Finite Group Databasebeta

← #13277396

Subgroups — #13277396

Order 1792.

1442 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
2C2×#89700C211yesmaximal, characteristic
3C2×#89705C211yesmaximal, characteristic
4C2×C4×Dic7⋊C4C211yesmaximal, characteristic
5C2×#89426C211yesmaximal, characteristic
6#11729322C211yesmaximal, characteristic
7#11729321C211yesmaximal, characteristic
8#11729318C211yesmaximal, characteristic
9#11729318C211yesmaximal, characteristic
10#11729290C211yesmaximal, characteristic
11#11729290C211yesmaximal, characteristic
12#11729288C211yesmaximal, characteristic
13#11727177C211yesmaximal, characteristic
14#11727165C211yesmaximal, characteristic
15#11727161C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C4×C7×C4⋊C4—24no—
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
51C2×C7⋊#95C2211yescharacteristic
52#89705—24no—
53C4×Dic7⋊C4—24no—
54#89700C418yescomplemented
55#89426—24no—
56#14035—71nomaximal, Sylow
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4Q814yes—
78C2×C42×C7—22no—
79C2×C42×C7—22no—
80C2×C42×C7—22no—
81C2×C42×C7—22no—
82C2×C42×C7—22no—
83C2×C42×C7—22no—
84C2×C42×C7—41no—
85C2×C42×C7—41no—
86C2×C42×C7C2×C414yes—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7C2×C414yes—
92C2×C4⋊Dic7C2×C414yes—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—22no—
99C2×Dic7⋊C4—22no—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—41no—
103C2×Dic7⋊C4C2×C414yes—
104C2×Dic7⋊C4C2×C414yes—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—41no—
111C7×#95—22no—
112C7×#95D414yes—
113C7⋊#95—22no—
114C7⋊#95—22no—
115C7⋊#95—22no—
116C7⋊#95—22no—
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—41no—
129C7⋊#95—41no—
130C7⋊#95C2×C414yes—
131C7⋊#95C2×C414yes—
132C7⋊#95D414yes—
133C2×#389—71no—
134C2×#387—71no—
135C2×#387—71no—
136C2×C4×C4⋊C4—71no—
137C2×C4×C4⋊C4D711yescharacteristic
138#1445—71no—
139#1444—71no—
140#1442—71no—
141#1441—71no—
142#1436—71no—
143#1436—71no—
144#1436—71no—
145#1436—71no—
146#1436—71no—
147#1434—71no—
148C24×C7C2411yescharacteristic
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×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
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×C7C22×C412yes—
184C22×C4×C7C22×C412yes—
185C22×C4×C7C22×C412yes—
186C22×C4×C7C2×D412yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7C2×D412yes—
190C22×C4×C7C2×Q812yes—
191C22×C4×C7C2×Q812yes—
192C22×C4×C7C2×Q812yes—
193C22×C4×C7#4112yes—
194C22×C4×C7#4112yes—
195C22×C4×C7#4112yes—
196C22×C4×C7#4112yes—
197C22×C4×C7#4112yes—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
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—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×Dic7C22×C412yes—
247C22×Dic7C22×C412yes—
248C22×Dic7C22×C412yes—
249C22×Dic7C22×C412yes—
250C22×Dic7C2×D412yes—
251C22×Dic7C2×D412yes—
252C22×Dic7#4112yes—
253C22×Dic7#4112yes—
254C7×C4⋊C4—28no—
255C7×C4⋊C4—28no—
256C42×C7—28no—
257C42×C7—44no—
258C42×C7—44no—
259C4⋊Dic7—28no—
260C4⋊Dic7—28no—
261Dic7⋊C4—28no—
262Dic7⋊C4—28no—
263Dic7⋊C4—28no—
264Dic7⋊C4—44no—
265C4×Dic7—28no—
266C4×Dic7—44no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4—71no—
273C22×C4⋊C4C2×D711yescharacteristic
274C22×C4⋊C4C2×D711yescharacteristic
275C22×C42—71no—
276C22×C42—71no—
277C22×C42C2×D711yescharacteristic
278C22×C42C2×D711yescharacteristic
279C22×C42C2×D711yescharacteristic
280#389—78no—
281#387—144no—
282#387—144no—
283C4×C4⋊C4—24no—
284C4×C4⋊C4—144no—
285C2×#95—71no—
286C2×#95—71no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
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×#95C2×D711yescharacteristic
306C2×#95C2×D711yescharacteristic
307C23×C7C23×C411yescharacteristic
308C23×C7C22×D411yescharacteristic
309C23×C7C22×D411yescharacteristic
310C23×C7C22×Q811yescharacteristic
311C23×C7C2×#4111yescharacteristic
312C23×C7C2×#4111yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7H(5,𝔽2)11yescharacteristic
319C23×C72−1+411yescharacteristic
320C23×C72−1+411yescharacteristic
321C23×C72−1+411yescharacteristic
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7C4×D414yes—
368C2×C4×C7C4×D414yes—
369C2×C4×C7C4×Q814yes—
370C2×C4×C7C22⋊Q814yes—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—41no—
393C2×Dic7—41no—
394C2×Dic7—41no—
395C2×Dic7—41no—
396C2×Dic7—41no—
397C2×Dic7—41no—
398C2×Dic7—41no—
399C2×Dic7—41no—
400C2×Dic7—41no—
401C2×Dic7—41no—
402C2×Dic7—41no—
403C2×Dic7—41no—
404C2×Dic7—41no—
405C2×Dic7—41no—
406C2×Dic7—41no—
407C2×Dic7—41no—
408C2×Dic7—41no—
409C2×Dic7—41no—
410C2×Dic7—41no—
411C2×Dic7—41no—
412C2×Dic7—41no—
413C2×Dic7—41no—
414C2×Dic7—41no—
415C2×Dic7—41no—
416C2×Dic7—41no—
417C2×Dic7—41no—
418C2×Dic7—41no—
419C2×Dic7—41no—
420C2×Dic7—41no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7—41no—
424C2×Dic7—41no—
425C2×Dic7—41no—
426C2×Dic7#11714yes—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4C22×D711yescharacteristic
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439C23×C4C22×D711yescharacteristic
440C23×C4C22×D711yescharacteristic
441C23×C4C22×D711yescharacteristic
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—74no—
450C2×C4⋊C4—74no—
451C2×C4⋊C4—142no—
452C2×C4⋊C4—142no—
453C2×C4⋊C4—142no—
454C2×C4⋊C4—142no—
455C2×C4⋊C4—142no—
456C2×C4⋊C4—142no—
457C2×C4⋊C4—142no—
458C2×C4⋊C4—142no—
459C2×C4⋊C4—142no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—142no—
463C2×C4⋊C4—142no—
464C2×C4⋊C4—281no—
465C2×C4⋊C4Dic1414yes—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—41no—
473C2×C42—41no—
474C2×C42—142no—
475C2×C42—142no—
476C2×C42—142no—
477C2×C42—142no—
478C2×C42—142no—
479C2×C42—281no—
480C2×C42C4×D714yes—
481#95—22no—
482#95—74no—
483#95—74no—
484#95—74no—
485#95—142no—
486#95—142no—
487#95—142no—
488#95—142no—
489#95—142no—
490#95—142no—
491#95—142no—
492#95—142no—
493#95—142no—
494#95—142no—
495#95—142no—
496#95—142no—
497#95—142no—
498#95—142no—
499#95—142no—
500#95—281no—
501#95—281no—
502#95C22⋊D714yes—
503C22×C7C2×#11711yescharacteristic
504C22×C7C2×C4×D411yescharacteristic
505C22×C7C2×C4×D411yescharacteristic
506C22×C7C2×C4×Q811yescharacteristic
507C22×C7C4×#4111yescharacteristic
508C22×C7#51911yescharacteristic
509C22×C7#52011yescharacteristic
510C22×C7C2×C22⋊Q811yescharacteristic
511C22×C7#52511yescharacteristic
512C22×C7#52511yescharacteristic
513C22×C7#52511yescharacteristic
514C22×C7#52911yescharacteristic
515C22×C7#52911yescharacteristic
516C22×C7#52911yescharacteristic
517C22×C7#53311yescharacteristic
518C22×C7#53911yescharacteristic
519C22×C7#53911yescharacteristic
520C22×C7#54111yescharacteristic
521C22×C7#54111yescharacteristic
522C22×C7D4211yescharacteristic
523C22×C7#54711yescharacteristic
524C22×C7#54711yescharacteristic
525C22×C7#54711yescharacteristic
526C22×C7#54711yescharacteristic
527C22×C7#54811yescharacteristic
528C22×C7D4×Q811yescharacteristic
529C22×C7#55211yescharacteristic
530C22×C7#55211yescharacteristic
531C22×C7#55311yescharacteristic
532C22×C7#55411yescharacteristic
533C22×C7#55611yescharacteristic
534C22×C7#55611yescharacteristic
535C22×C7#55711yescharacteristic
536C22×C7#55711yescharacteristic
537C22×C7#55911yescharacteristic
538C4×C7—24no—
539C4×C7—24no—
540C4×C7—24no—
541C4×C7—24no—
542C4×C7—42no—
543C4×C7—42no—
544C4×C7—42no—
545Dic7—24no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550Dic7—42no—
551Dic7—81no—
552Dic7—81no—
553C24C23×D711yescharacteristic
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—72no—
594C22×C4—72no—
595C22×C4—72no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—141no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—141no—
615C22×C4—141no—
616C22×C4—141no—
617C22×C4—141no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—141no—
625C22×C4—141no—
626C22×C4—141no—
627C22×C4—141no—
628C22×C4—141no—
629C22×C4—141no—
630C22×C4—141no—
631C22×C4—141no—
632C22×C4—141no—
633C22×C4—141no—
634C22×C4—141no—
635C22×C4—141no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—141no—
642C22×C4—141no—
643C22×C4—141no—
644C22×C4C2×Dic1412yes—
645C22×C4C2×Dic1412yes—
646C22×C4C2×Dic1412yes—
647C22×C4C2×C4×D712yes—
648C22×C4C2×C4×D712yes—
649C22×C4C2×C4×D712yes—
650C22×C4#115712yes—
651C22×C4#115712yes—
652C22×C4#115712yes—
653C22×C4#115712yes—
654C22×C4D4×D712yes—
655C22×C4#116112yes—
656C22×C4C2×C22⋊D712yes—
657C22×C4C2×C22⋊D712yes—
658C22×C4C2×C22⋊D712yes—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—148no—
662C4⋊C4—148no—
663C4⋊C4—148no—
664C4⋊C4—148no—
665C4⋊C4—148no—
666C4⋊C4—284no—
667C42—28no—
668C42—44no—
669C42—44no—
670C42—148no—
671C42—284no—
672C2×C7#229011yescharacteristic
673C2×C7C4×C22⋊Q811yescharacteristic
674C2×C7#233611yescharacteristic
675C2×C7#234411yescharacteristic
676C2×C7#235511yescharacteristic
677C2×C7#236111yescharacteristic
678C2×C7#236511yescharacteristic
679C2×C7#244911yescharacteristic
680C2×C7#245311yescharacteristic
681C2×C7#245511yescharacteristic
682C2×C7#246211yescharacteristic
683C2×C7#246911yescharacteristic
684C2×C7#247811yescharacteristic
685C2×C7#258511yescharacteristic
686C2×C7#259611yescharacteristic
687C23C22×Dic1411yescharacteristic
688C23C22×C4×D711yescharacteristic
689C23C2×#115711yescharacteristic
690C23C2×#115711yescharacteristic
691C23C2×#115711yescharacteristic
692C23C2×#115711yescharacteristic
693C23C2×D4×D711yescharacteristic
694C23#654811yescharacteristic
695C23C2×#116111yescharacteristic
696C23#655111yescharacteristic
697C23D7×#4111yescharacteristic
698C23D7×#4111yescharacteristic
699C23#655411yescharacteristic
700C23#655411yescharacteristic
701C23C22×C22⋊D711yescharacteristic
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—74no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—281no—
770C2×C4—281no—
771C2×C4—281no—
772C2×C4—281no—
773C2×C4—281no—
774C2×C4—281no—
775C2×C4—281no—
776C2×C4—281no—
777C2×C4—281no—
778C2×C4—281no—
779C2×C4—281no—
780C2×C4—281no—
781C2×C4—281no—
782C2×C4—281no—
783C2×C4—281no—
784C2×C4—281no—
785C2×C4—281no—
786C2×C4—281no—
787C2×C4—281no—
788C2×C4—281no—
789C2×C4—281no—
790C2×C4—281no—
791C2×C4—281no—
792C2×C4—281no—
793C2×C4—281no—
794C2×C4—281no—
795C2×C4—281no—
796C2×C4—281no—
797C2×C4—281no—
798C2×C4—281no—
799C2×C4—281no—
800C2×C4—281no—
801C2×C4—281no—
802C2×C4—281no—
803C2×C4C4×Dic1414yes—
804C2×C4#645614yes—
805C2×C4#648714yes—
806C2×C4C4×C22⋊D714yes—
807C7#1403511yescharacteristic, complemented, Sylow
808C22C2×C4×Dic1411yescharacteristic
809C22#9016111yescharacteristic
810C22C4×#115711yescharacteristic
811C22#9017011yescharacteristic
812C22C2×#645611yescharacteristic
813C22#9019511yescharacteristic
814C22#9019811yescharacteristic
815C22#9020511yescharacteristic
816C22#9020711yescharacteristic
817C22D7×#11711yescharacteristic
818C22#9022211yescharacteristic
819C22#9022211yescharacteristic
820C22D4×Dic1411yescharacteristic
821C22#9023011yescharacteristic
822C22#9023811yescharacteristic
823C22#9023811yescharacteristic
824C22#9024211yescharacteristic
825C22#9025011yescharacteristic
826C22#9025511yescharacteristic
827C22#9025511yescharacteristic
828C22#9025911yescharacteristic
829C22#9026011yescharacteristic
830C22#9026111yescharacteristic
831C22#9027111yescharacteristic
832C22#9027111yescharacteristic
833C22#9027411yescharacteristic
834C22#9027411yescharacteristic
835C22#9027511yescharacteristic
836C22C2×#648711yescharacteristic
837C22C2×C4×C22⋊D711yescharacteristic
838C22#9048211yescharacteristic
839C22D4×C22⋊D711yescharacteristic
840C22#9050811yescharacteristic
841C22#9051511yescharacteristic
842C22#9051511yescharacteristic
843C4—24no—
844C4—24no—
845C4—24no—
846C4—24no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—144no—
851C4—282no—
852C4—282no—
853C4—282no—
854C4—282no—
855C4—282no—
856C4—561no—
857C4—561no—
858C2#1173107511yescharacteristic
859C2#1173108711yescharacteristic
860C2#1173109611yescharacteristic
861C2#1173112311yescharacteristic
862C2#1173117411yescharacteristic
863C2#1173118511yescharacteristic
864C2#1173119911yescharacteristic
865C2#1173123011yescharacteristic
866C2C4×#648711yescharacteristic
867C2#1173960811yescharacteristic
868C2#1173968311yescharacteristic
869C2#1173980511yescharacteristic
870C2#1173985511yescharacteristic
871C2#1173991611yescharacteristic
872C2#1173991811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#14035
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
54. #89700C4semidirect
807. C7#14035semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
C2×#897002
C2×#897052
C2×C4×Dic7⋊C42
C2×#894262
#117293222
#117293212
#117293182
#117292902
#117292882
#117271772
#117271652
#117271612
#140357