Finite Group Databasebeta

← C2×#10594198 #11903193

Subgroups — C2×#10594198 #11903193

Order 1152.

2627 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64088C211yesmaximal, characteristic, complemented
2C2×C3×#884C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×Dic3×#67C211yesmaximal, characteristic, complemented
5C2×#63970C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8C2×#63908C211yesmaximal, characteristic, complemented
9C2×#63902C211yesmaximal, characteristic, complemented
10C2×#63884C211yesmaximal, characteristic, complemented
11C2×#63879C211yesmaximal, characteristic, complemented
12C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C2×#63859C211yesmaximal, characteristic, complemented
14C2×#63855C211yesmaximal, characteristic, complemented
15C2×#63845C211yesmaximal, characteristic, complemented
16#10594198C2116yesmaximal, direct product factor
17C2×#5614—31nomaximal
18C2×#5540—31nomaximal
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38#64088C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#884C2218yescomplemented
45C3×#67⋊C4C2218yescomplemented
46Dic3×#67C2218yescomplemented
47#63970C2218yescomplemented
48#63970C2218yescomplemented
49C2×#3724C2211yescharacteristic
50C2×#3724C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54#63961C2218yescomplemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63908C2218yescomplemented
62#63902C2218yescomplemented
63#63884C2218yescomplemented
64#63879C2218yescomplemented
65D3×Dic3⋊C4C2218yescomplemented
66#63859C2218yescomplemented
67#63855C2218yescomplemented
68#63845C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#938—31no—
74C2×#938—31no—
75C2×#938—31no—
76C2×#935—31no—
77C2×#935—31no—
78C2×D4×Dic3—31no—
79C2×#930—31no—
80C2×#929—31no—
81C2×C4×#67—31no—
82C2×C4×#67—31no—
83C2×#926—31no—
84C22×Dic3⋊C4—31no—
85#5614—316no—
86#5540—316no—
87C2×#894—31no—
88C2×D3×C4⋊C4—31no—
89C2×#890—31no—
90C2×#889—31no—
91C2×#884D311yescharacteristic, complemented
92C2×#67⋊C4—31no—
93C2×#67⋊C4—31no—
94C2×#67⋊C4—31no—
95C2×#67⋊C4D311yescharacteristic, complemented
96C2×#879—31no—
97C2×#879—31no—
98C2×#879—31no—
99C2×#879—61no—
100C2×#876—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×C3×#67—24no—
113C2×C3×#67—24no—
114C2×C3×#67—42no—
115C2×C3×#67C2314yes—
116C2×C3×#67C2314yes—
117C2×C3×#67C2314yes—
118C22×C3×Dic3—42no—
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×D12—42no—
126C2×C3×D12C2314yes—
127C2×C3×C4×D3—24no—
128C2×C3×C4×D3—42no—
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2314yes—
131C2×#625—24no—
132C2×#625—24no—
133C2×#625C2314yes—
134C2×#625C2314yes—
135C2×D3×Dic3—24no—
136C2×D3×Dic3—42no—
137C2×D3×Dic3—42no—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141C32×C22⋊C4C2314yes—
142#3757C2314yes—
143#3757C2314yes—
144C4⋊(C3⋊Dic3)C2314yes—
145#3750C2314yes—
146#3750C2314yes—
147C4×C3⋊Dic3C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×C4×Dic3C2314yes—
153#3724C2314yes—
154#3724C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164C2×#553—91noSylow
165C22×C3×D4—31no—
166C22×C3×D4—31no—
167C22×C3×D4—31no—
168C22×C3×D4—31no—
169C23×C3×C4—31no—
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67C2×D311yescharacteristic
177C22×#67C2×D311yescharacteristic
178C22×#67C2×D311yescharacteristic
179C23×Dic3—31no—
180C23×Dic3—31no—
181C23×Dic3—31no—
182C23×Dic3C2×D311yescharacteristic
183C22×D12C2×D311yescharacteristic
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3C2×D311yescharacteristic
188C22×C4×D3C2×D311yescharacteristic
189C3×#121—38no—
190C3×C4×D4—38no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C22⋊C4—21no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C42—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—61no—
209C2×#217—61no—
210#939—38no—
211#939—38no—
212#938—38no—
213#938—38no—
214#938—38no—
215#935—38no—
216#935—38no—
217D4×Dic3—38no—
218#930—38no—
219#929—38no—
220C4×#67—38no—
221C4×#67—38no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229#926—38no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—61no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—38no—
248C2×Dic3⋊C4—61no—
249C2×Dic3⋊C4—61no—
250C2×Dic3⋊C4C2×D311yescharacteristic
251C2×Dic3⋊C4C2×D311yescharacteristic
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3—31no—
255C2×C4×Dic3—31no—
256C2×C4×Dic3—61no—
257C2×C4×Dic3C2×D311yescharacteristic
258#894—38no—
259D3×C4⋊C4—38no—
260#890—38no—
261#889—38no—
262#884C2×D318yescomplemented
263#67⋊C4—38no—
264#67⋊C4—38no—
265#67⋊C4—38no—
266#67⋊C4C2×D318yescomplemented
267#879—38no—
268#879—38no—
269#879—38no—
270#879—68no—
271#876—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3#4114yes—
287C22×C3×D3C2412yes—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×C32×C4—22no—
291C2×C32×C4—22no—
292C2×C32×C4C2412yes—
293C2×C32×C4C2412yes—
294C2×C3⋊Dic3—22no—
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3C2412yes—
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C3×#67—28no—
303C3×#67—28no—
304C3×#67—44no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—44no—
310C2×C3×Dic3#4114yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C3×D12—44no—
317C3×C4×D3—28no—
318C3×C4×D3—44no—
319#625—28no—
320#625—28no—
321D3×Dic3—28no—
322D3×Dic3—44no—
323D3×Dic3—44no—
324#553—916no—
325C2×#126—91no—
326C2×#126—91no—
327C2×#125—91no—
328C2×#123—91no—
329C2×#123—91no—
330C2×#121—31no—
331C2×#121—91no—
332C2×#121—91no—
333C2×#121—91no—
334C2×C4×D4—31no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338C2×#117—91no—
339C22×C4⋊C4—91no—
340C24×C3—21no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3—31no—
344C24×C3C22×D311yescharacteristic
345C24×C3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C2×C3×D4—34no—
350C2×C3×D4—34no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—64no—
354C2×C3×D4—64no—
355C2×C3×D4—122no—
356C2×C3×D4—122no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—34no—
365C22×C3×C4—34no—
366C22×C3×C4—34no—
367C22×C3×C4—64no—
368C22×C3×C4—122no—
369C22×C3×C4—122no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C2×#67—24no—
375C2×#67—24no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—42no—
381C2×#67—64no—
382C2×#67—64no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67C22×D314yes—
386C2×#67C22×D314yes—
387C2×#67C22×D314yes—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—34no—
397C22×Dic3—34no—
398C22×Dic3—34no—
399C22×Dic3—42no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—64no—
405C22×Dic3—122no—
406C22×Dic3—122no—
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D314yes—
412C22×Dic3C22×D311yescharacteristic
413C2×D12—42no—
414C2×D12C22×D314yes—
415C2×C4×D3—24no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—42no—
420C2×C4×D3—64no—
421C2×C4×D3—122no—
422C2×C4×D3—122no—
423C2×C4×D3C22×D314yes—
424C2×C4×D3C22×D314yes—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—34no—
427C3×C22⋊C4—24no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4C22×D314yes—
431C3×C22⋊C4C22×D314yes—
432C3×C42—34no—
433#217—34no—
434#217—34no—
435#217—34no—
436#217—34no—
437#217—34no—
438#217—34no—
439#217—34no—
440#217—34no—
441#217—34no—
442#217—64no—
443#217—64no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4C22×D314yes—
450(C2×D3)⋊C4C22×D314yes—
451C4⋊Dic3—34no—
452C4⋊Dic3—34no—
453C4⋊Dic3—34no—
454C4⋊Dic3—34no—
455C4⋊Dic3—34no—
456C4⋊Dic3—64no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—64no—
469Dic3⋊C4—64no—
470Dic3⋊C4C22×D314yes—
471Dic3⋊C4C22×D314yes—
472C4×Dic3—34no—
473C4×Dic3—34no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—64no—
477C4×Dic3C22×D314yes—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—44no—
482C22×C32C2×#4112yes—
483C22×C32C2×#4112yes—
484C22×C32H(5,𝔽2)12yes—
485C22×C32C2511yescharacteristic
486C2×C3×D3—28no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—44no—
496C2×C3×D3—44no—
497C2×C3×D3C2×#4114yes—
498C32×C4—22no—
499C32×C4—22no—
500C3⋊Dic3—22no—
501C3⋊Dic3—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3C2×#4114yes—
509C22×D4—31no—
510C22×D4—31no—
511C22×D4—31no—
512C22×D4—31no—
513C22×D4—91no—
514C22×D4—91no—
515C23×C4—31no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—91no—
519C23×C4—91no—
520C23×C4—91no—
521#126—98no—
522#126—98no—
523#125—98no—
524#123—98no—
525#123—98no—
526#121—38no—
527#121—98no—
528#121—98no—
529#121—98no—
530C4×D4—38no—
531C4×D4—98no—
532C4×D4—98no—
533C4×D4—98no—
534#117—98no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—98no—
538C2×C4⋊C4—91no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4D3211yescharacteristic
556C2×C42—31no—
557C2×C42—91no—
558C2×C42—91no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—21no—
567C23×C3—34no—
568C23×C3—32no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3—42no—
572C23×C3—42no—
573C23×C3—42no—
574C23×C3—62no—
575C23×C3—62no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3C23×D312yes—
583C23×C3C23×D312yes—
584C23×C3C23×D311yescharacteristic
585C23×C3C23×D311yescharacteristic
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3#23514yes—
595C22×D3C23×D312yes—
596C22×D3C23×D312yes—
597C22×D3C23×D312yes—
598C3×D4—68no—
599C3×D4—68no—
600C3×D4—124no—
601C3×D4—124no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—34no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—42no—
615C2×C3×C4—42no—
616C2×C3×C4—68no—
617C2×C3×C4—62no—
618C2×C3×C4—62no—
619C2×C3×C4—62no—
620C2×C3×C4—62no—
621C2×C3×C4—124no—
622C2×C3×C4—124no—
623C2×C3×C4C23×D312yes—
624C2×C3×C4C23×D312yes—
625C2×C3×C4C23×D312yes—
626C2×C3×C4C23×D312yes—
627#67—28no—
628#67—28no—
629#67—44no—
630#67—68no—
631#67—68no—
632#67—68no—
633#67—68no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—44no—
647C2×Dic3—62no—
648C2×Dic3—62no—
649C2×Dic3—62no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—68no—
660C2×Dic3—122no—
661C2×Dic3—122no—
662C2×Dic3—122no—
663C2×Dic3—122no—
664C2×Dic3—124no—
665C2×Dic3—124no—
666C2×Dic3#23714yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672D12—44no—
673C4×D3—28no—
674C4×D3—44no—
675C4×D3—68no—
676C4×D3—124no—
677C4×D3—124no—
678C2×C32—42no—
679C2×C32#55314yescomplemented
680C2×C32C22×#4111yescharacteristic
681C2×C32C22×#4111yescharacteristic
682C2×C32C2×H(5,𝔽2)11yescharacteristic
683C3×D3—24no—
684C3×D3—42no—
685C3×D3—42no—
686C24—31no—
687C24—31no—
688C24—31no—
689C24C2×D3211yescharacteristic
690C2×D4—34no—
691C2×D4—34no—
692C2×D4—34no—
693C2×D4—34no—
694C2×D4—64no—
695C2×D4—64no—
696C2×D4—94no—
697C2×D4—94no—
698C2×D4—122no—
699C2×D4—122no—
700C2×D4—184no—
701C2×D4—184no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—34no—
708C22×C4—34no—
709C22×C4—34no—
710C22×C4—64no—
711C22×C4—94no—
712C22×C4—94no—
713C22×C4—94no—
714C22×C4—91no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—122no—
719C22×C4—122no—
720C22×C4—184no—
721C22×C4—362no—
722C22×C4—362no—
723C22×C4C2×D3211yescharacteristic
724C22×C4C2×D3211yescharacteristic
725C4⋊C4—34no—
726C4⋊C4—34no—
727C4⋊C4—94no—
728C4⋊C4—94no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—94no—
738C22⋊C4—94no—
739C22⋊C4—94no—
740C22⋊C4—94no—
741C22⋊C4—94no—
742C22⋊C4—94no—
743C22⋊C4—94no—
744C22⋊C4C2×D3214yes—
745C42—34no—
746C42—94no—
747C42—94no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—21no—
758C22×C3—34no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—44no—
763C22×C3—44no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—68no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—84no—
774C22×C3—124no—
775C22×C3—124no—
776C22×C3C2×#23512yes—
777C22×C3C2×#23712yes—
778C22×C3#100412yes—
779C22×C3#100412yes—
780C22×C3D3×#4112yes—
781C22×C3D3×#4112yes—
782C22×C3C24×D311yescharacteristic
783C22×C3C24×D311yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—28no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—44no—
794C2×D3—44no—
795C2×D3C2×#23514yes—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—34no—
801C3×C4—42no—
802C3×C4—42no—
803C3×C4—62no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—62no—
807Dic3—22no—
808Dic3—22no—
809Dic3—22no—
810Dic3—22no—
811Dic3—62no—
812Dic3—62no—
813Dic3—62no—
814Dic3—62no—
815Dic3—62no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—122no—
820Dic3—122no—
821Dic3—122no—
822Dic3—122no—
823Dic3C2×#23714yes—
824C32C2×#55311yescharacteristic, complemented, Sylow
825C23—22no—
826C23—22no—
827C23—22no—
828C23—34no—
829C23—32no—
830C23—32no—
831C23—32no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23C22×D3212yes—
841C23C22×D3211yescharacteristic
842D4—68no—
843D4—68no—
844D4—124no—
845D4—124no—
846D4—188no—
847D4—188no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—34no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—68no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—92no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—92no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—188no—
868C2×C4—182no—
869C2×C4—182no—
870C2×C4—182no—
871C2×C4—182no—
872C2×C4—364no—
873C2×C4—364no—
874C2×C4C22×D3212yes—
875C2×C4C22×D3212yes—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—24no—
880C2×C3—42no—
881C2×C3—42no—
882C2×C3—64no—
883C2×C3—82no—
884C2×C3—122no—
885C2×C3—122no—
886C2×C3#554014yescomplemented
887C2×C3#561414yescomplemented
888C2×C3C22×#23511yescharacteristic
889C2×C3C22×#23711yescharacteristic
890C2×C3C2×#100411yescharacteristic
891C2×C3C2×#100411yescharacteristic
892C2×C3C2×D3×#4111yescharacteristic
893C2×C3C2×D3×#4111yescharacteristic
894D3—24no—
895D3—42no—
896D3—42no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—34no—
901C22—44no—
902C22—62no—
903C22—62no—
904C22—68no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—124no—
912C22—124no—
913C22D3×#23512yes—
914C22D3×#23712yes—
915C22#6431312yes—
916C22C23×D3211yescharacteristic
917C4—22no—
918C4—22no—
919C4—34no—
920C4—62no—
921C4—62no—
922C4—62no—
923C4—62no—
924C4—182no—
925C4—182no—
926C4—182no—
927C4—182no—
928C3—21no—
929C3C2×#554011yescharacteristic, complemented
930C3C2×#561411yescharacteristic, complemented
931C2—42no—
932C2—64no—
933C2—122no—
934C2—122no—
935C2#1059419814yesdirect product factor
936C2C2×D3×#23511yescharacteristic
937C2C2×D3×#23711yescharacteristic
938C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64088C2semidirect
2. C2×C3×#884C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C2×Dic3×#67C2semidirect
5. C2×#63970C2semidirect
6. C2×#63970C2semidirect
7. C2×#63961C2semidirect
8. C2×#63908C2semidirect
9. C2×#63902C2semidirect
10. C2×#63884C2semidirect
11. C2×#63879C2semidirect
12. C2×D3×Dic3⋊C4C2semidirect
13. C2×#63859C2semidirect
14. C2×#63855C2semidirect
15. C2×#63845C2semidirect
16. #10594198C2direct (N × H)
38. #64088C22semidirect
44. C3×#884C22semidirect
45. C3×#67⋊C4C22semidirect
46. Dic3×#67C22semidirect
47. #63970C22semidirect
48. #63970C22semidirect
54. #63961C22semidirect
61. #63908C22semidirect
62. #63902C22semidirect
63. #63884C22semidirect
64. #63879C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. #63859C22semidirect
67. #63855C22semidirect
68. #63845C22semidirect
91. C2×#884D3semidirect
95. C2×#67⋊C4D3semidirect
262. #884C2×D3semidirect
266. #67⋊C4C2×D3semidirect
679. C2×C32#553semidirect
824. C32C2×#553semidirect
886. C2×C3#5540semidirect
887. C2×C3#5614semidirect
929. C3C2×#5540semidirect
930. C3C2×#5614semidirect
935. C2#10594198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640882
C2×C3×#8842
C2×C3×#67⋊C42
C2×Dic3×#672
C2×#639702
C2×#639612
C2×#639082
C2×#639022
C2×#638842
C2×#638792
C2×D3×Dic3⋊C42
C2×#638592
C2×#638552
C2×#638452
#105941982
C2×#56143
C2×#55403