Finite Group Databasebeta

← C2×#72241333 #72341612

Subgroups — C2×#72241333 #72341612

Order 2048.

At least 6549 conjugacy classes of subgroups; only the 1160 normal subgroups are shown.

The subgroup lattice has 598 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6379033C211yesmaximal, characteristic
2C2×#128079C212yesmaximal, complemented
3C2×#493430C211yesmaximal, characteristic
4C2×#493430C211yesmaximal, characteristic
5C2×#146577C212yesmaximal, complemented
6#72241333C218yesmaximal, direct product factor
7C22×#3498C2211yescharacteristic
8C22×#2888C411yescharacteristic, complemented
9C22×#2888C2211yescharacteristic
10C22×#2127C412yescomplemented
11C23×#353C412yescomplemented
12#6379033C414yescomplemented
13#6379033C2214yes—
14C2×#20637C411yescharacteristic, complemented
15C2×#20592C411yescharacteristic, complemented
16C2×#20592C2211yescharacteristic
17C2×#20585C2212yes—
18C2×#20585C2212yes—
19C2×C4×#413C411yescharacteristic, complemented
20#493430C414yescomplemented
21#493430C414yescomplemented
22#493430C2214yes—
23#493430C2214yes—
24C2×#12697C412yescomplemented
25C2×#12695C412yescomplemented
26#146577C2218yescomplemented
27#128079C2218yescomplemented
28C23×H(5,𝔽2)C2×C411yescharacteristic
29C23×H(5,𝔽2)C2311yescharacteristic
30C2×#3498C2×C412yes—
31C2×#3498C2×C412yes—
32C2×#3498C2×C412yes—
33C2×#3498D412yes—
34C2×#3498D412yes—
35C2×#3498D412yes—
36C2×#3498Q812yes—
37C2×#3498C2312yes—
38C22×#535C2×C411yescharacteristic
39C22×#535C2×C411yescharacteristic
40C22×#535D411yescharacteristic
41C22×#535D411yescharacteristic
42C22×#535D411yescharacteristic
43C22×#535Q811yescharacteristic
44C22×#532C2×C411yescharacteristic
45C22×#532D411yescharacteristic
46C22×#532Q811yescharacteristic
47C23×#127C2×C411yescharacteristic
48C23×#127D411yescharacteristic
49C23×#127D411yescharacteristic
50C22×C4×#41C2×C411yescharacteristic
51C2×#2888C2×C412yes—
52C2×#2888C2×C414yescomplemented
53C2×#2888D414yes—
54C2×#2888C2312yes—
55C22×#413C2×C411yescharacteristic
56C22×#413C2×C411yescharacteristic
57C22×#413C2×C411yescharacteristic
58C22×#413C2×C411yescharacteristic
59C23×#100D414yes—
60C23×#99C2×C414yes—
61C2×#2127C2×C418yescomplemented
62C22×#353C2×C418yescomplemented
63#20637C2×C414yescomplemented
64#20592C2×C412yes—
65#20592C2×C414yescomplemented
66#20592D414yes—
67#20592C2312yes—
68C2×#1785D414yes—
69#20585C2×C414yes—
70#20585C2×C414yes—
71#20585C2314yes—
72#20585C2314yes—
73C2×#1782C2×C414yes—
74C4×#413C2×C414yescomplemented
75#12697C2×C418yescomplemented
76#12695C2×C418yescomplemented
77C22×H(5,𝔽2)C4212yes—
78C22×H(5,𝔽2)C22⋊C412yes—
79C22×H(5,𝔽2)C4⋊C412yes—
80C22×H(5,𝔽2)C22×C412yes—
81C22×H(5,𝔽2)C22×C411yescharacteristic
82C22×H(5,𝔽2)C22×C411yescharacteristic
83C22×H(5,𝔽2)C22×C411yescharacteristic
84C22×H(5,𝔽2)C2×D411yescharacteristic
85C22×H(5,𝔽2)C2×D411yescharacteristic
86C22×H(5,𝔽2)C2×D411yescharacteristic
87C22×H(5,𝔽2)C2×D412yes—
88C22×H(5,𝔽2)C2×D412yes—
89C22×H(5,𝔽2)C2×Q811yescharacteristic
90C22×H(5,𝔽2)#4112yes—
91C22×H(5,𝔽2)#4112yes—
92C22×H(5,𝔽2)C2411yescharacteristic
93C23×#41C4211yescharacteristic
94C23×#41C22⋊C411yescharacteristic
95C23×#41C4⋊C411yescharacteristic
96C23×#41C22×C411yescharacteristic
97C23×#41C22×C411yescharacteristic
98C23×#41C2×D411yescharacteristic
99C23×#41C2×D412yes—
100C23×#41C2×Q811yescharacteristic
101C24×D4C4211yescharacteristic
102C24×D4C22⋊C411yescharacteristic
103C24×D4C4⋊C411yescharacteristic
104C24×D4C22×C411yescharacteristic
105C24×D4C2×D411yescharacteristic
106C24×D4C2×D411yescharacteristic
107C24×D4C2×D412yes—
108C24×D4#4112yes—
109C24×D4#4112yes—
110C2×#535C4212yes—
111C2×#535C4212yes—
112C2×#535C22⋊C412yes—
113C2×#535C22⋊C412yes—
114C2×#535C22⋊C412yes—
115C2×#535C22⋊C412yes—
116C2×#535C22⋊C412yes—
117C2×#535C22⋊C412yes—
118C2×#535C22⋊C412yes—
119C2×#535C22⋊C412yes—
120C2×#535C4⋊C412yes—
121C2×#535C4⋊C412yes—
122C2×#535C4⋊C412yes—
123C2×#535C4⋊C412yes—
124C2×#535C4⋊C412yes—
125C2×#535C4⋊C412yes—
126C2×#535C4⋊C412yes—
127C2×#535C4⋊C412yes—
128C2×#535C22×C412yes—
129C2×#535C22×C412yes—
130C2×#535C2×D412yes—
131C2×#535C2×D412yes—
132C2×#535C2×D412yes—
133C2×#535C2×Q812yes—
134C2×#532C4212yes—
135C2×#532C22⋊C412yes—
136C2×#532C22⋊C412yes—
137C2×#532C22⋊C412yes—
138C2×#532C4⋊C412yes—
139C2×#532C4⋊C412yes—
140C2×#532C4⋊C412yes—
141C2×#532C4⋊C412yes—
142C2×#532C4⋊C412yes—
143C2×#532C22×C412yes—
144C2×#532C2×D412yes—
145C2×#532C2×Q812yes—
146C22×C4⋊Q8C4⋊C411yescharacteristic
147C22×#127C4212yes—
148C22×#127C22⋊C411yescharacteristic
149C22×#127C22⋊C411yescharacteristic
150C22×#127C22⋊C412yes—
151C22×#127C22⋊C412yes—
152C22×#127C22⋊C411yescharacteristic
153C22×#127C22⋊C411yescharacteristic
154C22×#127C22⋊C411yescharacteristic
155C22×#127C22⋊C412yes—
156C22×#127C22⋊C411yescharacteristic
157C22×#127C22⋊C412yes—
158C22×#127C22⋊C412yes—
159C22×#127C4⋊C412yes—
160C22×#127C4⋊C412yes—
161C22×#127C4⋊C411yescharacteristic
162C22×#127C4⋊C411yescharacteristic
163C22×#127C4⋊C411yescharacteristic
164C22×#127C4⋊C412yes—
165C22×#127C22×C412yes—
166C22×#127C2×D412yes—
167C22×#127C2×D412yes—
168C22×#124C22⋊C411yescharacteristic
169C22×#124C22⋊C411yescharacteristic
170C22×#124C4⋊C411yescharacteristic
171C22×#124C4⋊C411yescharacteristic
172C22×#124C4⋊C411yescharacteristic
173C22×#124C4⋊C411yescharacteristic
174C2×C4×#41C4212yes—
175C2×C4×#41C22⋊C412yes—
176C2×C4×#41C4⋊C412yes—
177C2×C4×#41C22×C412yes—
178C22×#117C4211yescharacteristic
179C22×#117C22⋊C411yescharacteristic
180C22×#117C4⋊C411yescharacteristic
181C23×C42C4211yescharacteristic
182C23×C42C22⋊C411yescharacteristic
183C23×C42C4⋊C411yescharacteristic
184C2×#413C22⋊C412yes—
185C2×#413C22⋊C412yes—
186C2×#413C22⋊C412yes—
187C2×#413C22⋊C412yes—
188C2×#413C22×C412yes—
189C2×#413C22×C412yes—
190C2×#413C22×C412yes—
191C2×#413C22×C412yes—
192C22×#101C22⋊C412yes—
193C22×#101C22⋊C412yes—
194C22×#100C22⋊C412yes—
195C22×#100C22⋊C418yes—
196C22×#100C22⋊C412yes—
197C22×#100C2×D418yes—
198C22×#99C22×C418yes—
199#1785C22⋊C418yes—
200#1785C2×D418yes—
201#1782C22×C418yes—
202C26C4×D412yes—
203C26#12112yes—
204C26#12312yes—
205C22×#41#9512yes—
206C22×#41#9512yes—
207C22×#41#9512yes—
208C22×#41C2×C4212yes—
209C22×#41C2×C4211yescharacteristic
210C22×#41C2×C4211yescharacteristic
211C22×#41C2×C22⋊C412yes—
212C22×#41C2×C22⋊C411yescharacteristic
213C22×#41C2×C22⋊C411yescharacteristic
214C22×#41C2×C22⋊C411yescharacteristic
215C22×#41C2×C22⋊C411yescharacteristic
216C22×#41C2×C22⋊C411yescharacteristic
217C22×#41C2×C22⋊C411yescharacteristic
218C22×#41C2×C22⋊C412yes—
219C22×#41C2×C4⋊C412yes—
220C22×#41C2×C4⋊C411yescharacteristic
221C22×#41C2×C4⋊C411yescharacteristic
222C22×#41C2×C4⋊C411yescharacteristic
223C22×#41C2×C4⋊C411yescharacteristic
224C22×#41C2×C4⋊C411yescharacteristic
225C22×#41C2×C4⋊C411yescharacteristic
226C22×#41#11711yescharacteristic
227C22×#41#11711yescharacteristic
228C22×#41C4×D412yes—
229C22×#41C4×D412yes—
230C22×#41C4×D412yes—
231C22×#41C4×D412yes—
232C22×#41#12012yes—
233C22×#41#12012yes—
234C22×#41#12012yes—
235C22×#41#12112yes—
236C22×#41C22⋊Q812yes—
237C22×#41C22⋊Q812yes—
238C22×#41C22⋊Q812yes—
239C22×#41#12312yes—
240C22×#41C23×C411yescharacteristic
241C22×#41C23×C411yescharacteristic
242C22×#41C22×D411yescharacteristic
243C22×#41C22×D412yes—
244C22×#41C22×Q811yescharacteristic
245C23×Q8#9511yescharacteristic
246C23×Q8C2×C22⋊C411yescharacteristic
247C23×Q8C2×C4⋊C411yescharacteristic
248C23×D4#9511yescharacteristic
249C23×D4#9511yescharacteristic
250C23×D4#9511yescharacteristic
251C23×D4#9512yes—
252C23×D4#9512yes—
253C23×D4#9512yes—
254C23×D4C2×C4211yescharacteristic
255C23×D4C2×C4212yes—
256C23×D4C2×C22⋊C412yes—
257C23×D4C2×C22⋊C411yescharacteristic
258C23×D4C2×C22⋊C411yescharacteristic
259C23×D4C2×C22⋊C411yescharacteristic
260C23×D4C2×C22⋊C411yescharacteristic
261C23×D4C2×C22⋊C411yescharacteristic
262C23×D4C2×C22⋊C411yescharacteristic
263C23×D4C2×C22⋊C411yescharacteristic
264C23×D4C2×C22⋊C412yes—
265C23×D4C2×C22⋊C411yescharacteristic
266C23×D4C2×C4⋊C411yescharacteristic
267C23×D4C2×C4⋊C412yes—
268C23×D4C2×C4⋊C411yescharacteristic
269C23×D4C2×C4⋊C411yescharacteristic
270C23×D4C2×C4⋊C411yescharacteristic
271C23×D4#11711yescharacteristic
272C23×D4#11712yes—
273C23×D4#11711yescharacteristic
274C23×D4#11712yes—
275C23×D4C4×D412yes—
276C23×D4C4×D412yes—
277C23×D4C4×D412yes—
278C23×D4C4×D412yes—
279C23×D4C4×D412yes—
280C23×D4C4×D412yes—
281C23×D4C4×D412yes—
282C23×D4C4×D412yes—
283C23×D4C4×D412yes—
284C23×D4C4×D412yes—
285C23×D4#12012yes—
286C23×D4#12012yes—
287C23×D4#12012yes—
288C23×D4#12012yes—
289C23×D4#12112yes—
290C23×D4#12112yes—
291C23×D4#12112yes—
292C23×D4#12112yes—
293C23×D4#12112yes—
294C23×D4#12112yes—
295C23×D4C22⋊Q812yes—
296C23×D4C22⋊Q812yes—
297C23×D4C22⋊Q812yes—
298C23×D4C22⋊Q812yes—
299C23×D4#12312yes—
300C23×D4#12312yes—
301C23×D4#12312yes—
302C23×D4#12312yes—
303C23×D4#12312yes—
304C23×D4#12312yes—
305C23×D4C23×C411yescharacteristic
306C23×D4C22×D411yescharacteristic
307C23×D4C22×D411yescharacteristic
308C23×D4C22×D412yes—
309C23×D4C2×#4112yes—
310C23×D4C2×#4112yes—
311C24×C4C2×C4211yescharacteristic
312C24×C4C2×C22⋊C411yescharacteristic
313C24×C4C2×C4⋊C411yescharacteristic
314C24×C4C4×D412yes—
315C24×C4#12012yes—
316C24×C4C22⋊Q812yes—
317C2×C4⋊Q8#9512yes—
318C2×C4⋊Q8C2×C4⋊C412yes—
319C2×#127#9512yes—
320C2×#127#9512yes—
321C2×#127#9512yes—
322C2×#127#9512yes—
323C2×#127#9512yes—
324C2×#127#9512yes—
325C2×#127#9512yes—
326C2×#127#9512yes—
327C2×#127#9512yes—
328C2×#127#9912yes—
329C2×#127#9912yes—
330C2×#127#9914yes—
331C2×#127C2×C22⋊C412yes—
332C2×#127C2×C22⋊C412yes—
333C2×#127C2×C22⋊C412yes—
334C2×#127C2×C22⋊C412yes—
335C2×#127C2×C22⋊C412yes—
336C2×#127C2×C22⋊C412yes—
337C2×#127C2×C4⋊C412yes—
338C2×#127C2×C4⋊C412yes—
339C2×#127C2×C4⋊C412yes—
340C2×#124#9512yes—
341C2×#124#9512yes—
342C2×#124#9512yes—
343C2×#124#9512yes—
344C2×#124#9512yes—
345C2×#124#9512yes—
346C2×#124#9914yes—
347C2×#124#9914yes—
348C2×#124C2×C22⋊C412yes—
349C2×#124C2×C22⋊C412yes—
350C2×#124C2×C4⋊C412yes—
351C2×#124C2×C4⋊C412yes—
352C2×#124C2×C4⋊C412yes—
353C2×#124C2×C4⋊C412yes—
354C2×#117#9512yes—
355C2×#117#9512yes—
356C2×#117#9512yes—
357C2×#117C2×C4212yes—
358C2×#117C2×C22⋊C412yes—
359C2×#117C2×C4⋊C412yes—
360C22×C42#9511yescharacteristic
361C22×C42#9512yes—
362C22×C42#9511yescharacteristic
363C22×C42#9512yes—
364C22×C42#9512yes—
365C22×C42#9511yescharacteristic
366C22×C42#9511yescharacteristic
367C22×C42C2×C4212yes—
368C22×C42C2×C22⋊C412yes—
369C22×C42C2×C4⋊C412yes—
370C2×#101C2×C22⋊C414yes—
371C2×#101C2×C22⋊C414yes—
372C2×#100#9914yes—
373C2×#100#9914yes—
374C2×#100C2×C22⋊C414yes—
375C2×#100C2×C22⋊C414yes—
376C25C4×C22⋊C412yes—
377C25C4×C22⋊C411yescharacteristic
378C25#38012yes—
379C25#38011yescharacteristic
380C25#38111yescharacteristic
381C25#38112yes—
382C25#38512yes—
383C25#38512yes—
384C25#38512yes—
385C25#38612yes—
386C25#38612yes—
387C25#38612yes—
388C25#38612yes—
389C25#38612yes—
390C25#38612yes—
391C25C2×C4×D412yes—
392C25C2×#12112yes—
393C25C2×#12312yes—
394C22×Q8#34212yes—
395C22×Q8#34212yes—
396C22×Q8C2×#9512yes—
397C22×Q8C2×#9511yescharacteristic
398C22×Q8C4×C22⋊C411yescharacteristic
399C22×Q8#37911yescharacteristic
400C22×Q8#38011yescharacteristic
401C22×Q8#38512yes—
402C22×Q8C22×C22⋊C411yescharacteristic
403C22×Q8C22×C4⋊C411yescharacteristic
404C22×D4#34212yes—
405C22×D4#34212yes—
406C22×D4C2×#9512yes—
407C22×D4C2×#9512yes—
408C22×D4C2×#9511yescharacteristic
409C22×D4C2×#9511yescharacteristic
410C22×D4C2×#9512yes—
411C22×D4C2×#9511yescharacteristic
412C22×D4C4×C22⋊C411yescharacteristic
413C22×D4C4×C22⋊C412yes—
414C22×D4C4×C22⋊C411yescharacteristic
415C22×D4C4×C22⋊C411yescharacteristic
416C22×D4C4×C22⋊C412yes—
417C22×D4#37912yes—
418C22×D4#37911yescharacteristic
419C22×D4#38011yescharacteristic
420C22×D4#38012yes—
421C22×D4#38011yescharacteristic
422C22×D4#38011yescharacteristic
423C22×D4#38012yes—
424C22×D4#38111yescharacteristic
425C22×D4#38111yescharacteristic
426C22×D4#38112yes—
427C22×D4#38512yes—
428C22×D4#38512yes—
429C22×D4#38512yes—
430C22×D4#38512yes—
431C22×D4#38512yes—
432C22×D4#38512yes—
433C22×D4#38512yes—
434C22×D4#38612yes—
435C22×D4#38612yes—
436C22×D4#38612yes—
437C22×D4#38612yes—
438C22×D4#38612yes—
439C22×D4#38612yes—
440C22×D4#38612yes—
441C22×D4#38612yes—
442C22×D4C2×#9912yes—
443C22×D4C2×#9912yes—
444C22×D4C2×#9912yes—
445C22×D4C2×#9912yes—
446C22×D4C2×#9912yes—
447C22×D4C2×#9912yes—
448C22×D4#41012yes—
449C22×D4#41012yes—
450C22×D4C22×C22⋊C411yescharacteristic
451C22×D4C22×C22⋊C411yescharacteristic
452C22×D4C22×C22⋊C411yescharacteristic
453C22×D4C22×C4⋊C411yescharacteristic
454C22×D4C2×#11711yescharacteristic
455C22×D4C2×#11711yescharacteristic
456C22×D4C2×C4×D412yes—
457C22×D4C2×C4×D412yes—
458C22×D4C2×#12012yes—
459C22×D4C2×#12112yes—
460C22×D4C2×C22⋊Q812yes—
461C22×D4C2×#12312yes—
462C23×C4C2×#9511yescharacteristic
463C23×C4C2×#9511yescharacteristic
464C23×C4C2×#9511yescharacteristic
465C23×C4C2×#9511yescharacteristic
466C23×C4C4×C22⋊C411yescharacteristic
467C23×C4C4×C22⋊C411yescharacteristic
468C23×C4C4×C22⋊C411yescharacteristic
469C23×C4C4×C22⋊C412yes—
470C23×C4#37911yescharacteristic
471C23×C4#37912yes—
472C23×C4#37911yescharacteristic
473C23×C4#38011yescharacteristic
474C23×C4#38011yescharacteristic
475C23×C4#38011yescharacteristic
476C23×C4#38012yes—
477C23×C4#38111yescharacteristic
478C23×C4#38512yes—
479C23×C4#38512yes—
480C23×C4#38512yes—
481C23×C4#38512yes—
482C23×C4#38512yes—
483C23×C4#38612yes—
484C23×C4#38612yes—
485C23×C4C22×C4211yescharacteristic
486C23×C4C22×C22⋊C411yescharacteristic
487C23×C4C22×C4⋊C411yescharacteristic
488C23×C4C2×C4×D412yes—
489C23×C4C2×#12012yes—
490C23×C4C2×C22⋊Q812yes—
491#127#34214yes—
492#127#34214yes—
493#127C2×#9914yes—
494#127C2×#9914yes—
495#124#34218yes—
496#124C2×#9918yes—
497C2×C42#34212yes—
498C2×C42#34212yes—
499C2×C42#34211yescharacteristic
500C2×C42#34211yescharacteristic
501C2×C42#34212yes—
502C2×C42C2×#9512yes—
503C2×C42C2×#9512yes—
504C2×C42C2×#9512yes—
505C2×C42C2×#9512yes—
506#100C2×#9918yes—
507C24C22⋊#9512yes—
508C24C22⋊#9512yes—
509C24C22⋊#9511yescharacteristic
510C24C22⋊#9511yescharacteristic
511C24C22⋊#9511yescharacteristic
512C24C22⋊#9512yes—
513C24C22⋊#9511yescharacteristic
514C24C4×#9912yes—
515C24C4×#9912yes—
516C24#179912yes—
517C24#179912yes—
518C24#182812yes—
519C24#182812yes—
520C24#189814yes—
521C24#189814yes—
522C24C2×C4×C22⋊C411yescharacteristic
523C24C2×#38011yescharacteristic
524C24C2×#38111yescharacteristic
525C24C2×#38512yes—
526C24C2×#38612yes—
527C24C2×#38612yes—
528C2×Q8C2×#34214yes—
529C2×D4C2×#34214yes—
530C2×D4C2×#34212yes—
531C2×D4C2×#34212yes—
532C2×D4C4×#9912yes—
533C2×D4C4×#9912yes—
534C2×D4#178112yes—
535C2×D4#178212yes—
536C2×D4#179912yes—
537C2×D4#179912yes—
538C2×D4#189814yes—
539C2×D4#189814yes—
540C2×D4C22×#9912yes—
541C2×D4C22×#9912yes—
542C2×D4C22×#9912yes—
543C2×D4C2×#41012yes—
544C22×C4C22⋊#9511yescharacteristic
545C22×C4C22⋊#9511yescharacteristic
546C22×C4C22⋊#9512yes—
547C22×C4C22⋊#9511yescharacteristic
548C22×C4C22⋊#9511yescharacteristic
549C22×C4C2×#34211yescharacteristic
550C22×C4C2×#34211yescharacteristic
551C22×C4C2×#34211yescharacteristic
552C22×C4C2×#34211yescharacteristic
553C22×C4#178111yescharacteristic
554C22×C4#178111yescharacteristic
555C22×C4#178211yescharacteristic
556C22×C4#178211yescharacteristic
557C22×C4C22×#9511yescharacteristic
558C22×C4C2×C4×C22⋊C411yescharacteristic
559C22×C4C2×#37911yescharacteristic
560C22×C4C2×#38011yescharacteristic
561C22×C4C2×#38512yes—
562C42C2×#34212yes—
563C42C2×#34212yes—
564C42C2×#34214yes—
565C23#1073511yescharacteristic
566C23#1073514yes—
567C23#1073511yescharacteristic
568C23#1076111yescharacteristic
569C23#1076112yes—
570C23#1076112yes—
571C23#1076111yescharacteristic
572C23#1076811yescharacteristic
573C23#1076812yes—
574C23#1076811yescharacteristic
575C23C2×C22⋊#9511yescharacteristic
576C23C2×C4×#9912yes—
577C23C2×#179912yes—
578C23C2×#182812yes—
579C23C2×#189814yes—
580C2×C4#1073511yescharacteristic
581C2×C4#1073511yescharacteristic
582C2×C4#1076111yescharacteristic
583C2×C4#1076111yescharacteristic
584C2×C4C22×#34211yescharacteristic
585C2×C4C22×#34211yescharacteristic
586C2×C4C2×#178111yescharacteristic
587C2×C4C2×#178211yescharacteristic
588C22#10665411yescharacteristic
589C22#10665411yescharacteristic
590C22#10665411yescharacteristic
591C22#10665411yescharacteristic
592C22C2×#1076111yescharacteristic
593C22C2×#1076811yescharacteristic
594C22C2×#1073511yescharacteristic
595C2C2×#10665411yescharacteristic
596C2#7224133312yesdirect product factor
subgroupG/H
center, socleC22#106654
commutatorC23×C4C22×C42
Frattini, cosocleC22×H(5,𝔽2)C24
prime radicalC22×#3498C22
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C23×H(5,𝔽2) ◁ G
LECSG ▷ C22×H(5,𝔽2) ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#128079C2semidirect
5. C2×#146577C2semidirect
6. #72241333C2direct (N × H)
8. C22×#2888C4semidirect
10. C22×#2127C4semidirect
11. C23×#353C4semidirect
12. #6379033C4semidirect
14. C2×#20637C4semidirect
15. C2×#20592C4semidirect
19. C2×C4×#413C4semidirect
20. #493430C4semidirect
21. #493430C4semidirect
24. C2×#12697C4semidirect
25. C2×#12695C4semidirect
26. #146577C22semidirect
27. #128079C22semidirect
52. C2×#2888C2×C4semidirect
61. C2×#2127C2×C4semidirect
62. C22×#353C2×C4semidirect
63. #20637C2×C4semidirect
65. #20592C2×C4semidirect
74. C4×#413C2×C4semidirect
75. #12697C2×C4semidirect
76. #12695C2×C4semidirect
596. C2#72241333direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#63790332
C2×#1280792
C2×#4934302
C2×#1465772
#722413332