Finite Group Databasebeta

← C2×#10594246 #11902727

Subgroups — C2×#10594246 #11902727

Order 1152.

3685 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#63979C211yesmaximal, characteristic, complemented
7C2×#63979C211yesmaximal, characteristic, complemented
8C2×#63978C211yesmaximal, characteristic, complemented
9C2×#63911C211yesmaximal, characteristic, complemented
10C2×#63910C211yesmaximal, characteristic, complemented
11C2×#63906C211yesmaximal, characteristic, complemented
12C2×#63904C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63881C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594246C2116yesmaximal, direct product factor
17C2×#5599—31nomaximal
18C2×#5553—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic
27C22×C3×D12C2211yescharacteristic
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×C4×D3C2211yescharacteristic
30C22×#627C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic
35C22×#626C2211yescharacteristic
36C22×#626C2211yescharacteristic
37C22×#625C2211yescharacteristic
38C22×#625C2211yescharacteristic
39C22×#624C2211yescharacteristic
40C2×#3804—28no—
41C2×#3804C2218yescomplemented
42C22×D3×Dic3C2211yescharacteristic
43C2×#3798—28no—
44C2×#3798C2218yescomplemented
45C2×C32×C22⋊C4C2211yescharacteristic
46C2×#3752C2211yescharacteristic
47C2×#3750C2211yescharacteristic
48#64093C2218yescomplemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic
51C2×C3×Dic3⋊C4C2211yescharacteristic
52C2×C3×Dic3⋊C4C2211yescharacteristic
53C2×C3×C4×Dic3C2211yescharacteristic
54C3×#884C2218yescomplemented
55C3×#67⋊C4C2218yescomplemented
56#63979C2218yescomplemented
57#63979C2218yescomplemented
58#63978C2218yescomplemented
59C2×Dic3⋊Dic3C2211yescharacteristic
60C2×#3722C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64#63911C2218yescomplemented
65#63910C2218yescomplemented
66#63906C2218yescomplemented
67#63904C2218yescomplemented
68#63885C2218yescomplemented
69#63881C2218yescomplemented
70#63837C2218yescomplemented
71C22×#237—31no—
72C22×#235—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×#121—31no—
76C2×C3×C4×D4—31no—
77C2×#940—31no—
78C2×#940—31no—
79C2×#940—31no—
80C2×#940—31no—
81C2×#940—31no—
82C2×#939—31no—
83C2×#939—31no—
84C2×#930—31no—
85C2×#930—31no—
86C2×C4×#67—31no—
87#5599—316no—
88#5553—316no—
89C2×#895—31no—
90C2×#893—31no—
91C2×#893—31no—
92C2×#887—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#884—61no—
99C2×#884D311yescharacteristic, complemented
100C2×#67⋊C4—31no—
101C2×#67⋊C4D311yescharacteristic, complemented
102C2×#874—31no—
103C2×C4×Dic6—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C2×#638—24no—
113C2×#638—42no—
114C2×#638C2314yes—
115C2×#638C2314yes—
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C2×C4⋊(C3⋊D3)—42no—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C4×C3⋊D3—24no—
121C2×C4×C3⋊D3C2314yes—
122C2×C3×#67—24no—
123C2×C3×#67—24no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C22×C3×Dic3—24no—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×D12—42no—
136C2×C3×D12C2314yes—
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3—24no—
139C2×C3×C4×D3C2314yes—
140C2×C3×C4×D3C2314yes—
141C2×#627D418yescomplemented
142C2×#627C2314yes—
143C2×#626—24no—
144C2×#626—24no—
145C2×#626—24no—
146C2×#626—24no—
147C2×#626—24no—
148C2×#626—42no—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#626C2314yes—
153C2×#626C2314yes—
154C2×#626C2314yes—
155C2×#625—24no—
156C2×#625—42no—
157C2×#625C2314yes—
158C2×#625C2314yes—
159C2×#624—24no—
160C2×#624C2314yes—
161#3804—232no—
162C2×D3×Dic3—24no—
163C2×D3×Dic3C2314yes—
164#3798—232no—
165C32×C22⋊C4C2314yes—
166#3752C2314yes—
167#3750C2314yes—
168C3×(C2×D3)⋊C4C2314yes—
169C3×(C2×D3)⋊C4C2314yes—
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2314yes—
172C3×C4×Dic3C2314yes—
173Dic3⋊Dic3C2314yes—
174#3722C2314yes—
175(C2×D3)⋊Dic3C2314yes—
176Dic32C2314yes—
177Dic32C2314yes—
178C2×#550—91noSylow
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C23×C3×C4—31no—
184C23×C3×C4—31no—
185C23×C3×C4—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—61no—
201C22×#67—61no—
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic
204C22×#67C2×D311yescharacteristic
205C23×Dic3—31no—
206C23×Dic3C2×D311yescharacteristic
207C2×#237—38no—
208C2×#237—68no—
209C2×#235—38no—
210C2×#235—38no—
211C2×#235—38no—
212C2×#235—68no—
213C2×#235—68no—
214C2×#235—68no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12—31no—
219C22×D12—31no—
220C22×D12—31no—
221C22×D12—31no—
222C22×D12—31no—
223C22×D12—61no—
224C22×D12C2×D311yescharacteristic
225C22×C4×D3—31no—
226C22×C4×D3—31no—
227C22×C4×D3—31no—
228C22×C4×D3—31no—
229C22×C4×D3—31no—
230C22×C4×D3—61no—
231C22×C4×D3C2×D311yescharacteristic
232C22×C4×D3C2×D311yescharacteristic
233C22×Dic6—31no—
234C22×Dic6—31no—
235C3×#121—38no—
236C3×C4×D4—38no—
237C2×C3×C4⋊C4—31no—
238C2×C3×C4⋊C4—31no—
239C2×C3×C22⋊C4—21no—
240C2×C3×C22⋊C4—31no—
241C2×C3×C22⋊C4—31no—
242C2×C3×C22⋊C4C2×D311yescharacteristic
243C2×C3×C22⋊C4C2×D311yescharacteristic
244C2×C3×C42—31no—
245C2×#217—31no—
246#940—38no—
247#940—38no—
248#940—38no—
249#940—38no—
250#940—38no—
251#939—38no—
252#939—38no—
253#930—38no—
254#930—38no—
255C4×#67—38no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4C2×D311yescharacteristic
263C2×(C2×D3)⋊C4C2×D311yescharacteristic
264C2×C4⋊Dic3—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—61no—
269C2×Dic3⋊C4C2×D311yescharacteristic
270C2×Dic3⋊C4C2×D311yescharacteristic
271C2×C4×Dic3—31no—
272C2×C4×Dic3—31no—
273C2×C4×Dic3—31no—
274C2×C4×Dic3—31no—
275C2×C4×Dic3C2×D311yescharacteristic
276#895—38no—
277#893—38no—
278#893—38no—
279#887—38no—
280#884—38no—
281#884—38no—
282#884—38no—
283#884—38no—
284#884—38no—
285#884—68no—
286#884C2×D318yescomplemented
287#67⋊C4—38no—
288#67⋊C4C2×D318yescomplemented
289#874—38no—
290C4×Dic6—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3C2412yes—
303C22×C3⋊D3C2412yes—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—22no—
313C22×C3×D3C2412yes—
314C22×C3×D3C2412yes—
315C22×C3×D3C2412yes—
316C2×C32×C4—22no—
317C2×C32×C4—22no—
318C2×C32×C4C2412yes—
319C2×C32×C4C2412yes—
320#638—28no—
321#638—44no—
322C2×C3⋊Dic3—22no—
323C2×C3⋊Dic3C2×D414yes—
324C2×C3⋊Dic3C2412yes—
325C2×C3⋊Dic3C2412yes—
326C4⋊(C3⋊D3)—44no—
327C4×C3⋊D3—28no—
328C3×#67—28no—
329C3×#67—28no—
330C3×#67—44no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—22no—
333C2×C3×Dic3—28no—
334C2×C3×Dic3C2×D414yes—
335C2×C3×Dic3C2×D414yes—
336C2×C3×Dic3#4114yescomplemented
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C2×C3×Dic3C2412yes—
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2412yes—
342C3×D12—44no—
343C3×C4×D3—28no—
344C3×C4×D3—28no—
345#627C2×D4116yescomplemented
346#626—28no—
347#626—28no—
348#626—28no—
349#626—28no—
350#626—28no—
351#626—44no—
352#625—28no—
353#625—44no—
354#624—28no—
355D3×Dic3—28no—
356C22×#41—91no—
357C22×#41—91no—
358#550—916no—
359C2×#127—91no—
360C2×#127—91no—
361C2×#127—91no—
362C2×#121—31no—
363C2×#121—91no—
364C2×#121—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×C4×Q8—91no—
369C2×C4×D4—31no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C24×C3—21no—
373C24×C3—31no—
374C24×C3—31no—
375C24×C3—31no—
376C24×C3C22×D311yescharacteristic
377C24×C3C22×D311yescharacteristic
378C23×D3—31no—
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—61no—
383C23×D3—61no—
384C23×D3C22×D311yescharacteristic
385C23×D3C22×D311yescharacteristic
386C23×D3C22×D311yescharacteristic
387C2×C3×D4—34no—
388C2×C3×D4—34no—
389C2×C3×D4—34no—
390C2×C3×D4—34no—
391C2×C3×D4—64no—
392C2×C3×D4—64no—
393C2×C3×D4—122no—
394C2×C3×D4—122no—
395C22×C3×C4—21no—
396C22×C3×C4—21no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—34no—
403C22×C3×C4—34no—
404C22×C3×C4—34no—
405C22×C3×C4—64no—
406C22×C3×C4—64no—
407C22×C3×C4—64no—
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C22×C3×C4C22×D311yescharacteristic
411C22×C3×C4C22×D311yescharacteristic
412C2×#67—24no—
413C2×#67—24no—
414C2×#67—34no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—34no—
421C2×#67—34no—
422C2×#67—34no—
423C2×#67—34no—
424C2×#67—34no—
425C2×#67—34no—
426C2×#67—34no—
427C2×#67—34no—
428C2×#67—42no—
429C2×#67—64no—
430C2×#67—64no—
431C2×#67—64no—
432C2×#67—64no—
433C2×#67—64no—
434C2×#67—64no—
435C2×#67—64no—
436C2×#67—64no—
437C2×#67—64no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—124no—
441C2×#67—122no—
442C2×#67—122no—
443C2×#67—122no—
444C2×#67—122no—
445C2×#67—122no—
446C2×#67—124no—
447C2×#67C22×D314yes—
448C2×#67C22×D314yes—
449C2×#67C22×D314yes—
450C22×Dic3—24no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—34no—
456C22×Dic3—61no—
457C22×Dic3—61no—
458C22×Dic3—64no—
459C22×Dic3C22×D314yes—
460C22×Dic3C22×D311yescharacteristic
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D311yescharacteristic
464C22×Dic3C22×D311yescharacteristic
465#237—632no—
466#235—632no—
467#235—632no—
468#235—632no—
469C2×D12—34no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—34no—
474C2×D12—34no—
475C2×D12—34no—
476C2×D12—34no—
477C2×D12—42no—
478C2×D12—64no—
479C2×D12—64no—
480C2×D12—64no—
481C2×D12—64no—
482C2×D12—64no—
483C2×D12—64no—
484C2×D12—122no—
485C2×D12—122no—
486C2×D12—124no—
487C2×D12—122no—
488C2×D12C22×D314yes—
489C2×C4×D3—24no—
490C2×C4×D3—24no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—34no—
494C2×C4×D3—34no—
495C2×C4×D3—34no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3—64no—
499C2×C4×D3—64no—
500C2×C4×D3—64no—
501C2×C4×D3—64no—
502C2×C4×D3—124no—
503C2×C4×D3C22×D314yes—
504C2×C4×D3C22×D314yes—
505C2×Dic6—38no—
506C2×Dic6—38no—
507C2×Dic6—34no—
508C2×Dic6—34no—
509C3×C4⋊C4—34no—
510C3×C4⋊C4—34no—
511C3×C22⋊C4—24no—
512C3×C22⋊C4—34no—
513C3×C22⋊C4—34no—
514C3×C22⋊C4C22×D314yes—
515C3×C22⋊C4C22×D314yes—
516C3×C42—34no—
517#217—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—64no—
524(C2×D3)⋊C4C22×D314yes—
525(C2×D3)⋊C4C22×D314yes—
526C4⋊Dic3—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—64no—
531Dic3⋊C4C22×D314yes—
532Dic3⋊C4C22×D314yes—
533C4×Dic3—34no—
534C4×Dic3—34no—
535C4×Dic3—34no—
536C4×Dic3—34no—
537C4×Dic3C22×D314yes—
538C22×C32—22no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32—44no—
542C22×C32C22×D412yes—
543C22×C32C2×#4112yes—
544C22×C32H(5,𝔽2)12yes—
545C22×C32C2511yescharacteristic
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3—22no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—44no—
553C2×C3⋊D3—44no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—44no—
564C2×C3×D3—44no—
565C2×C3×D3—44no—
566C32×C4—22no—
567C32×C4—22no—
568C3⋊Dic3—22no—
569C3⋊Dic3C22×D414yes—
570C3×Dic3—22no—
571C3×Dic3—22no—
572C3×Dic3C22×D414yes—
573C3×Dic3C22×D414yes—
574C3×Dic3C2×#4114yescomplemented
575C2×#41—98no—
576C2×#41—98no—
577C2×#41—188no—
578C2×#41—188no—
579C22×Q8—91no—
580C22×D4—31no—
581C22×D4—31no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—91no—
585C22×D4—91no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4—91no—
595C23×C4—31no—
596C23×C4—31no—
597C23×C4—31no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601#127—98no—
602#127—98no—
603#127—98no—
604#121—38no—
605#121—98no—
606#121—98no—
607#121—98no—
608#121—98no—
609#121—98no—
610C4×Q8—98no—
611C4×D4—38no—
612C4×D4—98no—
613C4×D4—98no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—91no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4D3211yescharacteristic
624C2×C42—31no—
625C2×C42—91no—
626C2×C42—91no—
627C23×C3—22no—
628C23×C3—22no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—21no—
635C23×C3—32no—
636C23×C3—32no—
637C23×C3—32no—
638C23×C3—42no—
639C23×C3—42no—
640C23×C3—42no—
641C23×C3—62no—
642C23×C3—62no—
643C23×C3—62no—
644C23×C3—62no—
645C23×C3—62no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3C23×D312yes—
651C23×C3C23×D312yes—
652C23×C3C23×D311yescharacteristic
653C23×C3C23×D311yescharacteristic
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—32no—
664C22×D3—32no—
665C22×D3—32no—
666C22×D3—32no—
667C22×D3—62no—
668C22×D3—62no—
669C22×D3—64no—
670C22×D3—62no—
671C22×D3—62no—
672C22×D3—62no—
673C22×D3—62no—
674C22×D3—62no—
675C22×D3—62no—
676C22×D3—62no—
677C22×D3—62no—
678C22×D3—62no—
679C22×D3—62no—
680C22×D3—62no—
681C22×D3—62no—
682C22×D3—122no—
683C22×D3—122no—
684C22×D3—122no—
685C22×D3—122no—
686C22×D3—122no—
687C22×D3C23×D312yes—
688C22×D3C23×D312yes—
689C22×D3C23×D312yes—
690C3×D4—68no—
691C3×D4—68no—
692C3×D4—124no—
693C3×D4—124no—
694C2×C3×C4—22no—
695C2×C3×C4—22no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—22no—
699C2×C3×C4—22no—
700C2×C3×C4—34no—
701C2×C3×C4—34no—
702C2×C3×C4—34no—
703C2×C3×C4—32no—
704C2×C3×C4—32no—
705C2×C3×C4—32no—
706C2×C3×C4—32no—
707C2×C3×C4—32no—
708C2×C3×C4—42no—
709C2×C3×C4—42no—
710C2×C3×C4—68no—
711C2×C3×C4—68no—
712C2×C3×C4—68no—
713C2×C3×C4—62no—
714C2×C3×C4—62no—
715C2×C3×C4C23×D312yes—
716C2×C3×C4C23×D312yes—
717C2×C3×C4C23×D312yes—
718C2×C3×C4C23×D312yes—
719#67—28no—
720#67—28no—
721#67—44no—
722#67—68no—
723#67—68no—
724#67—68no—
725#67—68no—
726#67—68no—
727#67—68no—
728#67—68no—
729#67—68no—
730#67—68no—
731#67—128no—
732#67—124no—
733#67—124no—
734#67—124no—
735#67—124no—
736#67—124no—
737#67—128no—
738C2×Dic3—22no—
739C2×Dic3—22no—
740C2×Dic3—28no—
741C2×Dic3—34no—
742C2×Dic3—34no—
743C2×Dic3—32no—
744C2×Dic3—32no—
745C2×Dic3—32no—
746C2×Dic3—32no—
747C2×Dic3—64no—
748C2×Dic3—62no—
749C2×Dic3—62no—
750C2×Dic3—68no—
751C2×Dic3—62no—
752C2×Dic3—62no—
753C2×Dic3—122no—
754C2×Dic3#23514yescomplemented
755C2×Dic3D3×D414yes—
756C2×Dic3D3×D414yes—
757C2×Dic3C23×D312yes—
758C2×Dic3C23×D312yes—
759C2×Dic3C23×D312yes—
760C2×Dic3C23×D312yes—
761C2×Dic3C23×D312yes—
762D12—44no—
763D12—68no—
764D12—68no—
765D12—68no—
766D12—68no—
767D12—68no—
768D12—124no—
769D12—124no—
770D12—128no—
771D12—124no—
772C4×D3—28no—
773C4×D3—28no—
774C4×D3—68no—
775C4×D3—68no—
776C4×D3—68no—
777C4×D3—68no—
778C4×D3—68no—
779C4×D3—128no—
780Dic6—316no—
781Dic6—316no—
782C2×C32—42no—
783C2×C32#55014yescomplemented
784C2×C32C23×D411yescharacteristic
785C2×C32C22×#4111yescharacteristic
786C2×C32C2×H(5,𝔽2)11yescharacteristic
787C3⋊D3—42no—
788C3⋊D3—42no—
789C3×D3—42no—
790C3×D3—42no—
791C3×D3—42no—
792C24—31no—
793C24—31no—
794C24—31no—
795C24—91no—
796C24—91no—
797C24C2×D3211yescharacteristic
798#41—1832no—
799#41—1832no—
800C2×Q8—94no—
801C2×Q8—98no—
802C2×D4—34no—
803C2×D4—34no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—64no—
807C2×D4—64no—
808C2×D4—94no—
809C2×D4—94no—
810C2×D4—94no—
811C2×D4—94no—
812C2×D4—94no—
813C2×D4—94no—
814C2×D4—94no—
815C2×D4—94no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4—94no—
819C2×D4—122no—
820C2×D4—122no—
821C2×D4—184no—
822C2×D4—184no—
823C2×D4—184no—
824C2×D4—184no—
825C2×D4—184no—
826C2×D4—184no—
827C2×D4—184no—
828C2×D4—362no—
829C2×D4—362no—
830C2×D4—362no—
831C2×D4—362no—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—31no—
835C22×C4—34no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—34no—
839C22×C4—34no—
840C22×C4—64no—
841C22×C4—64no—
842C22×C4—64no—
843C22×C4—94no—
844C22×C4—94no—
845C22×C4—91no—
846C22×C4—91no—
847C22×C4—94no—
848C22×C4—184no—
849C22×C4—184no—
850C22×C4—184no—
851C22×C4C2×D3211yescharacteristic
852C22×C4C2×D3211yescharacteristic
853C4⋊C4—34no—
854C4⋊C4—34no—
855C4⋊C4—94no—
856C4⋊C4—94no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4C2×D3214yes—
863C42—34no—
864C42—94no—
865C42—94no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—21no—
876C22×C3—42no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—44no—
880C22×C3—44no—
881C22×C3—62no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—84no—
891C22×C3—124no—
892C22×C3—124no—
893C22×C3—124no—
894C22×C3C2×#23512yes—
895C22×C3C2×D3×D412yes—
896C22×C3C2×D3×D412yes—
897C22×C3#100412yes—
898C22×C3D3×#4112yes—
899C22×C3#100912yes—
900C22×C3C24×D311yescharacteristic
901C22×C3C24×D311yescharacteristic
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—22no—
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—44no—
912C2×D3—44no—
913C2×D3—44no—
914C2×D3—64no—
915C2×D3—62no—
916C2×D3—62no—
917C2×D3—62no—
918C2×D3—62no—
919C2×D3—62no—
920C2×D3—62no—
921C2×D3—62no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—122no—
928C2×D3—122no—
929C2×D3—122no—
930C2×D3—122no—
931C2×D3—122no—
932C2×D3—128no—
933C2×D3—124no—
934C2×D3—124no—
935C2×D3—124no—
936C2×D3—124no—
937C2×D3—244no—
938C3×C4—22no—
939C3×C4—22no—
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—34no—
943C3×C4—34no—
944C3×C4—34no—
945C3×C4—42no—
946C3×C4—42no—
947C3×C4—62no—
948C3×C4—62no—
949Dic3—22no—
950Dic3—22no—
951Dic3—34no—
952Dic3—34no—
953Dic3—64no—
954Dic3—62no—
955Dic3—62no—
956Dic3—122no—
957Dic3C2×#23514yescomplemented
958Dic3C2×D3×D414yes—
959Dic3C2×D3×D414yes—
960C32C2×#55011yescharacteristic, complemented, Sylow
961C23—22no—
962C23—22no—
963C23—22no—
964C23—32no—
965C23—32no—
966C23—32no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—92no—
977C23—92no—
978C23—182no—
979C23—182no—
980C23—182no—
981C23—182no—
982C23—182no—
983C23—182no—
984C23C22×D3212yes—
985C23C22×D3211yescharacteristic
986Q8—916no—
987D4—68no—
988D4—68no—
989D4—124no—
990D4—124no—
991D4—188no—
992D4—188no—
993D4—188no—
994D4—188no—
995D4—188no—
996D4—188no—
997D4—188no—
998D4—364no—
999D4—364no—
1000D4—364no—
1001D4—364no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—34no—
1005C2×C4—34no—
1006C2×C4—34no—
1007C2×C4—32no—
1008C2×C4—32no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—68no—
1013C2×C4—68no—
1014C2×C4—68no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—94no—
1018C2×C4—92no—
1019C2×C4—92no—
1020C2×C4—188no—
1021C2×C4—188no—
1022C2×C4—188no—
1023C2×C4—182no—
1024C2×C4C22×D3212yes—
1025C2×C4C22×D3212yes—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—24no—
1030C2×C3—42no—
1031C2×C3—42no—
1032C2×C3—82no—
1033C2×C3—122no—
1034C2×C3—122no—
1035C2×C3—122no—
1036C2×C3#555314yescomplemented
1037C2×C3#559914yescomplemented
1038C2×C3C22×#23511yescharacteristic
1039C2×C3C22×D3×D411yescharacteristic
1040C2×C3C22×D3×D411yescharacteristic
1041C2×C3C2×#100411yescharacteristic
1042C2×C3C2×D3×#4111yescharacteristic
1043C2×C3C2×#100911yescharacteristic
1044D3—42no—
1045D3—42no—
1046D3—42no—
1047D3—124no—
1048D3—122no—
1049D3—122no—
1050D3—122no—
1051D3—122no—
1052D3—242no—
1053C22—22no—
1054C22—22no—
1055C22—22no—
1056C22—44no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—62no—
1061C22—62no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—124no—
1067C22—124no—
1068C22—124no—
1069C22—182no—
1070C22—182no—
1071C22—182no—
1072C22—182no—
1073C22—182no—
1074C22—182no—
1075C22—364no—
1076C22—364no—
1077C22D3×#23512yes—
1078C22D32×D412yes—
1079C22#6431412yes—
1080C22C23×D3211yescharacteristic
1081C4—22no—
1082C4—22no—
1083C4—34no—
1084C4—34no—
1085C4—34no—
1086C4—62no—
1087C4—62no—
1088C4—94no—
1089C4—182no—
1090C3—21no—
1091C3C2×#555311yescharacteristic, complemented
1092C3C2×#559911yescharacteristic, complemented
1093C2—42no—
1094C2—122no—
1095C2—122no—
1096C2—122no—
1097C2—362no—
1098C2—362no—
1099C2#1059424614yesdirect product factor
1100C2C2×D3×#23511yescharacteristic
1101C2C2×D32×D411yescharacteristic
1102C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C22×#3798C2semidirect
3. C2×#64093C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×#63979C2semidirect
7. C2×#63979C2semidirect
8. C2×#63978C2semidirect
9. C2×#63911C2semidirect
10. C2×#63910C2semidirect
11. C2×#63906C2semidirect
12. C2×#63904C2semidirect
13. C2×#63885C2semidirect
14. C2×#63881C2semidirect
15. C2×#63837C2semidirect
16. #10594246C2direct (N × H)
41. C2×#3804C22semidirect
44. C2×#3798C22semidirect
48. #64093C22semidirect
54. C3×#884C22semidirect
55. C3×#67⋊C4C22semidirect
56. #63979C22semidirect
57. #63979C22semidirect
58. #63978C22semidirect
64. #63911C22semidirect
65. #63910C22semidirect
66. #63906C22semidirect
67. #63904C22semidirect
68. #63885C22semidirect
69. #63881C22semidirect
70. #63837C22semidirect
99. C2×#884D3semidirect
101. C2×#67⋊C4D3semidirect
141. C2×#627D4semidirect
286. #884C2×D3semidirect
288. #67⋊C4C2×D3semidirect
336. C2×C3×Dic3#41semidirect
345. #627C2×D4semidirect
574. C3×Dic3C2×#41semidirect
754. C2×Dic3#235semidirect
783. C2×C32#550semidirect
957. Dic3C2×#235semidirect
960. C32C2×#550semidirect
1036. C2×C3#5553semidirect
1037. C2×C3#5599semidirect
1091. C3C2×#5553semidirect
1092. C3C2×#5599semidirect
1099. C2#10594246direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C22×#37982
C2×#640932
C2×C3×#8842
C2×C3×#67⋊C42
C2×#639792
C2×#639782
C2×#639112
C2×#639102
C2×#639062
C2×#639042
C2×#638852
C2×#638812
C2×#638372
#105942462
C2×#55993
C2×#55533