dic3⋊C4—94no—
398Dic3⋊C4—94no—
399Dic3⋊C4—94no—
400Dic3⋊C4—94no—
401Dic3⋊C4—94no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—184no—
411Dic3⋊C4—184no—
412Dic3⋊C4C2×C3⋊D311yescharacteristic
413C4×Dic3—94no—
414C4×Dic3—91no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—24no—
421C22×C32—28no—
422C22×C32—24no—
423C22×C32—24no—
424C22×C32—24no—
425C22×C32—24no—
426C22×C32—24no—
427C22×C32—44no—
428C22×C32—44no—
429C22×C32—44no—
430C22×C32—44no—
431C22×C32—44no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32—61no—
435C22×C32D3×D418yes—
436C22×C32C2×#6712yes—
437C22×C32C23×D314yes—
438C22×C32C23×D311yescharacteristic
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3C2×#6712yes—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
444C2×C3×D3—24no—
445C2×C3×D3—38no—
446C2×C3×D3—64no—
447C2×C3×D3—64no—
448C32×C4—21no—
449C32×C4—24no—
450C32×C4—32no—
451C32×C4—44no—
452C32×C4—61no—
453C32×C4—61no—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3—61no—
457C3⋊Dic3—61no—
458C3⋊Dic3—61no—
459C3⋊Dic3—61no—
460C3⋊Dic3—64no—
461C3⋊Dic3—64no—
462C3⋊Dic3—64no—
463C3⋊Dic3—64no—
464C3⋊Dic3—124no—
465C3⋊Dic3—124no—
466C3⋊Dic3—124no—
467C3⋊Dic3—124no—
468C3⋊Dic3C2×#6712yes—
469C3×Dic3—24no—
470C3×Dic3—24no—
471C3×Dic3—38no—
472C3×Dic3—64no—
473C3×Dic3—64no—
474C3×Dic3#23718yescomplemented
475C2×#41—91no—
476C2×#41—271no—
477C4⋊Q8—271no—
478#123—271no—
479#123—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—271no—
483C22⋊Q8—271no—
484#121—31no—
485#121—271no—
486C4×D4—271no—
487C4×D4—271no—
488C2×C4⋊C4—271no—
489C2×C4⋊C4—271no—
490C33#54711yescharacteristic, complemented, Sylow
491C23×C3—24no—
492C23×C3—24no—
493C23×C3—34no—
494C23×C3—91no—
495C23×C3C2×D3214yes—
496C23×C3C2×D3214yes—
497C23×C3C22×C3⋊D311yescharacteristic
498C23×C3C22×C3⋊D311yescharacteristic
499C22×D3—34no—
500C22×D3C22×C3⋊D311yescharacteristic
501C3×Q8—182no—
502C3×D4—28no—
503C3×D4—22no—
504C3×D4—48no—
505C3×D4—68no—
506C3×D4—68no—
507C3×D4—94no—
508C3×D4—182no—
509C2×C3×C4—24no—
510C2×C3×C4—34no—
511C2×C3×C4—34no—
512C2×C3×C4—34no—
513C2×C3×C4—68no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—182no—
518C2×C3×C4—182no—
519C2×C3×C4—182no—
520C2×C3×C4C2×D3214yes—
521C2×C3×C4C22×C3⋊D311yescharacteristic
522#67—22no—
523#67—22no—
524#67—316no—
525#67—68no—
526#67—182no—
527#67—188no—
528C2×Dic3—22no—
529C2×Dic3—34no—
530C2×Dic3—34no—
531C2×Dic3—34no—
532C2×Dic3—68no—
533C2×Dic3—68no—
534C2×Dic3—94no—
535C2×Dic3—94no—
536C2×Dic3—94no—
537C2×Dic3—94no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—184no—
543C2×Dic3—184no—
544C2×Dic3—184no—
545C2×Dic3—184no—
546C2×Dic3—182no—
547C2×Dic3—188no—
548C2×Dic3—188no—
549C2×Dic3—182no—
550C2×Dic3—182no—
551C2×Dic3—368no—
552C2×Dic3C22×C3⋊D311yescharacteristic
553C2×Dic3C22×C3⋊D311yescharacteristic
554C2×Dic3C22×C3⋊D311yescharacteristic
555C4×D3—68no—
556C4×D3—188no—
557C4×D3—188no—
558C4×D3—182no—
559Dic6—68no—
560Dic6—182no—
561Dic6—188no—
562C2×C32—22no—
563C2×C32—24no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—28no—
567C2×C32—48no—
568C2×C32—41no—
569C2×C32—44no—
570C2×C32—84no—
571C2×C32—121no—
572C2×C32C2×D3×D414yes—
573C2×C32C2×#23714yes—
574C2×C32D3×#4111yescharacteristic
575C2×C32#101014yes—
576C2×C32#101011yescharacteristic
577C2×C32C22×#6711yescharacteristic
578C3⋊D3—22no—
579C3×D3—44no—
580C3×D3—68no—
581#41—184no—
582#41—544no—
583C2×Q8—91no—
584C2×Q8—271no—
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—271no—
590C2×D4D3×C3⋊D311yescharacteristic
591C22×C4—31no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C22×C4—271no—
599C4⋊C4—31no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C4⋊C4—271no—
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C42—271no—
618C22×C3—24no—
619C22×C3—24no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—24no—
629C22×C3—28no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—64no—
636C22×C3—64no—
637C22×C3—64no—
638C22×C3—92no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3D3×#6718yes—
642C22×C3D4×C3⋊D312yes—
643C22×C3C22×D3214yes—
644C22×C3C23×C3⋊D311yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—38no—
649C2×D3—64no—
650C2×D3—64no—
651C3×C4—24no—
652C3×C4—21no—
653C3×C4—38no—
654C3×C4—44no—
655C3×C4—64no—
656C3×C4—64no—
657C3×C4—92no—
658C3×C4—181no—
659C3×C4—181no—
660Dic3—21no—
661Dic3—21no—
662Dic3—38no—
663Dic3—64no—
664Dic3—64no—
665Dic3—184no—
666Dic3—184no—
667Dic3—184no—
668Dic3—184no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—364no—
674Dic3—364no—
675Dic3—364no—
676Dic3—364no—
677Dic3#383012yescomplemented
678C32—24no—
679C32#561114yescomplemented
680C32#582411yescharacteristic, complemented
681C23—31no—
682C23—91no—
683C23C2×D3×C3⋊D311yescharacteristic
684C23C2×D3×C3⋊D311yescharacteristic
685Q8—182no—
686Q8—542no—
687D4—22no—
688D4—62no—
689D4—62no—
690D4—94no—
691D4—182no—
692D4—542no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—62no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—182no—
701C2×C4—182no—
702C2×C4—182no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4—542no—
710C2×C4—542no—
711C2×C4C2×D3×C3⋊D311yescharacteristic
712C2×C3—28no—
713C2×C3—22no—
714C2×C3—24no—
715C2×C3—24no—
716C2×C3—24no—
717C2×C3—48no—
718C2×C3—44no—
719C2×C3—41no—
720C2×C3—84no—
721C2×C3—124no—
722C2×C3—182no—
723C2×C3#6430914yes—
724C2×C3D3×#23714yes—
725C2×C3C2×D3×#6714yes—
726C2×C3C2×D4×C3⋊D311yescharacteristic
727C2×C3C2×#383011yescharacteristic
728C2×C3#6436711yescharacteristic
729D3—41no—
730D3—68no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—92no—
740C22—181no—
741C22—181no—
742C22C3⋊D3×#6712yes—
743C22C22×D3×C3⋊D311yescharacteristic
744C4—21no—
745C4—32no—
746C4—61no—
747C4—61no—
748C4—92no—
749C4—181no—
750C4—181no—
751C4—541no—
752C4—541no—
753C4—541no—
754C4—541no—
755C3—24no—
756C3#1059515114yescomplemented
757C3#1059608211yescharacteristic, complemented
758C2—22no—
759C2—41no—
760C2—121no—
761C2—182no—
762C2#1172458211yescharacteristic
763C2D3×#383011yescharacteristic
764C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×#89029C2semidirect
3. #11723976C2semidirect
4. C32×#939C2semidirect
5. #11723641C2semidirect
6. #11723631C2semidirect
7. #11723621C2semidirect
8. #67×C3⋊Dic3C2semidirect
9. Dic3×#638C2semidirect
10. C2×Dic3⋊(C3⋊Dic3)C2semidirect
11. #11723602C2semidirect
12. #11723518C2semidirect
13. #11723487C2semidirect
14. C3⋊D3×Dic3⋊C4C2semidirect
15. #11723394C2semidirect
56. C2×#3830D3semidirect
74. C3×#939D3semidirect
98. C3×#638D4semidirect
223. C32×Dic3#41semidirect
232. #939C3⋊D3semidirect
279. #638#67semidirect
474. C3×Dic3#237semidirect
490. C33#547semidirect
677. Dic3#3830semidirect
679. C32#5611semidirect
680. C32#5824semidirect
756. C3#10595151semidirect
757. C3#10596082semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×#890292
#117239762
C32×#9392
#117236412
#117236312
#117236212
#67×C3⋊Dic32
Dic3×#6382
C2×Dic3⋊(C3⋊Dic3)2
#117236022
#117235182
#117234872
C3⋊D3×Dic3⋊C42
#117233942
#105960823
#105951513