Finite Group Databasebeta

← #11813005

Subgroups — #11813005

Order 1152.

1339 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63909C211yesmaximal, characteristic
2C2×#63880C211yesmaximal, characteristic, complemented
3#10592690C211yesmaximal, characteristic, complemented
4C3×#4989C211yesmaximal, characteristic, complemented
5C3×#4980C211yesmaximal, characteristic, complemented
6#10591380C211yesmaximal, characteristic, complemented
7#10591371C211yesmaximal, characteristic, complemented
8#10591364C211yesmaximal, characteristic, complemented
9#10591364C211yesmaximal, characteristic, complemented
10#10591364C211yesmaximal, characteristic, complemented
11D3×C3⋊#95C211yesmaximal, characteristic, complemented
12#10591343C211yesmaximal, characteristic, complemented
13#10591289C211yesmaximal, characteristic, complemented
14#10591208C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#75320—31nomaximal
17#74419—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41#63909—24no—
42#63880—24no—
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#930—31no—
56C2×#895—31no—
57C2×#67⋊C4—31no—
58C2×C4×D12—31no—
59C3×#387—31no—
60C3×#385—31no—
61C2×C3⋊#95—31no—
62#4992—31no—
63#4991—31no—
64#4991—31no—
65#4991—61no—
66#4990—31no—
67#4989D311yescharacteristic, complemented
68#4986—31no—
69#4980D311yescharacteristic, complemented
70#4958—31no—
71#4958—31no—
72#4958—31no—
73#4940—31no—
74#4675—31no—
75#4675—31no—
76#4674—31no—
77#4665—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4665—31no—
82#4664—31no—
83#4664—31no—
84D3×#95—31no—
85#4660—31no—
86C23×C3⋊D3C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—41no—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—41no—
107C2×#626—22no—
108C2×#626—22no—
109C2×#626—22no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#626D414yes—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—41no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3—41no—
122C32×C4⋊C4—22no—
123#3752—22no—
124#3752—41no—
125#3752—41no—
126#3752—41no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×C4⋊Dic3—22no—
130C3×Dic3⋊C4—41no—
131C3×C4×Dic3—22no—
132Dic3⋊Dic3—22no—
133#3722—22no—
134#3722—22no—
135#3722—22no—
136#3722—41no—
137#3722—41no—
138#2444—91noSylow
139C23×C3×C4—31no—
140C22×#67—31no—
141C22×#67—31no—
142C23×Dic3—31no—
143C23×Dic3—31no—
144C22×D12—31no—
145C22×D12—31no—
146C22×D12—31no—
147C22×D12—31no—
148C22×D12—61no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3C2×D311yescharacteristic
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4C2×D311yescharacteristic
158C2×C3×C4⋊C4C2×D311yescharacteristic
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C42—31no—
162#930—64no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—61no—
182C2×(C2×D3)⋊C4—61no—
183C2×(C2×D3)⋊C4—61no—
184C2×(C2×D3)⋊C4—61no—
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3C2×D311yescharacteristic
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4C2×D311yescharacteristic
191C2×C4×Dic3C2×D311yescharacteristic
192#895—64no—
193#67⋊C4—64no—
194C4×D12—64no—
195C3×#95—31no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—61no—
214C3⋊#95C2×D311yescharacteristic
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C23×C32C2411yescharacteristic
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3C2×D412yes—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D412yes—
240C22×C3×D3#4112yes—
241C22×C3×D3#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4#4112yes—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C4⋊(C3⋊D3)—44no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D412yes—
278C2×C3×Dic3#4112yes—
279C3×C4×D3—44no—
280#626—28no—
281#626—44no—
282#624—44no—
283D3×Dic3—44no—
284D3×Dic3—44no—
285C2×#121—91no—
286C2×C4×D4—91no—
287#400—91no—
288#397—91no—
289#397—91no—
290#394—91no—
291#388—91no—
292#387—31no—
293#386—91no—
294#386—91no—
295#386—91no—
296#386—91no—
297#385—31no—
298#381—91no—
299C2×#95—91no—
300C24×C3—31no—
301C23×D3—31no—
302C23×D3—31no—
303C23×D3—31no—
304C23×D3—31no—
305C23×D3—61no—
306C23×D3—61no—
307C23×D3C22×D311yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—62no—
319C22×C3×C4—62no—
320C22×C3×C4—121no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—34no—
328C2×#67—62no—
329C2×#67—62no—
330C2×#67—62no—
331C2×#67—62no—
332C2×#67—62no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—62no—
340C22×Dic3—62no—
341C22×Dic3—62no—
342C22×Dic3—121no—
343C22×Dic3—121no—
344C22×Dic3—121no—
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C2×D12—34no—
353C2×D12—62no—
354C2×D12—62no—
355C2×D12—62no—
356C2×D12—62no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—62no—
360C2×D12—62no—
361C2×D12—62no—
362C2×D12—122no—
363C2×D12—122no—
364C2×D12—121no—
365C2×D12—121no—
366C2×D12—122no—
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—41no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—42no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—121no—
387C3×C22⋊C4—62no—
388C3×C22⋊C4—62no—
389C3×C42—62no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—122no—
401(C2×D3)⋊C4—121no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4—121no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—121no—
408(C2×D3)⋊C4—121no—
409(C2×D3)⋊C4—121no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—122no—
412(C2×D3)⋊C4—122no—
413(C2×D3)⋊C4—122no—
414C4⋊Dic3—22no—
415C4⋊Dic3—62no—
416Dic3⋊C4—41no—
417Dic3⋊C4—62no—
418C4×Dic3—22no—
419C22×C32C22×D411yescharacteristic
420C22×C32C2×#4111yescharacteristic
421C22×C32C2×#4111yescharacteristic
422C22×C32C2×#4111yescharacteristic
423C22×C32C2×#4111yescharacteristic
424C22×C32H(5,𝔽2)11yescharacteristic
425C22×C32H(5,𝔽2)11yescharacteristic
426C2×C3⋊D3—22no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—22no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—41no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3#12314yes—
447C32×C4—22no—
448C32×C4—41no—
449C32×C4—41no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C22×D4—91no—
460C22×D4—91no—
461C22×D4—91no—
462C23×C4—31no—
463C23×C4—91no—
464C23×C4—91no—
465C23×C4—91no—
466#121—184no—
467C4×D4—184no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4D3211yescharacteristic
472C2×C22⋊C4—31no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C22⋊C4—91no—
481C2×C22⋊C4—91no—
482C2×C22⋊C4—91no—
483C2×C42—31no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—31no—
489#95—31no—
490#95—91no—
491#95—91no—
492#95—91no—
493#95—91no—
494#95—91no—
495#95—91no—
496C23×C3—21no—
497C23×C3—32no—
498C23×C3—32no—
499C23×C3—32no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3C23×D311yescharacteristic
505C23×C3C23×D311yescharacteristic
506C22×D3—21no—
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—32no—
511C22×D3—32no—
512C22×D3—62no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—62no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—121no—
542C22×D3—121no—
543C22×D3—121no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—121no—
550C22×D3—121no—
551C22×D3—121no—
552C22×D3#23512yes—
553C22×D3D3×D412yes—
554C22×D3#23912yes—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—22no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—124no—
602C2×C3×C4#23512yes—
603C2×C3×C4#23712yes—
604#67—68no—
605#67—124no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—121no—
638C2×Dic3—121no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—124no—
644C2×Dic3—124no—
645C2×Dic3D3×D412yes—
646C2×Dic3#23912yes—
647D12—68no—
648D12—124no—
649D12—124no—
650D12—128no—
651D12—124no—
652C4×D3—44no—
653C4×D3—124no—
654C4×D3—124no—
655C4×D3—124no—
656C4×D3—124no—
657C2×C32C2×#12311yescharacteristic
658C2×C32#52911yescharacteristic
659C2×C32#53811yescharacteristic
660C2×C32#54611yescharacteristic
661C2×C32#54611yescharacteristic
662C2×C32#55311yescharacteristic
663C2×C32#55311yescharacteristic
664C3⋊D3—42no—
665C3⋊D3—81no—
666C3×D3—24no—
667C24—31no—
668C24—91no—
669C24—91no—
670C2×D4—94no—
671C2×D4—182no—
672C2×D4—182no—
673C2×D4—182no—
674C2×D4—182no—
675C2×D4—182no—
676C2×D4—182no—
677C2×D4—182no—
678C2×D4—361no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—121no—
691C22×C4—182no—
692C22×C4—182no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—361no—
697C22×C4—361no—
698C22×C4—361no—
699C22×C4—361no—
700C22×C4C2×D3211yescharacteristic
701C22×C4C2×D3211yescharacteristic
702C22×C4C2×D3211yescharacteristic
703C4⋊C4—22no—
704C4⋊C4—62no—
705C4⋊C4—121no—
706C4⋊C4—182no—
707C22⋊C4—62no—
708C22⋊C4—62no—
709C22⋊C4—182no—
710C22⋊C4—182no—
711C22⋊C4—182no—
712C22⋊C4—182no—
713C22⋊C4—361no—
714C22⋊C4—361no—
715C22⋊C4—361no—
716C22⋊C4—361no—
717C22⋊C4—361no—
718C42—62no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—34no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3C2×#23511yescharacteristic
734C22×C3C2×#23511yescharacteristic
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C2×D3×D411yescharacteristic
737C22×C3C2×#23711yescharacteristic
738C22×C3#100411yescharacteristic
739C22×C3C2×#23911yescharacteristic
740C22×C3C2×#23911yescharacteristic
741C22×C3D3×#4111yescharacteristic
742C22×C3D3×#4111yescharacteristic
743C22×C3D3×#4111yescharacteristic
744C22×C3#100911yescharacteristic
745C22×C3#100911yescharacteristic
746C22×C3#100911yescharacteristic
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—122no—
771C2×D3—122no—
772C2×D3—122no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—241no—
791C2×D3—241no—
792C2×D3—241no—
793C2×D3—241no—
794C2×D3—241no—
795C2×D3#89414yes—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—42no—
799C3×C4—42no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—81no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4—121no—
811C3×C4—121no—
812Dic3—22no—
813Dic3—22no—
814Dic3—41no—
815Dic3—41no—
816Dic3—41no—
817Dic3—41no—
818Dic3—41no—
819Dic3—121no—
820Dic3—121no—
821Dic3—121no—
822Dic3—121no—
823Dic3—241no—
824Dic3—241no—
825C32#244411yescharacteristic, complemented, Sylow
826C23—32no—
827C23—32no—
828C23—32no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—92no—
834C23—181no—
835C23—181no—
836C23—181no—
837C23—181no—
838C23—181no—
839C23—181no—
840C23—181no—
841C23—181no—
842C23—181no—
843C23—181no—
844C23—181no—
845C23—181no—
846C23—181no—
847C23C22×D3211yescharacteristic
848D4—188no—
849D4—364no—
850D4—364no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—124no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—364no—
888C2×C4—364no—
889C2×C4—364no—
890C2×C4#380412yes—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—64no—
899C2×C3C2×#89411yescharacteristic
900C2×C3#553011yescharacteristic
901C2×C3#554011yescharacteristic
902C2×C3#555011yescharacteristic
903C2×C3#556511yescharacteristic
904C2×C3#558011yescharacteristic
905C2×C3#559111yescharacteristic
906C2×C3#562411yescharacteristic
907C2×C3#563011yescharacteristic
908C2×C3#564411yescharacteristic
909C2×C3D3×#12311yescharacteristic
910C2×C3#565411yescharacteristic
911C2×C3#569511yescharacteristic
912C2×C3#570411yescharacteristic
913D3—24no—
914D3—122no—
915D3—122no—
916D3—242no—
917D3—242no—
918D3—241no—
919D3—241no—
920C22—34no—
921C22—62no—
922C22—62no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—182no—
928C22—182no—
929C22—182no—
930C22—361no—
931C22—361no—
932C22—361no—
933C22—361no—
934C22—361no—
935C22—361no—
936C22—361no—
937C22—361no—
938C22—361no—
939C22—361no—
940C22—361no—
941C22D3×#23511yescharacteristic
942C22#6430811yescharacteristic
943C22D32×D411yescharacteristic
944C22#6431411yescharacteristic
945C22D3×#23911yescharacteristic
946C22D3×#23911yescharacteristic
947C22C2×#380411yescharacteristic
948C4—22no—
949C4—41no—
950C4—41no—
951C4—62no—
952C4—62no—
953C4—121no—
954C4—121no—
955C4—121no—
956C4—121no—
957C4—121no—
958C4—361no—
959C4—361no—
960C3—21no—
961C3#7441911yescharacteristic, complemented
962C3#7532011yescharacteristic, complemented
963C2—64no—
964C2—362no—
965C2—721no—
966C2#1059441511yescharacteristic
967C2D3×#89411yescharacteristic
968C2#1059462011yescharacteristic
969C2#1059465211yescharacteristic
970C2#1059494611yescharacteristic
971C2#1059513511yescharacteristic
972C2#1059537611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63909C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63880C2semidirect
3. #10592690C2semidirect
4. C3×#4989C2semidirect
5. C3×#4980C2semidirect
6. #10591380C2semidirect
7. #10591371C2semidirect
8. #10591364C2semidirect
9. #10591364C2semidirect
10. #10591364C2semidirect
11. D3×C3⋊#95C2semidirect
12. #10591343C2semidirect
13. #10591289C2semidirect
14. #10591208C2semidirect
15. #10591204C2semidirect
67. #4989D3semidirect
69. #4980D3semidirect
825. C32#2444semidirect
961. C3#74419semidirect
962. C3#75320semidirect

Maximal subgroups

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

subgroupindex
C2×#639092
C2×#638802
#105926902
C3×#49892
C3×#49802
#105913802
#105913712
#105913642
D3×C3⋊#952
#105913432
#105912892
#105912082
#105912042
#753203
#744193