Finite Group Databasebeta

← #13372815

Subgroups — #13372815

Order 1792.

1052 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic7⋊C8C211yesmaximal, characteristic, complemented
2C4×D4×Dic7C211yesmaximal, characteristic
3C2×#89490C211yesmaximal, characteristic, complemented
4C7×#1869C211yesmaximal, characteristic
5C8×C22⋊Dic7C211yesmaximal, characteristic, complemented
6#11729364C211yesmaximal, characteristic
7#11727701C211yesmaximal, characteristic, complemented
8#11727667C211yesmaximal, characteristic, complemented
9#11727666C211yesmaximal, characteristic, complemented
10#11727662C211yesmaximal, characteristic, complemented
11#11727662C211yesmaximal, characteristic, complemented
12#11726364C211yesmaximal, characteristic, complemented
13#11726363C211yesmaximal, characteristic, complemented
14#11726359C211yesmaximal, characteristic, complemented
15#11726356C211yesmaximal, 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⋊C8—24no—
32C2×Dic7⋊C8C2211yescharacteristic
33C2×Dic7⋊C8C2211yescharacteristic
34C2×Dic7⋊C8C2211yescharacteristic
35C2×Dic7⋊C8C2211yescharacteristic
36C2×Dic7⋊C8C2211yescharacteristic
37C2×Dic7⋊C8C2211yescharacteristic
38C2×C8×Dic7C2211yescharacteristic
39C2×C8×Dic7C2211yescharacteristic
40C2×C8×Dic7C2211yescharacteristic
41C2×C8×Dic7C2211yescharacteristic
42C4⋊C4×Dic7C411yescharacteristic
43C4⋊C4×Dic7C411yescharacteristic
44C22⋊C4×Dic7C411yescharacteristic
45C22⋊C4×Dic7C411yescharacteristic
46C22⋊C4×Dic7C411yescharacteristic
47C22⋊C4×Dic7C411yescharacteristic
48C4×C4⋊Dic7C2211yescharacteristic
49C42×Dic7C2211yescharacteristic
50#89490—24no—
51C7×#336C2211yescharacteristic
52C7×#336C2211yescharacteristic
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89345C2211yescharacteristic
58#89345C2211yescharacteristic
59#89319C2211yescharacteristic
60#89319C2211yescharacteristic
61#22748—71nomaximal, Sylow
62C22×C7×D4C2×C411yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2×C411yescharacteristic
66C23×Dic7C2×C411yescharacteristic
67C23×Dic7C2×C411yescharacteristic
68C23×Dic7C2×C411yescharacteristic
69C22×C7×C8—22no—
70C22×C7×C8—22no—
71C22×C7×C8—41no—
72C22×C7×C8C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C22×C7×C8C2311yescharacteristic
75C22×C7×C8C2311yescharacteristic
76C4×C7×D4—22no—
77C4×C7×D4—22no—
78C2×C7×C4⋊C4C2×C411yescharacteristic
79C2×C7×C22⋊C4C2×C411yescharacteristic
80C2×C7×C22⋊C4C2×C411yescharacteristic
81C2×C42×C7C2311yescharacteristic
82C2×C22⋊Dic7C2×C411yescharacteristic
83C2×C22⋊Dic7C2×C411yescharacteristic
84C2×C22⋊Dic7C2×C411yescharacteristic
85C2×C22⋊Dic7C2×C411yescharacteristic
86D4×Dic7—24no—
87D4×Dic7C818yescomplemented
88C2×C4⋊Dic7C2×C411yescharacteristic
89C2×C4⋊Dic7C2×C411yescharacteristic
90C2×C4×Dic7—22no—
91C2×C4×Dic7—22no—
92C2×C4×Dic7—22no—
93C2×C4×Dic7—22no—
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×Dic7C2×C411yescharacteristic
101C2×C4×Dic7C2×C411yescharacteristic
102C2×C4×Dic7C2311yescharacteristic
103C2×C4×Dic7C2311yescharacteristic
104C2×C4×Dic7C2311yescharacteristic
105C2×C4×Dic7C2311yescharacteristic
106C22×C7⋊C8—22no—
107C22×C7⋊C8—22no—
108C22×C7⋊C8—41no—
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113C7×C22⋊C8—22no—
114C7×C22⋊C8—22no—
115C7×C22⋊C8—41no—
116C7⋊#95C2×C411yescharacteristic
117C7⋊#95C2×C411yescharacteristic
118C7⋊#95C2×C411yescharacteristic
119C7⋊#95C2×C411yescharacteristic
120C7⋊#95C2×C411yescharacteristic
121C7⋊#95C2×C411yescharacteristic
122C22⋊(C7⋊C8)—22no—
123C22⋊(C7⋊C8)—22no—
124C22⋊(C7⋊C8)—41no—
125Dic7⋊C8—22no—
126Dic7⋊C8—22no—
127Dic7⋊C8—22no—
128Dic7⋊C8—22no—
129Dic7⋊C8—22no—
130Dic7⋊C8D414yescomplemented
131C8×Dic7—22no—
132C8×Dic7—22no—
133C8×Dic7—41no—
134C8×Dic7—41no—
135C2×#431—71no—
136C22×C4⋊C8—71no—
137C42×D4—71no—
138#1923—71no—
139#1923—71no—
140#1916—71no—
141#1916—71no—
142#1869—71no—
143#1869D711yescharacteristic
144#1831—71no—
145#1797—71no—
146#1797—71no—
147C4×C4⋊C8—71no—
148C8×C22⋊C4—71no—
149C8×C22⋊C4—71no—
150C24×C7C22×C411yescharacteristic
151C24×C7C22×C411yescharacteristic
152C2×C7×D4—22no—
153C2×C7×D4—22no—
154C2×C7×D4C2×C814yes—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7C22×C411yescharacteristic
166C22×C4×C7C22×C411yescharacteristic
167C22×C4×C7C22×C411yescharacteristic
168C22×C4×C7C22×C411yescharacteristic
169C22×C4×C7#4112yes—
170C22×C4×C7#4112yes—
171C22×C4×C7C2411yescharacteristic
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—41no—
181C22×Dic7—41no—
182C22×Dic7C2×C814yes—
183C22×Dic7C2×C814yescomplemented
184C22×Dic7C22×C411yescharacteristic
185C22×Dic7C22×C411yescharacteristic
186C22×Dic7C22×C411yescharacteristic
187C22×Dic7C22×C411yescharacteristic
188C22×Dic7C22×C411yescharacteristic
189C22×Dic7C22×C411yescharacteristic
190C22×Dic7C22×C411yescharacteristic
191C22×Dic7C22×C411yescharacteristic
192C2×C7×C8—21no—
193C2×C7×C8—21no—
194C2×C7×C8—21no—
195C2×C7×C8—21no—
196C2×C7×C8—21no—
197C2×C7×C8—21no—
198C2×C7×C8—21no—
199C2×C7×C8—21no—
200C2×C7×C8—21no—
201C2×C7×C8—21no—
202C2×C7×C8—21no—
203C2×C7×C8—44no—
204C2×C7×C8C2×D412yes—
205C7×C4⋊C4—22no—
206C7×C22⋊C4—22no—
207C7×C22⋊C4—22no—
208C42×C7—21no—
209C42×C7—21no—
210C22⋊Dic7—22no—
211C22⋊Dic7C2×C814yes—
212C22⋊Dic7C2×C814yescomplemented
213C22⋊Dic7M1614yes—
214C4⋊Dic7—22no—
215C4⋊Dic7C2×C814yescomplemented
216C4×Dic7—21no—
217C4×Dic7—21no—
218C4×Dic7—21no—
219C4×Dic7—21no—
220C4×Dic7—21no—
221C4×Dic7—21no—
222C4×Dic7—22no—
223C4×Dic7—22no—
224C4×Dic7—22no—
225C4×Dic7—22no—
226C4×Dic7—22no—
227C4×Dic7—22no—
228C4×Dic7—41no—
229C4×Dic7C2×C814yescomplemented
230C4×Dic7C2×D412yes—
231C4×Dic7#4112yes—
232C2×C7⋊C8—21no—
233C2×C7⋊C8—21no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8—21no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8—21no—
238C2×C7⋊C8—21no—
239C2×C7⋊C8—21no—
240C2×C7⋊C8—21no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—44no—
244C2×C7⋊C8C2×D412yes—
245C23×C8—71no—
246C23×C8C2×D711yescharacteristic
247C2×C4×D4—71no—
248C2×C4×D4—71no—
249C2×C4×D4C2×D711yescharacteristic
250C22×C42—71no—
251C22×C42—71no—
252#431—144no—
253C2×C4⋊C8—71no—
254C2×C4⋊C8—71no—
255C2×C4⋊C8—71no—
256C2×C4⋊C8—71no—
257C2×C4⋊C8—71no—
258C2×C4⋊C8—71no—
259C2×C4⋊C8—144no—
260C2×C22⋊C8—71no—
261C2×C22⋊C8—71no—
262C2×C22⋊C8—71no—
263C2×C22⋊C8C2×D711yescharacteristic
264C2×C22⋊C8C2×D711yescharacteristic
265C2×C22⋊C8C2×D711yescharacteristic
266C2×C4×C8—71no—
267C2×C4×C8—71no—
268C2×C4×C8—71no—
269C2×C4×C8—71no—
270C4×C4⋊C4—71no—
271C4×C4⋊C4—71no—
272C4×C4⋊C4—71no—
273C4×C22⋊C4—71no—
274C4×C22⋊C4—71no—
275C4×C22⋊C4—71no—
276C4×C22⋊C4—71no—
277C4×C22⋊C4—71no—
278C4×C22⋊C4—71no—
279C43—71no—
280#336—71no—
281#336—71no—
282#336—71no—
283#336—71no—
284#336—71no—
285#336—71no—
286#336—71no—
287#336—71no—
288#336C2×D711yescharacteristic
289#336C2×D711yescharacteristic
290C23×C7—21no—
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—21no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7#11712yes—
301C23×C7C22×C812yes—
302C23×C7C22×C812yes—
303C23×C7C2×M1612yes—
304C23×C7C23×C411yescharacteristic
305C7×D4—28no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7#11712yes—
325C2×C4×C7C22×C812yes—
326C2×C4×C7C22×D411yescharacteristic
327C2×C4×C7C2×#4111yescharacteristic
328C2×C4×C7C2×#4111yescharacteristic
329C2×C4×C7C2×#4111yescharacteristic
330C2×C4×C7H(5,𝔽2)11yescharacteristic
331C2×C4×C72−1+411yescharacteristic
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—21no—
342C2×Dic7—21no—
343C2×Dic7—21no—
344C2×Dic7—28no—
345C2×Dic7—28no—
346C2×Dic7—21no—
347C2×Dic7—21no—
348C2×Dic7—21no—
349C2×Dic7—44no—
350C2×Dic7—44no—
351C2×Dic7C4×D412yes—
352C2×Dic7C4×D412yes—
353C2×Dic7C22×C812yes—
354C2×Dic7C22×C812yes—
355C2×Dic7C22×C812yes—
356C2×Dic7C22×C812yes—
357C2×Dic7C2×M1612yes—
358C2×Dic7C2×M1612yes—
359C2×Dic7#13112yes—
360C7×C8—22no—
361C7×C8—41no—
362C7×C8—41no—
363C7×C8—41no—
364C7⋊C8—22no—
365C7⋊C8—41no—
366C7⋊C8—41no—
367C7⋊C8—41no—
368C22×D4C4×D711yescharacteristic
369C23×C4—71no—
370C23×C4—71no—
371C23×C4—71no—
372C23×C4—71no—
373C23×C4C22×D711yescharacteristic
374C23×C4C22×D711yescharacteristic
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—41no—
378C22×C8—71no—
379C22×C8—71no—
380C22×C8—71no—
381C22×C8—71no—
382C22×C8—142no—
383C22×C8—142no—
384C22×C8—281no—
385C22×C8C22×D711yescharacteristic
386C22×C8C22×D711yescharacteristic
387C22×C8C22×D711yescharacteristic
388C22×C8C22×D711yescharacteristic
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—78no—
392C4×D4—144no—
393C2×C4⋊C4—71no—
394C2×C4⋊C4—71no—
395C2×C4⋊C4C4×D711yescharacteristic
396C2×C22⋊C4—71no—
397C2×C22⋊C4—71no—
398C2×C22⋊C4—71no—
399C2×C22⋊C4—71no—
400C2×C22⋊C4C4×D711yescharacteristic
401C2×C22⋊C4C4×D711yescharacteristic
402C2×C42—71no—
403C2×C42—71no—
404C2×C42—71no—
405C2×C42—71no—
406C2×C42—71no—
407C2×C42—71no—
408C2×C42—71no—
409C2×C42—71no—
410C2×C42—71no—
411C2×C42—71no—
412C2×C42—71no—
413C2×C42—71no—
414C2×C42—142no—
415C2×C42—142no—
416C2×C42—142no—
417C2×C42—142no—
418C2×C42C22×D711yescharacteristic
419C4⋊C8—74no—
420C4⋊C8—142no—
421C4⋊C8—142no—
422C4⋊C8—142no—
423C4⋊C8—142no—
424C4⋊C8—142no—
425C22⋊C8—22no—
426C22⋊C8—22no—
427C22⋊C8—41no—
428C22⋊C8—142no—
429C22⋊C8—142no—
430C22⋊C8—281no—
431C4×C8—142no—
432C4×C8—142no—
433C4×C8—281no—
434C4×C8—281no—
435#95—71no—
436#95—71no—
437#95—71no—
438#95—71no—
439#95—71no—
440#95—71no—
441C22×C7—22no—
442C22×C7—22no—
443C22×C7—22no—
444C22×C7—22no—
445C22×C7—22no—
446C22×C7—22no—
447C22×C7—22no—
448C22×C7—22no—
449C22×C7—22no—
450C22×C7—41no—
451C22×C7—41no—
452C22×C7—41no—
453C22×C7—41no—
454C22×C7#43114yescomplemented
455C22×C7C2×#11711yescharacteristic
456C22×C7C2×C4×D411yescharacteristic
457C22×C7#52011yescharacteristic
458C22×C7C23×C811yescharacteristic
459C22×C7C22×M1611yescharacteristic
460C22×C7C2×#13111yescharacteristic
461C22×C7#56811yescharacteristic
462C4×C7—22no—
463C4×C7—22no—
464C4×C7—41no—
465C4×C7—41no—
466C4×C7#54611yescharacteristic
467C4×C7#54811yescharacteristic
468C4×C7#55211yescharacteristic
469C4×C7#55311yescharacteristic
470Dic7—22no—
471Dic7—22no—
472Dic7—22no—
473Dic7—22no—
474Dic7—22no—
475Dic7—22no—
476Dic7—41no—
477Dic7C8×D414yes—
478C24C2×C4×D711yescharacteristic
479C24C2×C4×D711yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4C8×D714yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—71no—
494C22×C4—74no—
495C22×C4—74no—
496C22×C4—71no—
497C22×C4—71no—
498C22×C4—71no—
499C22×C4—71no—
500C22×C4—71no—
501C22×C4—71no—
502C22×C4—71no—
503C22×C4—142no—
504C22×C4—142no—
505C22×C4—142no—
506C22×C4—142no—
507C22×C4—142no—
508C22×C4—142no—
509C22×C4—142no—
510C22×C4—142no—
511C22×C4—281no—
512C22×C4—281no—
513C22×C4C2×C4×D711yescharacteristic
514C22×C4C2×C4×D711yescharacteristic
515C22×C4C2×C4×D711yescharacteristic
516C22×C4C2×C4×D711yescharacteristic
517C22×C4#115912yes—
518C22×C4#115912yes—
519C22×C4C23×D711yescharacteristic
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—44no—
532C2×C8—72no—
533C2×C8—141no—
534C2×C8—141no—
535C2×C8—141no—
536C2×C8—141no—
537C2×C8—141no—
538C2×C8—141no—
539C2×C8—141no—
540C2×C8—141no—
541C2×C8—141no—
542C2×C8—141no—
543C2×C8—141no—
544C2×C8—284no—
545C2×C8D4×D712yes—
546C4⋊C4—22no—
547C4⋊C4—74no—
548C4⋊C4—142no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—74no—
552C22⋊C4—74no—
553C22⋊C4—74no—
554C22⋊C4—142no—
555C42—21no—
556C42—21no—
557C42—74no—
558C42—72no—
559C42—72no—
560C42—142no—
561C42—142no—
562C42—142no—
563C42—142no—
564C42—142no—
565C42—142no—
566C42—141no—
567C42—141no—
568C42—141no—
569C42—141no—
570C42—141no—
571C42—141no—
572C42—281no—
573C2×C7—24no—
574C2×C7—42no—
575C2×C7#235211yescharacteristic
576C2×C7C2×#43111yescharacteristic
577C2×C7#292511yescharacteristic
578C2×C7C2×C8×D411yescharacteristic
579C2×C7D4×M1611yescharacteristic
580C2×C7#298811yescharacteristic
581C2×C7#299011yescharacteristic
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23#644012yes—
593C23C2×C8×D712yes—
594C23C2×C8×D712yes—
595C23D7×M1612yes—
596C23C22×C4×D711yescharacteristic
597D4—28no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—72no—
617C2×C4—72no—
618C2×C4—72no—
619C2×C4—72no—
620C2×C4—72no—
621C2×C4—72no—
622C2×C4—72no—
623C2×C4—72no—
624C2×C4—72no—
625C2×C4—148no—
626C2×C4—148no—
627C2×C4—141no—
628C2×C4—141no—
629C2×C4—141no—
630C2×C4—141no—
631C2×C4—141no—
632C2×C4—141no—
633C2×C4—141no—
634C2×C4—141no—
635C2×C4—141no—
636C2×C4—141no—
637C2×C4—141no—
638C2×C4—141no—
639C2×C4—141no—
640C2×C4—141no—
641C2×C4—141no—
642C2×C4—284no—
643C2×C4—284no—
644C2×C4#644012yes—
645C2×C4C2×C8×D712yes—
646C2×C4C2×D4×D711yescharacteristic
647C2×C4C2×#115911yescharacteristic
648C2×C4C2×#115911yescharacteristic
649C2×C4#654811yescharacteristic
650C2×C4D7×#4111yescharacteristic
651C2×C4#655411yescharacteristic
652C8—22no—
653C8—41no—
654C8—41no—
655C8—41no—
656C8—142no—
657C8—281no—
658C8—281no—
659C8—281no—
660C7#2274811yescharacteristic, complemented, Sylow
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22#8949014yescomplemented
675C22C2×#644011yescharacteristic
676C22C4×D4×D711yescharacteristic
677C22#9023711yescharacteristic
678C22C22×C8×D711yescharacteristic
679C22C2×D7×M1611yescharacteristic
680C22D7×#13111yescharacteristic
681C22#9044111yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—74no—
687C4—142no—
688C4—142no—
689C4—142no—
690C4—142no—
691C4—142no—
692C4—142no—
693C4—281no—
694C4#9028211yescharacteristic
695C4#9028911yescharacteristic
696C4#9029211yescharacteristic
697C4#9034111yescharacteristic
698C2—24no—
699C2—42no—
700C2#1173211811yescharacteristic
701C2C2×#8949011yescharacteristic
702C2#1173609511yescharacteristic
703C2#1173685011yescharacteristic
704C2C8×D4×D711yescharacteristic
705C2#1173690711yescharacteristic
706C2#1173692811yescharacteristic
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#22748
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C22×Dic7⋊C8C2semidirect
3. C2×#89490C2semidirect
5. C8×C22⋊Dic7C2semidirect
7. #11727701C2semidirect
8. #11727667C2semidirect
9. #11727666C2semidirect
10. #11727662C2semidirect
11. #11727662C2semidirect
12. #11726364C2semidirect
13. #11726363C2semidirect
14. #11726359C2semidirect
15. #11726356C2semidirect
87. D4×Dic7C8semidirect
130. Dic7⋊C8D4semidirect
183. C22×Dic7C2×C8semidirect
212. C22⋊Dic7C2×C8semidirect
215. C4⋊Dic7C2×C8semidirect
229. C4×Dic7C2×C8semidirect
454. C22×C7#431semidirect
660. C7#22748semidirect
674. C22#89490semidirect

Maximal subgroups

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

subgroupindex
C22×Dic7⋊C82
C4×D4×Dic72
C2×#894902
C7×#18692
C8×C22⋊Dic72
#117293642
#117277012
#117276672
#117276662
#117276622
#117263642
#117263632
#117263592
#117263562
#227487