Finite Group Databasebeta

← #11805672

Subgroups — #11805672

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic, complemented
3C2×#63849C211yesmaximal, characteristic, complemented
4C3×#4936C211yesmaximal, characteristic, complemented
5C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
6#10591380C212yesmaximal
7#10591325C211yesmaximal, characteristic, complemented
8#10591325C211yesmaximal, characteristic, complemented
9#10591271C212yesmaximal, complemented
10#10591233C212yesmaximal, complemented
11#10591202C212yesmaximal, complemented
12#74229—31nomaximal
13#73771—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#624C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C418yescomplemented
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×#3724C2212yes—
29C2×#3722C2212yes—
30C2×#3722C2212yes—
31C2×#3722C2212yes—
32C2×Dic32C2212yes—
33#63900—24no—
34#63849—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×#892—31no—
41C2×#892—31no—
42C2×D3×C4⋊C4—31no—
43C2×D3×C4⋊C4—31no—
44C2×C4×D12—31no—
45C2×C4×D12—31no—
46C2×C4×D12—61no—
47C3×#382—31no—
48C3×C4×C4⋊C4—31no—
49#4987—31no—
50#4987—31no—
51#4987—31no—
52#4987—31no—
53#4940—32no—
54C4×(C2×D3)⋊C4—32no—
55#4936D311yescharacteristic, complemented
56C4×C4⋊Dic3D311yescharacteristic, complemented
57#4669—32no—
58#4666—32no—
59#4665—32no—
60#4665—32no—
61#4654—32no—
62#4653—32no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)C2×C414yes—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3C2×C414yes—
78C2×C4×C3⋊D3C2×C414yescomplemented
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C2×#624—24no—
84C2×#624—24no—
85C2×#624—42no—
86C32×C42C2×C414yescomplemented
87#3752C2×C414yes—
88#3752C2×C414yescomplemented
89C4⋊(C3⋊Dic3)C2×C414yescomplemented
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3D414yescomplemented
94C3×C4×Dic3—42no—
95#3724—24no—
96#3722—24no—
97#3722—24no—
98#3722—42no—
99Dic32—24no—
100#2352—91noSylow
101C22×D12—31no—
102C22×D12—31no—
103C22×D12—61no—
104C22×C4×D3—31no—
105C22×C4×D3—31no—
106C22×C4×D3—31no—
107C22×C4×D3—31no—
108C22×C4×D3—32no—
109C22×C4×D3—32no—
110C22×C4×D3—61no—
111C22×C4×D3—61no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C42—21no—
117C2×C3×C42—32no—
118C2×C3×C42C2×D311yescharacteristic
119C2×C3×C42C2×D311yescharacteristic
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—61no—
131C2×(C2×D3)⋊C4—61no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3C2×D312yes—
144#892—64no—
145#892—64no—
146D3×C4⋊C4—64no—
147D3×C4⋊C4—64no—
148C4×D12—38no—
149C4×D12—38no—
150C4×D12—68no—
151C3×#95—32no—
152C3×#95—32no—
153C3×#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95C2×D312yes—
159C3⋊#95C2×D312yes—
160C3⋊#95C2×D312yes—
161C23×C32C2411yescharacteristic
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3C22×C412yes—
173C22×C3⋊D3C22×C412yes—
174C22×C3⋊D3#4112yes—
175C22×C3⋊D3#4112yes—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C22×C412yes—
181C2×C32×C4C22×C412yes—
182C2×C32×C4C22×C412yes—
183C2×C32×C4C2×D412yes—
184C2×C32×C4#4112yes—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3C22×C412yes—
190C2×C3⋊Dic3C22×C412yes—
191C4⋊(C3⋊D3)—28no—
192C4×C3⋊D3—28no—
193C4×C3⋊D3—28no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3C2×D414yes—
206#624—48no—
207C2×C4×D4—91no—
208C2×#117—91no—
209C22×C4⋊C4—91no—
210#388—92no—
211#387—92no—
212#386—92no—
213#382—31no—
214#380—91no—
215#380—91no—
216C4×C4⋊C4—31no—
217C4×C22⋊C4—92no—
218C23×D3—31no—
219C23×D3—31no—
220C23×D3—31no—
221C23×D3—31no—
222C23×D3—61no—
223C23×D3—61no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D312yes—
247C2×D12—34no—
248C2×D12—34no—
249C2×D12—64no—
250C2×D12—62no—
251C2×D12—62no—
252C2×D12—62no—
253C2×D12—62no—
254C2×D12—64no—
255C2×D12—64no—
256C2×C4×D3—34no—
257C2×C4×D3—34no—
258C2×C4×D3—34no—
259C2×C4×D3—34no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—122no—
275C2×C4×D3—122no—
276C2×C4×D3—122no—
277C2×C4×D3—122no—
278C2×C4×D3—122no—
279C2×C4×D3—122no—
280C3×C4⋊C4—34no—
281C3×C4⋊C4—62no—
282C3×C4⋊C4—62no—
283C3×C4⋊C4—62no—
284C3×C42—24no—
285C3×C42—122no—
286C3×C42C4×D314yescomplemented
287C3×C42C4×D314yescomplemented
288(C2×D3)⋊C4—34no—
289(C2×D3)⋊C4—34no—
290(C2×D3)⋊C4—34no—
291(C2×D3)⋊C4—34no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4—64no—
298(C2×D3)⋊C4—122no—
299(C2×D3)⋊C4—122no—
300C4⋊Dic3—22no—
301C4⋊Dic3—22no—
302C4⋊Dic3—22no—
303C4⋊Dic3—34no—
304C4⋊Dic3—34no—
305C4⋊Dic3—64no—
306C4⋊Dic3D1214yescomplemented
307Dic3⋊C4—64no—
308Dic3⋊C4—64no—
309C4×Dic3—42no—
310C4×Dic3—64no—
311C4×Dic3—64no—
312C22×C32C23×C411yescharacteristic
313C22×C32C22×D411yescharacteristic
314C22×C32C2×#4111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C22×C32H(5,𝔽2)11yescharacteristic
318C22×C322−1+411yescharacteristic
319C2×C3⋊D3—22no—
320C2×C3⋊D3—22no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3—22no—
325C2×C3⋊D3—22no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—41no—
332C2×C3⋊D3#11714yescomplemented
333C32×C4—22no—
334C32×C4—22no—
335C32×C4C4×D414yes—
336C3⋊Dic3—22no—
337C3⋊Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—42no—
340C3×Dic3—42no—
341C3×Dic3—42no—
342C22×D4—91no—
343C23×C4—92no—
344C23×C4—91no—
345C23×C4—91no—
346C4×D4—98no—
347#117—184no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—91no—
353C2×C4⋊C4—92no—
354C2×C4⋊C4—184no—
355C2×C22⋊C4—91no—
356C2×C22⋊C4—91no—
357C2×C22⋊C4—92no—
358C2×C22⋊C4—92no—
359C2×C22⋊C4—92no—
360C2×C42—32no—
361C2×C42—92no—
362C2×C42D3211yescharacteristic
363#95—32no—
364#95—32no—
365#95—32no—
366#95—92no—
367#95—92no—
368C23×C3—21no—
369C23×C3C23×D311yescharacteristic
370C23×C3C23×D311yescharacteristic
371C22×D3—32no—
372C22×D3—32no—
373C22×D3—32no—
374C22×D3—32no—
375C22×D3—32no—
376C22×D3—32no—
377C22×D3—32no—
378C22×D3—32no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—61no—
386C22×D3—61no—
387C22×D3—61no—
388C22×D3—61no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—61no—
402C22×D3—61no—
403C22×D3—61no—
404C22×D3—61no—
405C22×D3—121no—
406C22×D3—121no—
407C22×D3—121no—
408C22×D3—121no—
409C22×D3—121no—
410C22×D3—121no—
411C22×D3—121no—
412C22×D3—121no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—34no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—62no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4C2×C4×D312yes—
443C2×C3×C4C2×C4×D312yes—
444C2×C3×C4C2×C4×D312yes—
445C2×C3×C4C2×C4×D312yes—
446C2×C3×C4C2×C4×D312yes—
447C2×C3×C4C2×C4×D312yes—
448C2×C3×C4C2×D1212yes—
449C2×C3×C4#23512yes—
450C2×C3×C4D3×D412yes—
451C2×C3×C4#23912yes—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—32no—
464C2×Dic3—32no—
465C2×Dic3—32no—
466C2×Dic3—32no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—121no—
478C2×Dic3—121no—
479C2×Dic3—121no—
480C2×Dic3—121no—
481C2×Dic3C2×D1214yes—
482D12—68no—
483D12—68no—
484D12—616no—
485C4×D3—68no—
486C4×D3—68no—
487C4×D3—68no—
488C4×D3—68no—
489C4×D3—128no—
490C4×D3—128no—
491C4×D3—128no—
492C4×D3—128no—
493C2×C32C2×#11711yescharacteristic
494C2×C32C2×C4×D411yescharacteristic
495C2×C32#52011yescharacteristic
496C2×C32#54611yescharacteristic
497C2×C32#54811yescharacteristic
498C2×C32#55211yescharacteristic
499C2×C32#55311yescharacteristic
500C3⋊D3—24no—
501C3⋊D3—42no—
502C24—91no—
503C24—91no—
504C2×D4—94no—
505C2×D4—182no—
506C2×D4—182no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—91no—
512C22×C4—91no—
513C22×C4—94no—
514C22×C4—94no—
515C22×C4—184no—
516C22×C4—184no—
517C22×C4—182no—
518C22×C4—182no—
519C22×C4—182no—
520C22×C4—182no—
521C22×C4—362no—
522C22×C4C2×D3211yescharacteristic
523C22×C4C2×D3211yescharacteristic
524C22×C4C2×D3211yescharacteristic
525C4⋊C4—34no—
526C4⋊C4—62no—
527C4⋊C4—62no—
528C4⋊C4—62no—
529C4⋊C4—94no—
530C4⋊C4—184no—
531C22⋊C4—94no—
532C22⋊C4—94no—
533C22⋊C4—184no—
534C22⋊C4—184no—
535C22⋊C4—362no—
536C42—122no—
537C42—184no—
538C42#62414yescomplemented
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3C22×C4×D311yescharacteristic
547C22×C3C22×C4×D311yescharacteristic
548C22×C3C22×D1211yescharacteristic
549C22×C3C2×#23511yescharacteristic
550C22×C3C2×D3×D411yescharacteristic
551C22×C3#100411yescharacteristic
552C22×C3C2×#23911yescharacteristic
553C22×C3#100711yescharacteristic
554C22×C3D3×#4111yescharacteristic
555C22×C3D3×#4111yescharacteristic
556C22×C3D3×#4111yescharacteristic
557C22×C3D3×#4111yescharacteristic
558C22×C3#100911yescharacteristic
559C22×C3#101011yescharacteristic
560C2×D3—34no—
561C2×D3—34no—
562C2×D3—64no—
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—62no—
568C2×D3—62no—
569C2×D3—62no—
570C2×D3—62no—
571C2×D3—62no—
572C2×D3—62no—
573C2×D3—62no—
574C2×D3—62no—
575C2×D3—64no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—122no—
583C2×D3—122no—
584C2×D3—122no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—122no—
589C2×D3—122no—
590C2×D3—122no—
591C2×D3—122no—
592C2×D3—122no—
593C2×D3—122no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—121no—
597C2×D3—121no—
598C2×D3—121no—
599C2×D3—121no—
600C2×D3—121no—
601C2×D3—121no—
602C3×C4—24no—
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—24no—
608C3×C4—42no—
609C3×C4—64no—
610C3×C4—122no—
611C3×C4—122no—
612C3×C4—122no—
613C3×C4C4×D1214yes—
614C3×C4#89314yes—
615Dic3—24no—
616Dic3—42no—
617Dic3—42no—
618Dic3—42no—
619Dic3—62no—
620Dic3—62no—
621Dic3—62no—
622Dic3—62no—
623Dic3—122no—
624Dic3—122no—
625C32#235211yescharacteristic, complemented, Sylow
626C23—92no—
627C23—92no—
628C23—92no—
629C23—92no—
630C23—181no—
631C23—181no—
632C23—181no—
633C23—181no—
634C23—181no—
635C23—181no—
636C23—181no—
637C23—181no—
638C23—181no—
639C23—181no—
640C23C22×D3211yescharacteristic
641D4—188no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—34no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—92no—
659C2×C4—92no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—188no—
665C2×C4—188no—
666C2×C4—368no—
667C2×C4#379912yes—
668C2×C4D3×D1212yes—
669C2×C4C2×#62412yes—
670C2×C4C2×#62412yes—
671C2×C4C2×#62412yes—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3C2×C4×D1211yescharacteristic
680C2×C3C2×#89311yescharacteristic
681C2×C3#550411yescharacteristic
682C2×C3D3×#11711yescharacteristic
683C2×C3D3×#11711yescharacteristic
684C2×C3#552311yescharacteristic
685C2×C3#555411yescharacteristic
686C2×C3#555811yescharacteristic
687C2×C3#557611yescharacteristic
688C2×C3#558111yescharacteristic
689C2×C3#567611yescharacteristic
690C2×C3#567711yescharacteristic
691C2×C3#569411yescharacteristic
692C2×C3#569511yescharacteristic
693D3—64no—
694D3—64no—
695D3—124no—
696D3—124no—
697D3—122no—
698D3—122no—
699C22—94no—
700C22—182no—
701C22—182no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—182no—
706C22—182no—
707C22—182no—
708C22—182no—
709C22—361no—
710C22—361no—
711C22—361no—
712C22—361no—
713C22#6429711yescharacteristic
714C22C2×#379911yescharacteristic
715C22C2×D3×D1211yescharacteristic
716C22#6430611yescharacteristic
717C22#6430611yescharacteristic
718C22#6430711yescharacteristic
719C22C22×#62411yescharacteristic
720C4—22no—
721C4—22no—
722C4—64no—
723C4—122no—
724C4—122no—
725C4—122no—
726C4—182no—
727C4—182no—
728C4#6389414yes—
729C3—21no—
730C3#7377111yescharacteristic, complemented
731C3#7422911yescharacteristic, complemented
732C2—184no—
733C2—362no—
734C2#1059390111yescharacteristic
735C2#1059394711yescharacteristic
736C2#1059398211yescharacteristic
737C2#1059400511yescharacteristic
738C2C2×#6389411yescharacteristic
739C2#1059496911yescharacteristic
740C2#1059499011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63900C2semidirect
3. C2×#63849C2semidirect
4. C3×#4936C2semidirect
5. C3×C4×C4⋊Dic3C2semidirect
7. #10591325C2semidirect
8. #10591325C2semidirect
9. #10591271C2semidirect
10. #10591233C2semidirect
11. #10591202C2semidirect
22. C4×C4⋊(C3⋊D3)C4semidirect
55. #4936D3semidirect
56. C4×C4⋊Dic3D3semidirect
78. C2×C4×C3⋊D3C2×C4semidirect
86. C32×C42C2×C4semidirect
88. #3752C2×C4semidirect
89. C4⋊(C3⋊Dic3)C2×C4semidirect
93. C3×C4⋊Dic3D4semidirect
286. C3×C42C4×D3semidirect
287. C3×C42C4×D3semidirect
306. C4⋊Dic3D12semidirect
332. C2×C3⋊D3#117semidirect
538. C42#624semidirect
625. C32#2352semidirect
730. C3#73771semidirect
731. C3#74229semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×#639002
C2×#638492
C3×#49362
C3×C4×C4⋊Dic32
#105913802
#105913252
#105912712
#105912332
#105912022
#742293
#737713