Finite Group Databasebeta

← #13277432

Subgroups — #13277432

Order 1792.

1478 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89762C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
3C2×#89712C211yesmaximal, characteristic
4C7×#1436C211yesmaximal, characteristic, complemented
5C4×C7⋊#95C211yesmaximal, characteristic, complemented
6#11727183C211yesmaximal, characteristic
7#11727181C211yesmaximal, characteristic
8#11727169C211yesmaximal, characteristic, complemented
9#11727167C211yesmaximal, characteristic, complemented
10#11727162C211yesmaximal, characteristic
11#11727162C211yesmaximal, characteristic
12#11727162C211yesmaximal, characteristic
13#11727160C211yesmaximal, characteristic, complemented
14#11727155C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51#89762C418yescomplemented
52C4⋊C4×Dic7—24no—
53#89712—24no—
54#14037—71nomaximal, Sylow
55C24×D7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4C2×C414yes—
73C2×C42×C7—22no—
74C2×C42×C7—22no—
75C2×C42×C7—41no—
76C2×(C2×D7)⋊C4—22no—
77C2×(C2×D7)⋊C4—22no—
78C2×(C2×D7)⋊C4—22no—
79C2×(C2×D7)⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4—22no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—41no—
89C2×(C2×D7)⋊C4—41no—
90C2×(C2×D7)⋊C4—41no—
91C2×(C2×D7)⋊C4—41no—
92C2×(C2×D7)⋊C4—41no—
93C2×(C2×D7)⋊C4—41no—
94C2×(C2×D7)⋊C4C2×C414yes—
95C2×(C2×D7)⋊C4C2×C414yes—
96C2×(C2×D7)⋊C4C2×C414yes—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—22no—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—41no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—41no—
111C2×C4×Dic7—41no—
112C2×C4×Dic7—41no—
113C2×C4×Dic7—41no—
114C2×C4×Dic7C2×C414yes—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—41no—
120C7⋊#95—22no—
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95C2×C414yes—
133C7⋊#95C2×C414yes—
134C7⋊#95D414yes—
135C2×#388—71no—
136C2×#388—71no—
137C2×C4×C4⋊C4—71no—
138#1442—71no—
139#1442—71no—
140#1440—71no—
141#1439—71no—
142#1437—71no—
143#1437—71no—
144#1437—71no—
145#1436—71no—
146#1436D711yescharacteristic, complemented
147#1434—71no—
148#1434—71no—
149C4×#95—71no—
150C24×C7C2411yescharacteristic
151C23×D7—21no—
152C23×D7—21no—
153C23×D7—21no—
154C23×D7—21no—
155C23×D7—21no—
156C23×D7—21no—
157C23×D7—21no—
158C23×D7—21no—
159C23×D7—21no—
160C23×D7—21no—
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7C22×C412yes—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7C22×C412yes—
207C22×C4×C7C22×C412yes—
208C22×C4×C7C22×C412yes—
209C22×C4×C7C2×D412yes—
210C22×C4×C7#4112yes—
211C22×C4×C7#4112yes—
212C22×C4×C7#4112yes—
213C22×C4×C7#4112yes—
214C22×C4×C7#4112yes—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7C22×C412yes—
256C22×Dic7C22×C412yes—
257C22×Dic7C22×C412yes—
258C22×Dic7C2×D412yes—
259C22×Dic7C2×D412yes—
260C22×Dic7#4112yes—
261C22×Dic7#4112yes—
262C22×Dic7#4112yes—
263C22×Dic7#4112yes—
264C7×C4⋊C4—28no—
265C42×C7—44no—
266(C2×D7)⋊C4—28no—
267(C2×D7)⋊C4—28no—
268(C2×D7)⋊C4—44no—
269(C2×D7)⋊C4—44no—
270(C2×D7)⋊C4—44no—
271(C2×D7)⋊C4—44no—
272(C2×D7)⋊C4—44no—
273C4⋊Dic7—28no—
274Dic7⋊C4—44no—
275C4×Dic7—28no—
276C4×Dic7—44no—
277C4×Dic7—44no—
278C4×Dic7—44no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C22⋊C4—71no—
283C22×C22⋊C4—71no—
284C22×C22⋊C4—71no—
285C22×C22⋊C4—71no—
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C42—71no—
290C22×C42—71no—
291C22×C42—71no—
292C22×C42—71no—
293C22×C42C2×D711yescharacteristic
294#388—78no—
295#388—144no—
296C4×C4⋊C4—144no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95C2×D711yescharacteristic
313C2×#95C2×D711yescharacteristic
314C2×#95C2×D711yescharacteristic
315C2×#95C2×D711yescharacteristic
316C2×#95C2×D711yescharacteristic
317C23×C7C23×C411yescharacteristic
318C23×C7C22×D411yescharacteristic
319C23×C7C2×#4111yescharacteristic
320C23×C7C2×#4111yescharacteristic
321C23×C7C2×#4111yescharacteristic
322C23×C7C2×#4111yescharacteristic
323C23×C7C2×#4111yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4111yescharacteristic
327C23×C7C2×#4111yescharacteristic
328C23×C7H(5,𝔽2)11yescharacteristic
329C23×C7H(5,𝔽2)11yescharacteristic
330C23×C7H(5,𝔽2)11yescharacteristic
331C23×C72−1+411yescharacteristic
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—41no—
340C22×D7—41no—
341C22×D7—41no—
342C22×D7—41no—
343C22×D7—41no—
344C22×D7—41no—
345C22×D7—41no—
346C22×D7—41no—
347C22×D7—41no—
348C22×D7—41no—
349C22×D7—41no—
350C22×D7—41no—
351C22×D7—41no—
352C22×D7—41no—
353C22×D7—41no—
354C22×D7—41no—
355C22×D7—41no—
356C22×D7—41no—
357C22×D7—41no—
358C22×D7—41no—
359C22×D7—41no—
360C22×D7—41no—
361C22×D7—41no—
362C22×D7—41no—
363C22×D7—41no—
364C22×D7—41no—
365C22×D7—41no—
366C22×D7—41no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7#11714yes—
415C2×C4×C7C4×D414yes—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—41no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—41no—
445C2×Dic7—41no—
446C2×Dic7—41no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—41no—
450C2×Dic7—41no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7#12614yes—
465C25—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4C22×D711yescharacteristic
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—142no—
484C2×C4⋊C4—142no—
485C2×C4⋊C4—142no—
486C2×C4⋊C4—142no—
487C2×C4⋊C4—281no—
488C2×C4⋊C4C4×D714yes—
489C2×C22⋊C4—74no—
490C2×C22⋊C4—74no—
491C2×C22⋊C4—74no—
492C2×C22⋊C4—142no—
493C2×C22⋊C4—142no—
494C2×C22⋊C4—142no—
495C2×C22⋊C4—142no—
496C2×C22⋊C4—142no—
497C2×C22⋊C4—142no—
498C2×C22⋊C4—142no—
499C2×C22⋊C4—142no—
500C2×C22⋊C4—142no—
501C2×C22⋊C4—142no—
502C2×C22⋊C4—142no—
503C2×C22⋊C4—142no—
504C2×C22⋊C4—281no—
505C2×C22⋊C4—281no—
506C2×C22⋊C4—281no—
507C2×C22⋊C4—281no—
508C2×C22⋊C4—281no—
509C2×C22⋊C4—281no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—41no—
513C2×C42—74no—
514C2×C42—142no—
515C2×C42—142no—
516C2×C42—142no—
517C2×C42—142no—
518C2×C42—142no—
519C2×C42—142no—
520C2×C42—142no—
521C2×C42—281no—
522C2×C42—281no—
523C2×C42—281no—
524C2×C42—281no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—41no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95—142no—
534#95—142no—
535#95—142no—
536#95—142no—
537#95—142no—
538#95—142no—
539#95—142no—
540#95—281no—
541#95—281no—
542#95—281no—
543#95—281no—
544#95—281no—
545C22×C7C2×#11711yescharacteristic
546C22×C7C2×C4×D411yescharacteristic
547C22×C7C4×#4111yescharacteristic
548C22×C7C4×#4111yescharacteristic
549C22×C7C4×#4111yescharacteristic
550C22×C7#51811yescharacteristic
551C22×C7#52011yescharacteristic
552C22×C7#52511yescharacteristic
553C22×C7#52511yescharacteristic
554C22×C7C2×#12611yescharacteristic
555C22×C7#52911yescharacteristic
556C22×C7#52911yescharacteristic
557C22×C7#52911yescharacteristic
558C22×C7#52911yescharacteristic
559C22×C7#52911yescharacteristic
560C22×C7#53811yescharacteristic
561C22×C7#53911yescharacteristic
562C22×C7#54011yescharacteristic
563C22×C7#54211yescharacteristic
564C22×C7#54611yescharacteristic
565C22×C7#54611yescharacteristic
566C22×C7#54611yescharacteristic
567C22×C7#54811yescharacteristic
568C22×C7#55211yescharacteristic
569C22×C7#55211yescharacteristic
570C22×C7#55311yescharacteristic
571C22×C7#55311yescharacteristic
572C22×C7#55311yescharacteristic
573C22×C7#55311yescharacteristic
574C22×C7#55511yescharacteristic
575C22×C7#55511yescharacteristic
576C22×C7#55611yescharacteristic
577C22×C7#55911yescharacteristic
578C22×C7#55911yescharacteristic
579C22×C7#55911yescharacteristic
580C2×D7—42no—
581C2×D7—42no—
582C2×D7—42no—
583C2×D7—42no—
584C2×D7—42no—
585C2×D7—42no—
586C2×D7—42no—
587C2×D7—81no—
588C2×D7—81no—
589C2×D7—81no—
590C2×D7—81no—
591C2×D7—81no—
592C2×D7—81no—
593C2×D7—81no—
594C2×D7—81no—
595C4×C7—24no—
596C4×C7—24no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600C4×C7—81no—
601C4×C7—81no—
602Dic7—24no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606Dic7—42no—
607Dic7—42no—
608Dic7—42no—
609C24—72no—
610C24—141no—
611C24—141no—
612C24—141no—
613C24—141no—
614C24—141no—
615C24—141no—
616C24—141no—
617C24—141no—
618C24—141no—
619C24—141no—
620C24—141no—
621C24—141no—
622C24—141no—
623C24—141no—
624C24C23×D711yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
678C22×C4—141no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4—141no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—141no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4C2×C4×D712yes—
715C22×C4C2×C4×D712yes—
716C22×C4C2×C4×D712yes—
717C22×C4#115712yes—
718C22×C4#115712yes—
719C22×C4D4×D712yes—
720C22×C4#115912yes—
721C22×C4#115912yes—
722C22×C4#116112yes—
723C4⋊C4—28no—
724C4⋊C4—148no—
725C4⋊C4—284no—
726C22⋊C4—148no—
727C22⋊C4—148no—
728C22⋊C4—284no—
729C22⋊C4—284no—
730C22⋊C4—284no—
731C22⋊C4—284no—
732C22⋊C4—284no—
733C42—44no—
734C42—148no—
735C42—284no—
736C42—284no—
737C42—284no—
738C2×C7#229011yescharacteristic
739C2×C7C4×#12611yescharacteristic
740C2×C7#233511yescharacteristic
741C2×C7#234611yescharacteristic
742C2×C7#235711yescharacteristic
743C2×C7#236411yescharacteristic
744C2×C7#236711yescharacteristic
745C2×C7#245811yescharacteristic
746C2×C7#245911yescharacteristic
747C2×C7#247611yescharacteristic
748C2×C7#248111yescharacteristic
749C2×C7#251311yescharacteristic
750C2×C7#252511yescharacteristic
751C2×C7#259311yescharacteristic
752C2×C7#259611yescharacteristic
753D7—82no—
754C23—142no—
755C23—142no—
756C23—142no—
757C23—142no—
758C23—142no—
759C23—142no—
760C23—142no—
761C23—281no—
762C23—281no—
763C23—281no—
764C23—281no—
765C23—281no—
766C23—281no—
767C23—281no—
768C23—281no—
769C23—281no—
770C23—281no—
771C23—281no—
772C23—281no—
773C23—281no—
774C23—281no—
775C23—281no—
776C23—281no—
777C23—281no—
778C23—281no—
779C23—281no—
780C23—281no—
781C23—281no—
782C23—281no—
783C23—281no—
784C23—281no—
785C23—281no—
786C23—281no—
787C23—281no—
788C23—281no—
789C23C22×C4×D711yescharacteristic
790C23C2×#115711yescharacteristic
791C23C2×#115711yescharacteristic
792C23C2×D4×D711yescharacteristic
793C23C2×#115911yescharacteristic
794C23C2×#115911yescharacteristic
795C23#654811yescharacteristic
796C23C2×#116111yescharacteristic
797C23#655111yescharacteristic
798C23D7×#4111yescharacteristic
799C23D7×#4111yescharacteristic
800C23D7×#4111yescharacteristic
801C23D7×#4111yescharacteristic
802C23#655311yescharacteristic
803C23#655311yescharacteristic
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—74no—
852C2×C4—142no—
853C2×C4—142no—
854C2×C4—142no—
855C2×C4—142no—
856C2×C4—142no—
857C2×C4—142no—
858C2×C4—142no—
859C2×C4—142no—
860C2×C4—142no—
861C2×C4—142no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—142no—
865C2×C4—142no—
866C2×C4—142no—
867C2×C4—142no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—281no—
877C2×C4—281no—
878C2×C4—281no—
879C2×C4—281no—
880C2×C4—281no—
881C2×C4—281no—
882C2×C4—281no—
883C2×C4—281no—
884C2×C4—281no—
885C2×C4—281no—
886C2×C4—281no—
887C2×C4—281no—
888C2×C4—281no—
889C2×C4—281no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—281no—
893C2×C4—281no—
894C2×C4—281no—
895C2×C4—281no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4#643514yes—
901C2×C4(C22⋊D7)⋊C414yes—
902C7#1403711yescharacteristic, complemented, Sylow
903C22—282no—
904C22—282no—
905C22—282no—
906C22—282no—
907C22—282no—
908C22—282no—
909C22—282no—
910C22—561no—
911C22—561no—
912C22—561no—
913C22—561no—
914C22—561no—
915C22—561no—
916C22—561no—
917C22—561no—
918C22C2×#643511yescharacteristic
919C22C2×(C22⋊D7)⋊C411yescharacteristic
920C22#9020411yescharacteristic
921C22#9020511yescharacteristic
922C22#9021311yescharacteristic
923C22#9022111yescharacteristic
924C22#9022311yescharacteristic
925C22C4×#115911yescharacteristic
926C22#9022911yescharacteristic
927C22#9022911yescharacteristic
928C22#9023611yescharacteristic
929C22#9023811yescharacteristic
930C22#9023811yescharacteristic
931C22#9025011yescharacteristic
932C22#9025411yescharacteristic
933C22C4×#116111yescharacteristic
934C22#9026511yescharacteristic
935C22#9027211yescharacteristic
936C22#9027611yescharacteristic
937C22#9028211yescharacteristic
938C22#9029211yescharacteristic
939C22#9030911yescharacteristic
940C22#9031511yescharacteristic
941C22#9032111yescharacteristic
942C22#9032411yescharacteristic
943C22#9033111yescharacteristic
944C22#9034011yescharacteristic
945C22#9034511yescharacteristic
946C22#9035411yescharacteristic
947C22#9037211yescharacteristic
948C22#9038211yescharacteristic
949C22#9038311yescharacteristic
950C22D7×#12611yescharacteristic
951C22#9039511yescharacteristic
952C22#9042311yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—81no—
959C4—81no—
960C4—144no—
961C4—282no—
962C4—282no—
963C4—282no—
964C4—282no—
965C4—282no—
966C4—282no—
967C2—562no—
968C2#1173088311yescharacteristic
969C2#1173107811yescharacteristic
970C2#1173109111yescharacteristic
971C2#1173187311yescharacteristic
972C2#1173189211yescharacteristic
973C2#1173212311yescharacteristic
974C2#1173238711yescharacteristic
975C2#1173246411yescharacteristic
976C2#1173274711yescharacteristic
977C2#1173277111yescharacteristic
978C2#1173299811yescharacteristic
979C2#1173306611yescharacteristic
980C2#1173349811yescharacteristic
981C2#1173353911yescharacteristic
982C2#1173393811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#14037
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic7C2semidirect
4. C7×#1436C2semidirect
5. C4×C7⋊#95C2semidirect
8. #11727169C2semidirect
9. #11727167C2semidirect
13. #11727160C2semidirect
14. #11727155C2semidirect
15. #11727155C2semidirect
51. #89762C4semidirect
146. #1436D7semidirect
902. C7#14037semidirect

Maximal subgroups

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

subgroupindex
C2×#897622
C2×C4⋊C4×Dic72
C2×#897122
C7×#14362
C4×C7⋊#952
#117271832
#117271812
#117271692
#117271672
#117271622
#117271602
#117271552
#140377