Finite Group Databasebeta

← #13278092

Subgroups — #13278092

Order 1792.

1586 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89723C211yesmaximal, characteristic
2C2×C22⋊C4×Dic7C211yesmaximal, characteristic
3C2×#89425C211yesmaximal, characteristic, complemented
4C7×#1440C211yesmaximal, characteristic
5#11729301C211yesmaximal, characteristic
6#11729299C211yesmaximal, characteristic
7#11729298C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11727171C211yesmaximal, characteristic, complemented
10#11727167C211yesmaximal, characteristic, complemented
11#11727161C211yesmaximal, characteristic, complemented
12#11727157C211yesmaximal, characteristic, complemented
13#11727157C211yesmaximal, characteristic, complemented
14#11727156C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
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#89723C418yescomplemented
52C22⋊C4×Dic7—24no—
53#89425—24no—
54#14086—71nomaximal, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—22no—
63C23×Dic7—22no—
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—22no—
67C23×Dic7—41no—
68C23×Dic7—41no—
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—41no—
85C2×C7×C22⋊C4C2×C414yes—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—41no—
91C2×C22⋊Dic7—41no—
92C2×C22⋊Dic7—41no—
93C2×C22⋊Dic7C2×C414yes—
94C2×C22⋊Dic7C2×C414yes—
95C2×C4⋊Dic7—22no—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7C2×C414yescomplemented
98C2×Dic7⋊C4—22no—
99C2×Dic7⋊C4—41no—
100C2×Dic7⋊C4—41no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—41no—
106C2×C4×Dic7—41no—
107C2×C4×Dic7—41no—
108C2×C4×Dic7—41no—
109C2×C4×Dic7—41no—
110C2×C4×Dic7—41no—
111C2×C4×Dic7C2×C414yescomplemented
112C2×C4×Dic7D414yes—
113C7×#95—22no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—41no—
117C7⋊#95—22no—
118C7⋊#95—22no—
119C7⋊#95—22no—
120C7⋊#95—22no—
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95C2×C414yescomplemented
134C7⋊#95C2×C414yescomplemented
135C2×#388—71no—
136C2×#387—71no—
137C2×C4×C22⋊C4—71no—
138#1443—71no—
139#1442—71no—
140#1440D711yescharacteristic
141#1439—71no—
142#1437—71no—
143#1436—71no—
144#1434—71no—
145#1434—71no—
146#1434—71no—
147C22⋊#95—71no—
148C22⋊#95—71no—
149C4×#95—71no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7C22×C412yes—
163C24×C7#4112yes—
164C24×C7#4112yes—
165C24×C7C2411yescharacteristic
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×C7C22×C412yes—
204C22×C4×C7C22×C412yes—
205C22×C4×C7C2×D412yes—
206C22×C4×C7#4112yes—
207C22×C4×C7#4112yes—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—28no—
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—44no—
255C22×Dic7—44no—
256C22×Dic7—44no—
257C22×Dic7—44no—
258C22×Dic7—44no—
259C22×Dic7—44no—
260C22×Dic7C22×C412yes—
261C22×Dic7C22×C412yes—
262C22×Dic7C22×C412yes—
263C22×Dic7C22×C412yes—
264C22×Dic7C2×D412yes—
265C22×Dic7C2×D412yes—
266C22×Dic7#4112yes—
267C22×Dic7#4112yes—
268C22×Dic7#4112yes—
269C22×Dic7#4112yes—
270C22×Dic7#4112yes—
271C7×C22⋊C4—28no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—44no—
274C22⋊Dic7—28no—
275C22⋊Dic7—44no—
276C22⋊Dic7—44no—
277C4⋊Dic7—28no—
278Dic7⋊C4—44no—
279C4×Dic7—44no—
280C4×Dic7—44no—
281C4×Dic7—44no—
282C4×Dic7—44no—
283C24×C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4C2×D711yescharacteristic
290C22×C22⋊C4C2×D711yescharacteristic
291C22×C22⋊C4C2×D711yescharacteristic
292C22×C42—71no—
293C22×C42—71no—
294C22×C42—71no—
295C22×C42—71no—
296#388—78no—
297#387—144no—
298C4×C22⋊C4—144no—
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×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95C2×D711yescharacteristic
318C2×#95C2×D711yescharacteristic
319C2×#95C2×D711yescharacteristic
320C2×#95C2×D711yescharacteristic
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7#11714yes—
356C23×C7C23×C411yescharacteristic
357C23×C7C22×D411yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7C2×#4111yescharacteristic
363C23×C7C2×#4111yescharacteristic
364C23×C7C2×#4111yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7H(5,𝔽2)11yescharacteristic
368C23×C7H(5,𝔽2)11yescharacteristic
369C23×C7H(5,𝔽2)11yescharacteristic
370C23×C72−1+411yescharacteristic
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—41no—
387C2×C4×C7—41no—
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×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
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—416no—
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—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7C4×D414yes—
469C2×Dic7#12414yes—
470C25C22×D711yescharacteristic
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—142no—
480C23×C4—142no—
481C23×C4—142no—
482C23×C4—142no—
483C23×C4—142no—
484C23×C4—281no—
485C23×C4—281no—
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C23×C4C22×D711yescharacteristic
489C23×C4C22×D711yescharacteristic
490C23×C4C22×D711yescharacteristic
491C23×C4C22×D711yescharacteristic
492C2×C4⋊C4—74no—
493C2×C4⋊C4—142no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4—142no—
496C2×C4⋊C4—281no—
497C2×C4⋊C4—281no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—142no—
509C2×C22⋊C4—142no—
510C2×C22⋊C4—142no—
511C2×C22⋊C4—142no—
512C2×C22⋊C4—281no—
513C2×C22⋊C4—281no—
514C2×C22⋊C4—281no—
515C2×C22⋊C4C4×D714yes—
516C2×C42—74no—
517C2×C42—74no—
518C2×C42—142no—
519C2×C42—142no—
520C2×C42—142no—
521C2×C42—142no—
522C2×C42—281no—
523C2×C42—281no—
524C2×C42—281no—
525C2×C42—281no—
526C2×C42—281no—
527C2×C42—281no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—41no—
532#95—74no—
533#95—74no—
534#95—142no—
535#95—142no—
536#95—142no—
537#95—142no—
538#95—142no—
539#95—142no—
540#95—142no—
541#95—142no—
542#95—142no—
543#95—142no—
544#95—142no—
545#95—142no—
546#95—142no—
547#95—281no—
548#95—281no—
549#95—281no—
550C22×C7—24no—
551C22×C7—24no—
552C22×C7—24no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7C2×#11711yescharacteristic
566C22×C7C2×C4×D411yescharacteristic
567C22×C7C4×#4111yescharacteristic
568C22×C7C4×#4111yescharacteristic
569C22×C7C4×#4111yescharacteristic
570C22×C7#51811yescharacteristic
571C22×C7#52011yescharacteristic
572C22×C7#52511yescharacteristic
573C22×C7#52511yescharacteristic
574C22×C7C2×#12411yescharacteristic
575C22×C7#52911yescharacteristic
576C22×C7#52911yescharacteristic
577C22×C7#52911yescharacteristic
578C22×C7#52911yescharacteristic
579C22×C7#53211yescharacteristic
580C22×C7#53411yescharacteristic
581C22×C7#53711yescharacteristic
582C22×C7#53811yescharacteristic
583C22×C7#53911yescharacteristic
584C22×C7#55111yescharacteristic
585C22×C7#55111yescharacteristic
586C22×C7#55111yescharacteristic
587C22×C7#55111yescharacteristic
588C22×C7#55111yescharacteristic
589C22×C7#55111yescharacteristic
590C22×C7#55211yescharacteristic
591C22×C7#55211yescharacteristic
592C22×C7#55211yescharacteristic
593C22×C7#55311yescharacteristic
594C22×C7#55311yescharacteristic
595C22×C7#55311yescharacteristic
596C22×C7#55311yescharacteristic
597C22×C7#55311yescharacteristic
598C22×C7#55611yescharacteristic
599C22×C7#55911yescharacteristic
600C4×C7—42no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7—81no—
606Dic7—24no—
607Dic7—24no—
608Dic7—42no—
609Dic7—42no—
610Dic7—42no—
611Dic7—42no—
612Dic7—42no—
613Dic7—81no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C2×C4×D712yes—
627C24#115912yes—
628C24#115912yes—
629C24C23×D711yescharacteristic
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—21no—
666C22×C4—21no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—72no—
676C22×C4—72no—
677C22×C4—72no—
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—148no—
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×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—284no—
725C22×C4—284no—
726C22×C4—284no—
727C22×C4—284no—
728C22×C4—284no—
729C22×C4—284no—
730C22×C4C2×C4×D712yes—
731C22×C4C2×C4×D712yes—
732C22×C4D4×D712yes—
733C22×C4#115912yes—
734C22×C4#115912yes—
735C4⋊C4—148no—
736C4⋊C4—284no—
737C22⋊C4—28no—
738C22⋊C4—28no—
739C22⋊C4—44no—
740C22⋊C4—148no—
741C22⋊C4—284no—
742C22⋊C4—284no—
743C42—284no—
744C42—284no—
745C42—284no—
746C42—284no—
747C2×C7—44no—
748C2×C7#229011yescharacteristic
749C2×C7C4×#12411yescharacteristic
750C2×C7#232511yescharacteristic
751C2×C7#234311yescharacteristic
752C2×C7#235311yescharacteristic
753C2×C7#237311yescharacteristic
754C2×C7#237411yescharacteristic
755C2×C7#256111yescharacteristic
756C2×C7#256211yescharacteristic
757C2×C7#257511yescharacteristic
758C2×C7#257611yescharacteristic
759C2×C7#257711yescharacteristic
760C2×C7#257811yescharacteristic
761C2×C7#260111yescharacteristic
762C2×C7#260211yescharacteristic
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23#644014yes—
798C23C22×C4×D711yescharacteristic
799C23C2×D4×D711yescharacteristic
800C23C2×#115911yescharacteristic
801C23C2×#115911yescharacteristic
802C23C2×#115911yescharacteristic
803C23C2×#115911yescharacteristic
804C23#654811yescharacteristic
805C23D7×#4111yescharacteristic
806C23D7×#4111yescharacteristic
807C23D7×#4111yescharacteristic
808C23D7×#4111yescharacteristic
809C23D7×#4111yescharacteristic
810C23#655311yescharacteristic
811C23#655311yescharacteristic
812C23#655411yescharacteristic
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—22no—
826C2×C4—22no—
827C2×C4—22no—
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—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—74no—
856C2×C4—74no—
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—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—2816no—
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—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C7#1408611yescharacteristic, complemented, Sylow
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#644011yescharacteristic
929C22#9021311yescharacteristic
930C22#9021411yescharacteristic
931C22C4×#115911yescharacteristic
932C22C4×#115911yescharacteristic
933C22C4×D4×D711yescharacteristic
934C22#9023611yescharacteristic
935C22#9027711yescharacteristic
936C22#9027811yescharacteristic
937C22#9028711yescharacteristic
938C22#9029111yescharacteristic
939C22#9029211yescharacteristic
940C22#9029211yescharacteristic
941C22#9029711yescharacteristic
942C22#9029911yescharacteristic
943C22#9030911yescharacteristic
944C22#9030911yescharacteristic
945C22#9034011yescharacteristic
946C22#9034011yescharacteristic
947C22#9034111yescharacteristic
948C22#9034111yescharacteristic
949C22#9034111yescharacteristic
950C22#9034411yescharacteristic
951C22#9034911yescharacteristic
952C22#9034911yescharacteristic
953C22#9034911yescharacteristic
954C22#9035211yescharacteristic
955C22#9036211yescharacteristic
956C22D7×#12411yescharacteristic
957C22#9036911yescharacteristic
958C22#9037211yescharacteristic
959C22#9039611yescharacteristic
960C22#9039611yescharacteristic
961C22#9039711yescharacteristic
962C22#9039811yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—144no—
970C4—144no—
971C4—282no—
972C4—282no—
973C4—282no—
974C4—282no—
975C4—282no—
976C4—561no—
977C2—44no—
978C2#1173150411yescharacteristic
979C2#1173210211yescharacteristic
980C2#1173211911yescharacteristic
981C2#1173289911yescharacteristic
982C2#1173293111yescharacteristic
983C2#1173293211yescharacteristic
984C2#1173327411yescharacteristic
985C2#1173440011yescharacteristic
986C2#1173440211yescharacteristic
987C2#1173440911yescharacteristic
988C2#1173441011yescharacteristic
989C2#1173496511yescharacteristic
990C2#1173496811yescharacteristic
991C2#1173496911yescharacteristic
992C2#1173512811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1440C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1440D7
hypocenterC7#14086
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#89425C2semidirect
9. #11727171C2semidirect
10. #11727167C2semidirect
11. #11727161C2semidirect
12. #11727157C2semidirect
13. #11727157C2semidirect
14. #11727156C2semidirect
15. Dic7×#95C2semidirect
51. #89723C4semidirect
97. C2×C4⋊Dic7C2×C4semidirect
111. C2×C4×Dic7C2×C4semidirect
133. C7⋊#95C2×C4semidirect
134. C7⋊#95C2×C4semidirect
912. C7#14086semidirect

Maximal subgroups

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

subgroupindex
C2×#897232
C2×C22⋊C4×Dic72
C2×#894252
C7×#14402
#117293012
#117292992
#117292982
#117271712
#117271672
#117271612
#117271572
#117271562
Dic7×#952
#140867