Finite Group Databasebeta

← #11812857

Subgroups — #11812857

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic
2C2×#63897C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C2×#63883C211yesmaximal, characteristic, complemented
5C3×#4981C211yesmaximal, characteristic, complemented
6C3×#4978C211yesmaximal, characteristic, complemented
7#10591380C211yesmaximal, characteristic, complemented
8#10591380C211yesmaximal, characteristic, complemented
9#10591380C211yesmaximal, characteristic, complemented
10#10591375C211yesmaximal, characteristic, complemented
11#10591350C211yesmaximal, characteristic, complemented
12#10591321C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591208C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#77951—31nomaximal
17#75319—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28#64104—24no—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46#63897—24no—
47#63894—24no—
48#63883—24no—
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#895—31no—
58C2×#895—31no—
59C2×#895—61no—
60C2×#894—31no—
61C2×#894—31no—
62C2×#893—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C2×C4×D12—31no—
66C3×#398—31no—
67C3×#387—31no—
68#4993—31no—
69#4991—31no—
70#4989—31no—
71#4981D311yescharacteristic, complemented
72#4978D311yescharacteristic, complemented
73#4940—31no—
74#4677—31no—
75#4675—31no—
76#4674—31no—
77#4672—31no—
78#4670—31no—
79#4668—31no—
80#4668—31no—
81#4668—31no—
82#4665—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86#4665—31no—
87#4665—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—22no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)D414yes—
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—41no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—41no—
123C2×#624—41no—
124C32×C4⋊C4—22no—
125#3752—22no—
126#3752—22no—
127C3×C4⋊Dic3—22no—
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4D414yescomplemented
131C3×C4×Dic3—22no—
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—41no—
135#3722—22no—
136#3722—22no—
137#3722—22no—
138#3722—22no—
139#3722—22no—
140#3722—22no—
141#3722—22no—
142#3722—22no—
143#3722—41no—
144#2443—91noSylow
145C22×D12—31no—
146C22×D12—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—61no—
152C22×D12—61no—
153C22×D12—61no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—61no—
163C2×C3×C4⋊C4—21no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4C2×D311yescharacteristic
169C2×C3×C4⋊C4C2×D311yescharacteristic
170C2×C3×C42—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—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—61no—
194C2×(C2×D3)⋊C4—61no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3C2×D311yescharacteristic
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×C4×Dic3C2×D311yescharacteristic
206#895—64no—
207#895—64no—
208#895—68no—
209#894—64no—
210#894—64no—
211#893—64no—
212D3×C4⋊C4—64no—
213D3×C4⋊C4—64no—
214C4×D12—64no—
215C3×#95—31no—
216C3×#95—31no—
217C3×#95—31no—
218C3×#95—31no—
219C3×#95—31no—
220C3×#95—31no—
221C3×#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95C2×D311yescharacteristic
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C23×C32C2411yescharacteristic
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3C2×D412yes—
250C22×C3⋊D3C2×D412yes—
251C22×C3⋊D3#4112yes—
252C22×C3⋊D3#4112yes—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2×D412yes—
261C2×C32×C4C2×D412yes—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C4⋊(C3⋊D3)—28no—
266C4⋊(C3⋊D3)—44no—
267C4⋊(C3⋊D3)—44no—
268C4×C3⋊D3—44no—
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×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3#4112yes—
293#624—28no—
294#624—44no—
295#624—44no—
296C2×#123—91no—
297C2×#121—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300#399—91no—
301#398—31no—
302#397—91no—
303#394—91no—
304#388—91no—
305#387—31no—
306#386—91no—
307#386—91no—
308#386—91no—
309#385—91no—
310#385—91no—
311C23×D3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—31no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—61no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—61no—
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C2×D12—34no—
349C2×D12—34no—
350C2×D12—64no—
351C2×D12—62no—
352C2×D12—62no—
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—62no—
363C2×D12—64no—
364C2×D12—64no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—122no—
368C2×D12—122no—
369C2×D12—122no—
370C2×D12—122no—
371C2×D12—122no—
372C2×D12—121no—
373C2×D12—121no—
374C2×D12—122no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—64no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—122no—
395C2×C4×D3—121no—
396C2×C4×D3—121no—
397C2×C4×D3—121no—
398C2×C4×D3—121no—
399C2×C4×D3—121no—
400C2×C4×D3—121no—
401C2×C4×D3—122no—
402C3×C4⋊C4—24no—
403C3×C4⋊C4—22no—
404C3×C4⋊C4—22no—
405C3×C4⋊C4—34no—
406C3×C4⋊C4—62no—
407C3×C4⋊C4—62no—
408C3×C4⋊C4—62no—
409C3×C42—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—62no—
422(C2×D3)⋊C4—62no—
423(C2×D3)⋊C4—64no—
424(C2×D3)⋊C4—64no—
425(C2×D3)⋊C4—62no—
426(C2×D3)⋊C4—62no—
427(C2×D3)⋊C4—62no—
428(C2×D3)⋊C4—62no—
429(C2×D3)⋊C4—62no—
430(C2×D3)⋊C4—62no—
431(C2×D3)⋊C4—62no—
432(C2×D3)⋊C4—121no—
433(C2×D3)⋊C4—121no—
434C4⋊Dic3—22no—
435C4⋊Dic3—62no—
436C4⋊Dic3—62no—
437C4⋊Dic3—121no—
438Dic3⋊C4—22no—
439Dic3⋊C4—22no—
440Dic3⋊C4—62no—
441Dic3⋊C4—62no—
442Dic3⋊C4—121no—
443Dic3⋊C4D1214yescomplemented
444C4×Dic3—22no—
445C22×C32C22×D411yescharacteristic
446C22×C32C22×D411yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C22×C32C2×#4111yescharacteristic
450C22×C32H(5,𝔽2)11yescharacteristic
451C22×C322−1+411yescharacteristic
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—22no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3—22no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3#12314yescomplemented
473C32×C4—22no—
474C32×C4—22no—
475C32×C4—41no—
476C3⋊Dic3—41no—
477C3×Dic3—22no—
478C3×Dic3—22no—
479C3×Dic3—22no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C22×D4—91no—
486C22×D4—91no—
487C22×D4—91no—
488C23×C4—91no—
489C23×C4—91no—
490C23×C4—91no—
491C23×C4—91no—
492#123—184no—
493#121—184no—
494C4×D4—184no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—184no—
503C2×C4⋊C4D3211yescharacteristic
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C42—31no—
516#95—31no—
517#95—31no—
518#95—31no—
519#95—31no—
520#95—31no—
521#95—31no—
522#95—31no—
523#95—91no—
524C23×C3—21no—
525C23×C3C23×D311yescharacteristic
526C23×C3C23×D311yescharacteristic
527C22×D3—32no—
528C22×D3—32no—
529C22×D3—32no—
530C22×D3—32no—
531C22×D3—32no—
532C22×D3—32no—
533C22×D3—32no—
534C22×D3—32no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—62no—
560C22×D3—61no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—121no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3—121no—
578C22×D3—121no—
579C22×D3—121no—
580C22×D3—121no—
581C22×D3—121no—
582C22×D3—121no—
583C22×D3—121no—
584C22×D3—121no—
585C22×D3—121no—
586C22×D3—121no—
587C22×D3—121no—
588C22×D3—121no—
589C22×D3—121no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—22no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4C2×D1212yes—
638C2×C3×C4D3×D412yes—
639C2×C3×C4D3×D412yes—
640C2×C3×C4D3×D412yes—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—62no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3C2×D1212yes—
672C2×Dic3C2×D1212yes—
673C2×Dic3#23912yes—
674D12—68no—
675D12—68no—
676D12—128no—
677D12—124no—
678D12—124no—
679D12—128no—
680D12—124no—
681D12—124no—
682D12—128no—
683C4×D3—68no—
684C4×D3—68no—
685C4×D3—124no—
686C4×D3—124no—
687C4×D3—124no—
688C4×D3—124no—
689C4×D3—124no—
690C4×D3—124no—
691C4×D3—128no—
692C2×C32C2×#12311yescharacteristic
693C2×C32#52511yescharacteristic
694C2×C32#53911yescharacteristic
695C2×C32D4211yescharacteristic
696C2×C32#54711yescharacteristic
697C2×C32#54811yescharacteristic
698C2×C32#55311yescharacteristic
699C3⋊D3—24no—
700C3⋊D3—42no—
701C3⋊D3—81no—
702C24—91no—
703C24—91no—
704C24—91no—
705C2×D4—94no—
706C2×D4—182no—
707C2×D4—182no—
708C2×D4—182no—
709C2×D4—182no—
710C2×D4—182no—
711C2×D4—182no—
712C2×D4—182no—
713C2×D4—361no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—91no—
723C22×C4—182no—
724C22×C4—182no—
725C22×C4—182no—
726C22×C4—182no—
727C22×C4—182no—
728C22×C4—182no—
729C22×C4—182no—
730C22×C4—182no—
731C22×C4—182no—
732C22×C4—361no—
733C22×C4—361no—
734C22×C4—361no—
735C22×C4C2×D3211yescharacteristic
736C22×C4C2×D3211yescharacteristic
737C22×C4C2×D3211yescharacteristic
738C4⋊C4—22no—
739C4⋊C4—34no—
740C4⋊C4—62no—
741C4⋊C4—62no—
742C4⋊C4—62no—
743C4⋊C4—182no—
744C4⋊C4—182no—
745C4⋊C4—361no—
746C22⋊C4—182no—
747C22⋊C4—182no—
748C22⋊C4—182no—
749C22⋊C4—182no—
750C22⋊C4—182no—
751C22⋊C4—182no—
752C22⋊C4—182no—
753C22⋊C4—182no—
754C22⋊C4—182no—
755C22⋊C4—182no—
756C22⋊C4—361no—
757C42—62no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3C22×D1211yescharacteristic
766C22×C3C2×D3×D411yescharacteristic
767C22×C3C2×D3×D411yescharacteristic
768C22×C3C2×D3×D411yescharacteristic
769C22×C3C2×#23911yescharacteristic
770C22×C3#100711yescharacteristic
771C22×C3#100711yescharacteristic
772C22×C3D3×#4111yescharacteristic
773C22×C3D3×#4111yescharacteristic
774C22×C3D3×#4111yescharacteristic
775C22×C3D3×#4111yescharacteristic
776C22×C3D3×#4111yescharacteristic
777C22×C3#100911yescharacteristic
778C22×C3#100911yescharacteristic
779C2×D3—34no—
780C2×D3—34no—
781C2×D3—64no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—62no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—122no—
801C2×D3—122no—
802C2×D3—122no—
803C2×D3—122no—
804C2×D3—122no—
805C2×D3—122no—
806C2×D3—122no—
807C2×D3—122no—
808C2×D3—122no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—121no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—122no—
818C2×D3—122no—
819C2×D3—122no—
820C2×D3—121no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—241no—
835C2×D3—241no—
836C2×D3—241no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—241no—
841C2×D3—241no—
842C3×C4—24no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—42no—
848C3×C4—42no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—62no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—121no—
855C3×C4—121no—
856C3×C4—121no—
857C3×C4—121no—
858C3×C4—121no—
859Dic3—22no—
860Dic3—22no—
861Dic3—22no—
862Dic3—41no—
863Dic3—41no—
864Dic3—41no—
865Dic3—41no—
866Dic3—41no—
867Dic3—122no—
868Dic3—121no—
869Dic3—121no—
870C32#244311yescharacteristic, complemented, Sylow
871C23—92no—
872C23—92no—
873C23—92no—
874C23—92no—
875C23—181no—
876C23—181no—
877C23—181no—
878C23—181no—
879C23—181no—
880C23—181no—
881C23—181no—
882C23—181no—
883C23—181no—
884C23—181no—
885C23—181no—
886C23—181no—
887C23—181no—
888C23—181no—
889C23—181no—
890C23—181no—
891C23—181no—
892C23C22×D3211yescharacteristic
893D4—188no—
894D4—364no—
895D4—364no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—188no—
928C2×C4—181no—
929C2×C4—181no—
930C2×C4—181no—
931C2×C4—364no—
932C2×C4—364no—
933C2×C4—364no—
934C2×C4D3×D1212yes—
935C2×C4#381112yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3#552411yescharacteristic
944C2×C3D4×D1211yescharacteristic
945C2×C3#557611yescharacteristic
946C2×C3#560911yescharacteristic
947C2×C3#562711yescharacteristic
948C2×C3#563111yescharacteristic
949C2×C3#563311yescharacteristic
950C2×C3D3×#12311yescharacteristic
951C2×C3D3×#12311yescharacteristic
952C2×C3#569211yescharacteristic
953C2×C3#569211yescharacteristic
954C2×C3#569511yescharacteristic
955C2×C3#570911yescharacteristic
956C2×C3#572611yescharacteristic
957D3—64no—
958D3—64no—
959D3—124no—
960D3—122no—
961D3—122no—
962D3—242no—
963D3—242no—
964D3—241no—
965D3—241no—
966C22—94no—
967C22—182no—
968C22—182no—
969C22—182no—
970C22—182no—
971C22—182no—
972C22—182no—
973C22—182no—
974C22—182no—
975C22—182no—
976C22—361no—
977C22—361no—
978C22—361no—
979C22—361no—
980C22—361no—
981C22—361no—
982C22—361no—
983C22—361no—
984C22—361no—
985C22—361no—
986C22—361no—
987C22C2×D3×D1211yescharacteristic
988C22#6430811yescharacteristic
989C22#6431211yescharacteristic
990C22#6431211yescharacteristic
991C22#6431611yescharacteristic
992C22D3×#23911yescharacteristic
993C22C2×#381111yescharacteristic
994C4—22no—
995C4—22no—
996C4—41no—
997C4—62no—
998C4—62no—
999C4—62no—
1000C4—121no—
1001C4—121no—
1002C4—121no—
1003C4—121no—
1004C4—121no—
1005C4—361no—
1006C3—21no—
1007C3#7531911yescharacteristic, complemented
1008C3#7795111yescharacteristic, complemented
1009C2—184no—
1010C2—362no—
1011C2—721no—
1012C2#1059432911yescharacteristic
1013C2#1059446811yescharacteristic
1014C2#1059448311yescharacteristic
1015C2#1059462711yescharacteristic
1016C2#1059507411yescharacteristic
1017C2#1059516911yescharacteristic
1018C2#1059534111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#64104C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2443
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×#63897C2semidirect
3. C2×#63894C2semidirect
4. C2×#63883C2semidirect
5. C3×#4981C2semidirect
6. C3×#4978C2semidirect
7. #10591380C2semidirect
8. #10591380C2semidirect
9. #10591380C2semidirect
10. #10591375C2semidirect
11. #10591350C2semidirect
12. #10591321C2semidirect
13. #10591290C2semidirect
14. #10591208C2semidirect
15. #10591194C2semidirect
71. #4981D3semidirect
72. #4978D3semidirect
130. C3×Dic3⋊C4D4semidirect
443. Dic3⋊C4D12semidirect
472. C2×C3⋊D3#123semidirect
870. C32#2443semidirect
1007. C3#75319semidirect
1008. C3#77951semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#638972
C2×#638942
C2×#638832
C3×#49812
C3×#49782
#105913802
#105913752
#105913502
#105913212
#105912902
#105912082
#105911942
#779513
#753193