Finite Group Databasebeta

← #13373282

Subgroups — #13373282

Order 1792.

960 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Dic7C211yesmaximal, characteristic
2C7×#1869C211yesmaximal, characteristic
3C8×C22⋊Dic7C211yesmaximal, characteristic, complemented
4C2×#89345C211yesmaximal, characteristic, complemented
5#11729364C211yesmaximal, characteristic
6#11727701C211yesmaximal, characteristic, complemented
7#11727667C211yesmaximal, characteristic, complemented
8#11727666C211yesmaximal, characteristic, complemented
9#11727664C211yesmaximal, characteristic, complemented
10#11727662C211yesmaximal, characteristic, complemented
11Dic7×C22⋊C8C211yesmaximal, characteristic, complemented
12#11726364C211yesmaximal, characteristic, complemented
13#11726363C211yesmaximal, characteristic, complemented
14#11726361C211yesmaximal, characteristic, complemented
15#11726350C211yesmaximal, characteristic, complemented
16C23×C7×C8C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×D4×Dic7C411yescharacteristic
19C2×D4×Dic7C411yescharacteristic
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C23×C7⋊C8C2211yescharacteristic
23C2×C7×C22⋊C8C2211yescharacteristic
24C2×C7×C22⋊C8C2211yescharacteristic
25C2×C7×C22⋊C8C2211yescharacteristic
26C4×C22⋊Dic7C2211yescharacteristic
27C4×C22⋊Dic7C2211yescharacteristic
28C2×C22⋊(C7⋊C8)C2211yescharacteristic
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31C2×Dic7⋊C8C2211yescharacteristic
32C2×Dic7⋊C8C2211yescharacteristic
33C2×C8×Dic7C2211yescharacteristic
34C2×C8×Dic7C2211yescharacteristic
35C2×C8×Dic7C2211yescharacteristic
36C2×C8×Dic7C2211yescharacteristic
37C4⋊C4×Dic7C411yescharacteristic
38C4⋊C4×Dic7C411yescharacteristic
39C22⋊C4×Dic7C411yescharacteristic
40C22⋊C4×Dic7C411yescharacteristic
41C22⋊C4×Dic7C411yescharacteristic
42C22⋊C4×Dic7C411yescharacteristic
43C4×C4⋊Dic7C2211yescharacteristic
44C42×Dic7C2211yescharacteristic
45C7×#336C2211yescharacteristic
46C7×#336C2211yescharacteristic
47#89345C2211yescharacteristic
48#89345C2211yescharacteristic
49#89345C2211yescharacteristic
50#89345C2211yescharacteristic
51#89345C2211yescharacteristic
52#89345C2211yescharacteristic
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#22785—71nomaximal, Sylow
60C22×C7×D4C2×C411yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×Dic7C2×C411yescharacteristic
64C23×Dic7C2×C411yescharacteristic
65C23×Dic7C2×C411yescharacteristic
66C23×Dic7C2×C411yescharacteristic
67C22×C7×C8—22no—
68C22×C7×C8—22no—
69C22×C7×C8—41no—
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C22×C7×C8C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C4×C7×D4—22no—
75C4×C7×D4—22no—
76C2×C7×C4⋊C4C2×C411yescharacteristic
77C2×C7×C22⋊C4C2×C411yescharacteristic
78C2×C7×C22⋊C4C2×C411yescharacteristic
79C2×C42×C7C2311yescharacteristic
80C2×C22⋊Dic7C2×C411yescharacteristic
81C2×C22⋊Dic7C2×C411yescharacteristic
82C2×C22⋊Dic7C2×C411yescharacteristic
83C2×C22⋊Dic7C2×C411yescharacteristic
84D4×Dic7—24no—
85D4×Dic7C818yescomplemented
86C2×C4⋊Dic7C2×C411yescharacteristic
87C2×C4⋊Dic7C2×C411yescharacteristic
88C2×C4×Dic7—41no—
89C2×C4×Dic7—41no—
90C2×C4×Dic7—41no—
91C2×C4×Dic7—41no—
92C2×C4×Dic7C2×C411yescharacteristic
93C2×C4×Dic7C2×C411yescharacteristic
94C2×C4×Dic7C2×C411yescharacteristic
95C2×C4×Dic7C2×C411yescharacteristic
96C2×C4×Dic7C2×C411yescharacteristic
97C2×C4×Dic7C2×C411yescharacteristic
98C2×C4×Dic7C2×C411yescharacteristic
99C2×C4×Dic7C2×C411yescharacteristic
100C2×C4×Dic7C2311yescharacteristic
101C2×C4×Dic7C2311yescharacteristic
102C2×C4×Dic7C2311yescharacteristic
103C2×C4×Dic7C2311yescharacteristic
104C22×C7⋊C8—22no—
105C22×C7⋊C8—22no—
106C22×C7⋊C8—41no—
107C22×C7⋊C8C2311yescharacteristic
108C22×C7⋊C8C2311yescharacteristic
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C7×C22⋊C8—22no—
112C7×C22⋊C8—22no—
113C7×C22⋊C8—41no—
114C7⋊#95C2×C411yescharacteristic
115C7⋊#95C2×C411yescharacteristic
116C7⋊#95C2×C411yescharacteristic
117C7⋊#95C2×C411yescharacteristic
118C7⋊#95C2×C411yescharacteristic
119C7⋊#95C2×C411yescharacteristic
120C22⋊(C7⋊C8)—22no—
121C22⋊(C7⋊C8)—22no—
122C22⋊(C7⋊C8)—41no—
123Dic7⋊C8—41no—
124Dic7⋊C8—41no—
125C8×Dic7—22no—
126C8×Dic7—22no—
127C8×Dic7—41no—
128C8×Dic7—41no—
129C42×D4—71no—
130#1923—71no—
131#1923—71no—
132#1916—71no—
133#1916—71no—
134#1869—71no—
135#1869D711yescharacteristic
136#1839—71no—
137#1817—71no—
138#1797—71no—
139C8×C22⋊C4—71no—
140C8×C22⋊C4—71no—
141C4×C22⋊C8—71no—
142#1744—71no—
143C2×#336—71no—
144C24×C7C22×C411yescharacteristic
145C24×C7C22×C411yescharacteristic
146C2×C7×D4—22no—
147C2×C7×D4—22no—
148C2×C7×D4C2×C814yes—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7C22×C411yescharacteristic
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C22×C411yescharacteristic
162C22×C4×C7C22×C411yescharacteristic
163C22×C4×C7#4112yes—
164C22×C4×C7#4112yes—
165C22×C4×C7C2411yescharacteristic
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—41no—
171C22×Dic7—41no—
172C22×Dic7—41no—
173C22×Dic7—41no—
174C22×Dic7—41no—
175C22×Dic7—41no—
176C22×Dic7C2×C814yes—
177C22×Dic7C2×C814yescomplemented
178C22×Dic7C22×C411yescharacteristic
179C22×Dic7C22×C411yescharacteristic
180C22×Dic7C22×C411yescharacteristic
181C22×Dic7C22×C411yescharacteristic
182C22×Dic7C22×C411yescharacteristic
183C22×Dic7C22×C411yescharacteristic
184C22×Dic7C22×C411yescharacteristic
185C22×Dic7C22×C411yescharacteristic
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8—21no—
192C2×C7×C8—21no—
193C2×C7×C8—21no—
194C2×C7×C8—21no—
195C2×C7×C8—21no—
196C2×C7×C8—21no—
197C2×C7×C8—44no—
198C2×C7×C8#4112yes—
199C7×C4⋊C4—22no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—22no—
202C42×C7—21no—
203C42×C7—21no—
204C22⋊Dic7—22no—
205C22⋊Dic7C2×C814yes—
206C22⋊Dic7C2×C814yescomplemented
207C22⋊Dic7M1614yes—
208C4⋊Dic7—22no—
209C4⋊Dic7C2×C814yescomplemented
210C4×Dic7—21no—
211C4×Dic7—21no—
212C4×Dic7—21no—
213C4×Dic7—21no—
214C4×Dic7—21no—
215C4×Dic7—21no—
216C4×Dic7—21no—
217C4×Dic7—21no—
218C4×Dic7—22no—
219C4×Dic7—22no—
220C4×Dic7—41no—
221C4×Dic7—41no—
222C4×Dic7—41no—
223C4×Dic7—41no—
224C4×Dic7—41no—
225C4×Dic7C2×C814yescomplemented
226C2×C7⋊C8—21no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8—21no—
232C2×C7⋊C8—21no—
233C2×C7⋊C8—21no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8—21no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8—44no—
238C2×C7⋊C8#4112yes—
239C23×C8—71no—
240C23×C8C2×D711yescharacteristic
241C2×C4×D4—71no—
242C2×C4×D4—71no—
243C2×C4×D4C2×D711yescharacteristic
244C22×C42—71no—
245C22×C42—71no—
246C2×C4⋊C8—71no—
247C2×C4⋊C8—71no—
248C2×C22⋊C8—71no—
249C2×C22⋊C8—71no—
250C2×C22⋊C8—71no—
251C2×C22⋊C8C2×D711yescharacteristic
252C2×C22⋊C8C2×D711yescharacteristic
253C2×C22⋊C8C2×D711yescharacteristic
254C2×C4×C8—71no—
255C2×C4×C8—71no—
256C2×C4×C8—71no—
257C2×C4×C8—71no—
258C4×C4⋊C4—71no—
259C4×C4⋊C4—71no—
260C4×C4⋊C4—71no—
261C4×C22⋊C4—71no—
262C4×C22⋊C4—71no—
263C4×C22⋊C4—71no—
264C4×C22⋊C4—71no—
265C4×C22⋊C4—71no—
266C4×C22⋊C4—71no—
267C43—71no—
268#336—71no—
269#336—71no—
270#336—71no—
271#336—71no—
272#336—71no—
273#336—71no—
274#336—71no—
275#336—71no—
276#336—71no—
277#336—71no—
278#336—71no—
279#336—71no—
280#336C2×D711yescharacteristic
281#336C2×D711yescharacteristic
282C23×C7—21no—
283C23×C7—21no—
284C23×C7—21no—
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—21no—
288C23×C7—21no—
289C23×C7—21no—
290C23×C7—21no—
291C23×C7—21no—
292C23×C7#11712yes—
293C23×C7C22×C812yes—
294C23×C7C22×C812yes—
295C23×C7C2×M1612yes—
296C23×C7C23×C411yescharacteristic
297C7×D4—28no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
316C2×C4×C7#11712yes—
317C2×C4×C7C22×C812yes—
318C2×C4×C7C2×#4111yescharacteristic
319C2×C4×C7C2×#4111yescharacteristic
320C2×C4×C7C2×#4111yescharacteristic
321C2×C4×C7C2×#4111yescharacteristic
322C2×C4×C7H(5,𝔽2)11yescharacteristic
323C2×C4×C7H(5,𝔽2)11yescharacteristic
324C2×Dic7—21no—
325C2×Dic7—21no—
326C2×Dic7—21no—
327C2×Dic7—21no—
328C2×Dic7—21no—
329C2×Dic7—21no—
330C2×Dic7—21no—
331C2×Dic7—21no—
332C2×Dic7—21no—
333C2×Dic7—21no—
334C2×Dic7—21no—
335C2×Dic7—21no—
336C2×Dic7—21no—
337C2×Dic7—21no—
338C2×Dic7—21no—
339C2×Dic7—21no—
340C2×Dic7—21no—
341C2×Dic7—44no—
342C2×Dic7—44no—
343C2×Dic7—44no—
344C2×Dic7—44no—
345C2×Dic7C22×C812yes—
346C2×Dic7C22×C812yes—
347C2×Dic7C22×C812yes—
348C2×Dic7C22×C812yes—
349C2×Dic7C2×M1612yes—
350C2×Dic7C2×M1612yes—
351C2×Dic7#13112yes—
352C7×C8—22no—
353C7×C8—41no—
354C7×C8—41no—
355C7×C8—41no—
356C7⋊C8—22no—
357C7⋊C8—41no—
358C7⋊C8—41no—
359C7⋊C8—41no—
360C22×D4C4×D711yescharacteristic
361C23×C4—71no—
362C23×C4—71no—
363C23×C4—71no—
364C23×C4—71no—
365C23×C4C22×D711yescharacteristic
366C23×C4C22×D711yescharacteristic
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—41no—
370C22×C8—71no—
371C22×C8—71no—
372C22×C8—71no—
373C22×C8—71no—
374C22×C8—142no—
375C22×C8—142no—
376C22×C8—281no—
377C22×C8C22×D711yescharacteristic
378C22×C8C22×D711yescharacteristic
379C22×C8C22×D711yescharacteristic
380C22×C8C22×D711yescharacteristic
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—78no—
384C4×D4—144no—
385C2×C4⋊C4—71no—
386C2×C4⋊C4—71no—
387C2×C4⋊C4C4×D711yescharacteristic
388C2×C22⋊C4—71no—
389C2×C22⋊C4—71no—
390C2×C22⋊C4—71no—
391C2×C22⋊C4—71no—
392C2×C22⋊C4C4×D711yescharacteristic
393C2×C22⋊C4C4×D711yescharacteristic
394C2×C42—71no—
395C2×C42—71no—
396C2×C42—71no—
397C2×C42—71no—
398C2×C42—71no—
399C2×C42—71no—
400C2×C42—71no—
401C2×C42—71no—
402C2×C42—71no—
403C2×C42—71no—
404C2×C42—71no—
405C2×C42—71no—
406C2×C42—281no—
407C2×C42—281no—
408C2×C42—281no—
409C2×C42—281no—
410C2×C42C22×D711yescharacteristic
411C4⋊C8—281no—
412C4⋊C8—281no—
413C22⋊C8—22no—
414C22⋊C8—22no—
415C22⋊C8—41no—
416C22⋊C8—142no—
417C22⋊C8—142no—
418C22⋊C8—281no—
419C4×C8—142no—
420C4×C8—142no—
421C4×C8—281no—
422C4×C8—281no—
423#95—71no—
424#95—71no—
425#95—71no—
426#95—71no—
427#95—71no—
428#95—71no—
429C22×C7—22no—
430C22×C7—22no—
431C22×C7—22no—
432C22×C7—22no—
433C22×C7—22no—
434C22×C7—22no—
435C22×C7—22no—
436C22×C7—22no—
437C22×C7—22no—
438C22×C7—41no—
439C22×C7—41no—
440C22×C7—41no—
441C22×C7—41no—
442C22×C7#43114yes—
443C22×C7C2×#11711yescharacteristic
444C22×C7C4×#4111yescharacteristic
445C22×C7#51811yescharacteristic
446C22×C7C23×C811yescharacteristic
447C22×C7C22×M1611yescharacteristic
448C22×C7C2×#13111yescharacteristic
449C22×C7#56811yescharacteristic
450C4×C7—22no—
451C4×C7—22no—
452C4×C7—41no—
453C4×C7—41no—
454C4×C7#55111yescharacteristic
455C4×C7#55111yescharacteristic
456C4×C7#55311yescharacteristic
457C4×C7#55311yescharacteristic
458Dic7—22no—
459Dic7—22no—
460Dic7—22no—
461Dic7—22no—
462Dic7—22no—
463Dic7—22no—
464Dic7—22no—
465Dic7—41no—
466C24C2×C4×D711yescharacteristic
467C24C2×C4×D711yescharacteristic
468C2×D4—22no—
469C2×D4—22no—
470C2×D4C8×D714yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—71no—
482C22×C4—71no—
483C22×C4—71no—
484C22×C4—71no—
485C22×C4—71no—
486C22×C4—71no—
487C22×C4—71no—
488C22×C4—74no—
489C22×C4—74no—
490C22×C4—71no—
491C22×C4—142no—
492C22×C4—142no—
493C22×C4—142no—
494C22×C4—142no—
495C22×C4—281no—
496C22×C4—281no—
497C22×C4—281no—
498C22×C4—281no—
499C22×C4—281no—
500C22×C4—281no—
501C22×C4C2×C4×D711yescharacteristic
502C22×C4C2×C4×D711yescharacteristic
503C22×C4C2×C4×D711yescharacteristic
504C22×C4C2×C4×D711yescharacteristic
505C22×C4#115912yes—
506C22×C4#115912yes—
507C22×C4C23×D711yescharacteristic
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—44no—
520C2×C8—72no—
521C2×C8—141no—
522C2×C8—141no—
523C2×C8—141no—
524C2×C8—141no—
525C2×C8—141no—
526C2×C8—141no—
527C2×C8—141no—
528C2×C8—141no—
529C2×C8—141no—
530C2×C8—141no—
531C2×C8—141no—
532C2×C8—284no—
533C2×C8#115912yes—
534C4⋊C4—22no—
535C4⋊C4—74no—
536C4⋊C4—142no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—74no—
540C22⋊C4—74no—
541C22⋊C4—74no—
542C22⋊C4—142no—
543C42—21no—
544C42—21no—
545C42—74no—
546C42—142no—
547C42—142no—
548C42—141no—
549C42—141no—
550C42—141no—
551C42—141no—
552C42—141no—
553C42—141no—
554C42—141no—
555C42—141no—
556C42—281no—
557C42—281no—
558C42—281no—
559C42—281no—
560C42—281no—
561C2×C7—24no—
562C2×C7—42no—
563C2×C7#235311yescharacteristic
564C2×C7C2×#43111yescharacteristic
565C2×C7#292511yescharacteristic
566C2×C7C8×#4111yescharacteristic
567C2×C7#297011yescharacteristic
568C2×C7#297211yescharacteristic
569C2×C7#297411yescharacteristic
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23#644012yes—
581C23C2×C8×D712yes—
582C23C2×C8×D712yes—
583C23D7×M1612yes—
584C23C22×C4×D711yescharacteristic
585D4—28no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—72no—
605C2×C4—72no—
606C2×C4—72no—
607C2×C4—72no—
608C2×C4—72no—
609C2×C4—72no—
610C2×C4—72no—
611C2×C4—141no—
612C2×C4—141no—
613C2×C4—141no—
614C2×C4—141no—
615C2×C4—141no—
616C2×C4—141no—
617C2×C4—141no—
618C2×C4—141no—
619C2×C4—141no—
620C2×C4—141no—
621C2×C4—141no—
622C2×C4—141no—
623C2×C4—141no—
624C2×C4—141no—
625C2×C4—141no—
626C2×C4—141no—
627C2×C4—141no—
628C2×C4—284no—
629C2×C4—284no—
630C2×C4—284no—
631C2×C4—284no—
632C2×C4#644012yes—
633C2×C4C2×C8×D712yes—
634C2×C4C2×#115911yescharacteristic
635C2×C4C2×#115911yescharacteristic
636C2×C4C2×#115911yescharacteristic
637C2×C4#654811yescharacteristic
638C2×C4D7×#4111yescharacteristic
639C2×C4#655311yescharacteristic
640C8—22no—
641C8—41no—
642C8—41no—
643C8—41no—
644C8—142no—
645C8—281no—
646C8—281no—
647C8—281no—
648C7#2278511yescharacteristic, complemented, Sylow
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22#8949014yes—
663C22C2×#644011yescharacteristic
664C22C4×#115911yescharacteristic
665C22#9023611yescharacteristic
666C22C22×C8×D711yescharacteristic
667C22C2×D7×M1611yescharacteristic
668C22D7×#13111yescharacteristic
669C22#9044111yescharacteristic
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—142no—
675C4—142no—
676C4—142no—
677C4—142no—
678C4—142no—
679C4—142no—
680C4—142no—
681C4—281no—
682C4#9027811yescharacteristic
683C4#9029211yescharacteristic
684C4#9030911yescharacteristic
685C4#9034911yescharacteristic
686C2—24no—
687C2—42no—
688C2#1173211911yescharacteristic
689C2C2×#8949011yescharacteristic
690C2#1173609511yescharacteristic
691C2C8×#115911yescharacteristic
692C2#1173687111yescharacteristic
693C2#1173690511yescharacteristic
694C2#1173693111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutatorC22×C7C23×C8
FittingC7×#1869C2
socleC23×C7C23×C4
prime radicalC22×C7×D4C2×C4
cosocleC22×C4×C7C24
hypercenter#1869D7
hypocenterC7#22785
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
3. C8×C22⋊Dic7C2semidirect
4. C2×#89345C2semidirect
6. #11727701C2semidirect
7. #11727667C2semidirect
8. #11727666C2semidirect
9. #11727664C2semidirect
10. #11727662C2semidirect
11. Dic7×C22⋊C8C2semidirect
12. #11726364C2semidirect
13. #11726363C2semidirect
14. #11726361C2semidirect
15. #11726350C2semidirect
85. D4×Dic7C8semidirect
177. C22×Dic7C2×C8semidirect
206. C22⋊Dic7C2×C8semidirect
209. C4⋊Dic7C2×C8semidirect
225. C4×Dic7C2×C8semidirect
648. C7#22785semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Dic72
C7×#18692
C8×C22⋊Dic72
C2×#893452
#117293642
#117277012
#117276672
#117276662
#117276642
#117276622
Dic7×C22⋊C82
#117263642
#117263632
#117263612
#117263502
#227857