Finite Group Databasebeta

← #13374169

Subgroups — #13374169

Order 1792.

1134 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2339C211yesmaximal, characteristic
2C2×#90011C211yesmaximal, characteristic
3C2×#90004C211yesmaximal, characteristic
4C2×#89790C211yesmaximal, characteristic, complemented
5#11730910C211yesmaximal, characteristic, complemented
6#11729366C211yesmaximal, characteristic, complemented
7C4×#6406C211yesmaximal, characteristic, complemented
8#11729360C211yesmaximal, characteristic, complemented
9#11727444C211yesmaximal, characteristic, complemented
10#11727431C211yesmaximal, characteristic, complemented
11#11727429C211yesmaximal, characteristic, complemented
12#11727421C211yesmaximal, characteristic, complemented
13#11727270C211yesmaximal, characteristic, complemented
14#11727258C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C22×#1142C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C2×#6487C2211yescharacteristic
23C22×#1136C2211yescharacteristic
24C2×C4×Dic14C2211yescharacteristic
25C7×#391C2211yescharacteristic
26C7×#391C2211yescharacteristic
27C7×#386—21no—
28C7×#386—21no—
29C7×#381—21no—
30C7×#380C2211yescharacteristic
31C4×C7×C22⋊C4C2211yescharacteristic
32C2×C7×#95—21no—
33#90011C418yescomplemented
34#90004—24no—
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39C2×#6406C2211yescharacteristic
40C2×#6406C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89790—24no—
43C2×#6384C2211yescharacteristic
44C2×#6384C2211yescharacteristic
45C2×#6381C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47#89718—21no—
48C22⋊C4×Dic7—21no—
49C4×C4⋊Dic7C2211yescharacteristic
50#89701C2211yescharacteristic
51#89700C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54#89427—21no—
55#89419—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#22862—71nomaximal, Sylow
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C2×C7×#41C2×C414yes—
69C22×C7×Q8C2311yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7C2311yescharacteristic
76C23×Dic7—21no—
77C22×Dic14C2311yescharacteristic
78C4×C7×D4—22no—
79C4×C7×D4—22no—
80C4×C7×D4—41no—
81C4×C7×D4—41no—
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4D411yescharacteristic
88C2×C7×C22⋊C4D411yescharacteristic
89C2×C42×C7C2311yescharacteristic
90C2×C42×C7C2311yescharacteristic
91C2×C22⋊Dic7—21no—
92C2×#1144—41no—
93C2×#1144—41no—
94C2×#1144C2×C414yescomplemented
95C2×#1142—22no—
96C2×#1142—22no—
97C2×#1142C2×C414yescomplemented
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7—41no—
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4⋊Dic7C2311yescharacteristic
104#6487—22no—
105#6487C2×C414yescomplemented
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×C4×Dic7—21no—
110C2×C4×Dic7—21no—
111C2×#1136—22no—
112C2×#1136—22no—
113C2×#1136—41no—
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C4×Dic14—22no—
119C4×Dic14—41no—
120C7×#95—21no—
121C7×#95—21no—
122C7×#95—21no—
123C7×#95—21no—
124C7×#95—21no—
125C7×#95D411yescharacteristic
126C7×#95D411yescharacteristic
127#6409—22no—
128#6409—22no—
129#6409C2×C414yescomplemented
130#6406—22no—
131#6406C2×C414yescomplemented
132#6406D414yes—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C22⋊(C7⋊C8)C2×C414yescomplemented
138#6384—22no—
139#6384—41no—
140#6381—22no—
141#6381—41no—
142#6377—22no—
143C4×C7⋊C8—41no—
144C2×#452—71no—
145C2×#440—71no—
146C2×#417—71no—
147#2360—71no—
148#2339D711yescharacteristic
149#1969—71no—
150#1935—71no—
151#1928—71no—
152#1894—71no—
153#1878—71no—
154#1877—71no—
155#1862—71no—
156#1852—71no—
157C4×#102—71no—
158#1753—71no—
159C24×C7—21no—
160C24×C7C2×D411yescharacteristic
161C7×#41—28no—
162C7×#41—44no—
163C7×#41—44no—
164C7×#41—44no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8C22×C412yes—
171C2×C7×D4—24no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—42no—
176C2×C7×D4—42no—
177C2×C7×D4C22×C412yes—
178C2×C7×D4C2×D412yes—
179C2×C7×D4#4112yes—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—24no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—42no—
189C22×C4×C7—42no—
190C22×C4×C7—42no—
191C22×C4×C7—42no—
192C22×C4×C7—42no—
193C22×C4×C7—42no—
194C22×C4×C7—81no—
195C22×C4×C7—81no—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7#4112yes—
203C22×C4×C7C2411yescharacteristic
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—42no—
209C22×Dic7—42no—
210C22×Dic7—81no—
211C2×Dic14—21no—
212C2×Dic14—21no—
213C2×Dic14—21no—
214C2×Dic14—21no—
215C2×Dic14—21no—
216C2×Dic14C22×C412yes—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C22⋊C4—22no—
222C7×C22⋊C4—41no—
223C7×C22⋊C4—42no—
224C7×C22⋊C4—42no—
225C7×C22⋊C4—81no—
226C42×C7—21no—
227C42×C7—21no—
228C42×C7—21no—
229C42×C7—21no—
230C22⋊Dic7—24no—
231#1144—44no—
232#1142—28no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7—21no—
237C4⋊Dic7—42no—
238C4⋊Dic7C22×C412yes—
239C4⋊Dic7C2×D412yes—
240Dic7⋊C4—24no—
241Dic7⋊C4—42no—
242Dic7⋊C4—81no—
243C4×Dic7—42no—
244C4×Dic7—81no—
245#1136—44no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8C22×C412yes—
256C2×C7⋊C8C22×C412yes—
257C2×C7⋊C8C2×D412yes—
258C22×#41C2×D711yescharacteristic
259C22×Q16—71no—
260C22×SD16—71no—
261C22×M16—71no—
262C2×C22⋊Q8—71no—
263C2×C4×Q8—71no—
264C2×C4×D4C2×D711yescharacteristic
265C2×C4×D4C2×D711yescharacteristic
266C22×C4⋊C4—71no—
267#452—78no—
268#440—144no—
269C2×#107—71no—
270C2×#107—71no—
271#417—144no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×#103—71no—
277C2×#102—71no—
278C2×#102—71no—
279C2×#102—71no—
280C2×C22⋊C8—71no—
281C2×#97—71no—
282C2×C4×C8—71no—
283#391—71no—
284#391C2×D711yescharacteristic
285#391C2×D711yescharacteristic
286#389—71no—
287#389—141no—
288#387—141no—
289#386—21no—
290#386—21no—
291#385—141no—
292#381—21no—
293#380C2×D711yescharacteristic
294C4×C4⋊C4—71no—
295C4×C22⋊C4—141no—
296C4×C22⋊C4C2×D711yescharacteristic
297C2×#95—21no—
298#340—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#336—71no—
303#336—71no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—21no—
307C23×C7—22no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7C4×D412yes—
318C23×C7C22×D411yescharacteristic
319C7×Q8—22no—
320C7×Q8—22no—
321C7×Q8—41no—
322C7×Q8—41no—
323C7×D4—22no—
324C7×D4—22no—
325C7×D4—22no—
326C7×D4—48no—
327C7×D4C4×D414yes—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—48no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—84no—
356C2×C4×C7—84no—
357C2×C4×C7C4×D412yes—
358C2×C4×C7#13712yes—
359C2×C4×C7C23×C411yescharacteristic
360C2×C4×C7C22×D411yescharacteristic
361C2×C4×C7C2×#4111yescharacteristic
362C2×C4×C7C2×#4111yescharacteristic
363C2×C4×C7H(5,𝔽2)11yescharacteristic
364C2×C4×C7H(5,𝔽2)11yescharacteristic
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—84no—
378Dic14—22no—
379Dic14—22no—
380Dic14—41no—
381Dic14—41no—
382C7⋊C8—22no—
383C7⋊C8—22no—
384C7⋊C8—22no—
385C7⋊C8—41no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—41no—
390C2×#41—41no—
391C2×#41C4×D714yes—
392C22×Q8—71no—
393C22×Q8C22×D711yescharacteristic
394C22×D4—21no—
395C22×D4C22×D711yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—141no—
400C23×C4C22×D711yescharacteristic
401C2×Q16—74no—
402C2×Q16—281no—
403C2×Q16—281no—
404C2×SD16—74no—
405C2×SD16—142no—
406C2×SD16—142no—
407C2×M16—142no—
408C2×M16—142no—
409C2×M16—281no—
410C22×C8—71no—
411C22×C8—71no—
412C22×C8—71no—
413C22×C8—71no—
414C22⋊Q8—74no—
415C22⋊Q8—142no—
416C4×Q8—142no—
417C4×Q8—281no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—41no—
421C4×D4—41no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—71no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—142no—
426C2×C4⋊C4—141no—
427C2×C4⋊C4—141no—
428C2×C4⋊C4—141no—
429C2×C4⋊C4—141no—
430C2×C4⋊C4—281no—
431C2×C4⋊C4C22×D711yescharacteristic
432C2×C4⋊C4C22×D711yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4C22⋊D711yescharacteristic
438C2×C22⋊C4C22⋊D711yescharacteristic
439C2×C42—141no—
440C2×C42—141no—
441C2×C42C22×D711yescharacteristic
442C2×C42C22×D711yescharacteristic
443#107—142no—
444#107—281no—
445#103—74no—
446#103—142no—
447#103—142no—
448#103—142no—
449#103—281no—
450#102—74no—
451#102—74no—
452#102—142no—
453C22⋊C8—74no—
454#97—142no—
455C4×C8—281no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—141no—
462#95—141no—
463#95—141no—
464#95—141no—
465#95C22⋊D711yescharacteristic
466#95C22⋊D711yescharacteristic
467C22×C7—22no—
468C22×C7—24no—
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—41no—
474C22×C7—42no—
475C22×C7—41no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—42no—
481C22×C7C2×C4×D411yescharacteristic
482C22×C7D4211yescharacteristic
483C22×C7#54611yescharacteristic
484C22×C7C2×#13711yescharacteristic
485C22×C7#57511yescharacteristic
486C22×C7#57611yescharacteristic
487C22×C7#57811yescharacteristic
488C4×C7—22no—
489C4×C7—22no—
490C4×C7—42no—
491C4×C7—41no—
492C4×C7—41no—
493C4×C7—41no—
494C4×C7—81no—
495C4×C7—81no—
496C4×C7C2×C4×D411yescharacteristic
497C4×C7#51811yescharacteristic
498C4×C7#54611yescharacteristic
499C4×C7#55111yescharacteristic
500Dic7—42no—
501Dic7—42no—
502Dic7—42no—
503Dic7—81no—
504C24—21no—
505C24C2×C22⋊D711yescharacteristic
506#41—28no—
507#41—44no—
508#41—44no—
509#41—44no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—72no—
516C2×Q8—141no—
517C2×Q8—141no—
518C2×Q8—141no—
519C2×Q8—141no—
520C2×Q8—141no—
521C2×Q8C2×C4×D712yes—
522C2×D4—24no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4C2×C4×D712yes—
529C2×D4D4×D712yes—
530C2×D4#115912yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—141no—
550C22×C4—141no—
551C22×C4—282no—
552C22×C4—282no—
553C22×C4—561no—
554C22×C4C2×C4×D712yes—
555C22×C4#115712yes—
556C22×C4C2×C22⋊D711yescharacteristic
557C22×C4C2×C22⋊D711yescharacteristic
558C22×C4C2×C22⋊D711yescharacteristic
559C22×C4C2×C22⋊D711yescharacteristic
560C22×C4C2×C22⋊D711yescharacteristic
561C22×C4C23×D711yescharacteristic
562Q16—284no—
563SD16—148no—
564M16—284no—
565C2×C8—72no—
566C2×C8—72no—
567C2×C8—72no—
568C2×C8—141no—
569C2×C8—141no—
570C2×C8—141no—
571C2×C8—141no—
572C2×C8—141no—
573C2×C8—141no—
574C2×C8—141no—
575C2×C8—141no—
576C2×C8—141no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—72no—
582C4⋊C4—72no—
583C4⋊C4—144no—
584C4⋊C4—141no—
585C4⋊C4—141no—
586C4⋊C4—141no—
587C4⋊C4—141no—
588C4⋊C4—282no—
589C4⋊C4—282no—
590C4⋊C4—561no—
591C22⋊C4—22no—
592C22⋊C4—41no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C22⋊C4—144no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—282no—
602C42—561no—
603C2×C7—42no—
604C2×C7—44no—
605C2×C7#235811yescharacteristic
606C2×C7C4×#13711yescharacteristic
607C2×C7#295111yescharacteristic
608C2×C7#327311yescharacteristic
609C2×C7#327611yescharacteristic
610C2×C7#331411yescharacteristic
611C2×C7#331511yescharacteristic
612C23—22no—
613C23—22no—
614C23—21no—
615C23—22no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C4×C22⋊D712yes—
626C23C22×C22⋊D711yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—142no—
632Q8—142no—
633Q8—281no—
634Q8—281no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—48no—
639D4(C22⋊D7)⋊C414yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—48no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4—281no—
677C2×C4—281no—
678C2×C4—281no—
679C2×C4—281no—
680C2×C4—281no—
681C2×C4—564no—
682C2×C4C4×C22⋊D712yes—
683C2×C4#651412yes—
684C2×C4C22×C4×D711yescharacteristic
685C2×C4C2×#115711yescharacteristic
686C2×C4C2×D4×D711yescharacteristic
687C2×C4C2×#115911yescharacteristic
688C2×C4#654811yescharacteristic
689C2×C4#654811yescharacteristic
690C8—142no—
691C8—142no—
692C8—142no—
693C8—281no—
694C7#2286211yescharacteristic, complemented, Sylow
695C22—22no—
696C22—22no—
697C22—22no—
698C22—24no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22C2×C4×C22⋊D711yescharacteristic
710C22D4×C22⋊D711yescharacteristic
711C22#9049711yescharacteristic
712C22#9051311yescharacteristic
713C22C2×#651411yescharacteristic
714C22#9052611yescharacteristic
715C22#9052911yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—81no—
723C4—81no—
724C4—282no—
725C4—282no—
726C4—282no—
727C4—561no—
728C4C2×(C22⋊D7)⋊C411yescharacteristic
729C4#9017711yescharacteristic
730C4#9018111yescharacteristic
731C4#9018611yescharacteristic
732C2—42no—
733C2—44no—
734C2#1173954411yescharacteristic
735C2C4×#651411yescharacteristic
736C2#1174000211yescharacteristic
737C2#1174094311yescharacteristic
738C2#1174094911yescharacteristic
739C2#1174095811yescharacteristic
740C2#1174097411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2339C2
socleC23×C7C22×D4
prime radicalC22×C7×#41C22
cosocleC22×C4×C7C24
hypercenter#2339D7
hypocenterC7#22862
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
4. C2×#89790C2semidirect
5. #11730910C2semidirect
6. #11729366C2semidirect
7. C4×#6406C2semidirect
8. #11729360C2semidirect
9. #11727444C2semidirect
10. #11727431C2semidirect
11. #11727429C2semidirect
12. #11727421C2semidirect
13. #11727270C2semidirect
14. #11727258C2semidirect
15. #11727202C2semidirect
33. #90011C4semidirect
94. C2×#1144C2×C4semidirect
97. C2×#1142C2×C4semidirect
105. #6487C2×C4semidirect
129. #6409C2×C4semidirect
131. #6406C2×C4semidirect
137. C22⋊(C7⋊C8)C2×C4semidirect
694. C7#22862semidirect

Maximal subgroups

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

subgroupindex
C7×#23392
C2×#900112
C2×#900042
C2×#897902
#117309102
#117293662
C4×#64062
#117293602
#117274442
#117274312
#117274292
#117274212
#117272702
#117272582
#117272022
#228627