Finite Group Databasebeta

← #13370352

Subgroups — #13370352

Order 1792.

1114 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90230C211yesmaximal, characteristic
2#11730903C212yesmaximal, complemented
3C4×C7×#99C211yesmaximal, characteristic
4#11729373C211yesmaximal, characteristic
5#11727782C211yesmaximal, characteristic
6#11727782C211yesmaximal, characteristic
7Dic7×#99C211yesmaximal, characteristic
8Dic7×#99C211yesmaximal, characteristic
9#11727211C212yesmaximal, complemented
10#11726709C212yesmaximal, complemented
11#11726709C212yesmaximal, complemented
12C2×C4×C7×D4C2211yescharacteristic
13C2×D4×Dic7C2211yescharacteristic
14C2×D4×Dic7C2211yescharacteristic
15C2×#6487C411yescharacteristic, complemented
16C2×#6487C2211yescharacteristic
17C22×Dic7⋊C4C411yescharacteristic, complemented
18C22×Dic7⋊C4C2211yescharacteristic
19#90230—22no—
20#90230—22no—
21#90230—22no—
22#90230—22no—
23C2×#6453C411yescharacteristic, complemented
24C2×#6451C411yescharacteristic, complemented
25C2×#6441C411yescharacteristic, complemented
26C2×#6441C411yescharacteristic, complemented
27C2×#6441C2211yescharacteristic
28C2×#6441C2211yescharacteristic
29C2×#6433C411yescharacteristic, complemented
30C2×C4×Dic14C411yescharacteristic, complemented
31C2×C7×#99C2211yescharacteristic
32C2×C7×#99C2211yescharacteristic
33C4×C7×C22⋊C4C2212yes—
34C2×#6408C2211yescharacteristic
35C2×#6408C2211yescharacteristic
36#89984C2212yes—
37#89714C2212yes—
38#89714C2212yes—
39C22⋊C4×Dic7C2212yes—
40C22⋊C4×Dic7C2212yes—
41#89705—22no—
42C4×Dic7⋊C4—22no—
43#89427—22no—
44#89419—22no—
45C7×#342C2212yes—
46#89322C2212yes—
47#89322C2212yes—
48#89322C2212yes—
49#89322C2212yes—
50#89321C2212yes—
51#22513—71nomaximal, Sylow
52C22×C7×D4C2311yescharacteristic
53C23×C4×C7C2×C411yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×Dic7C2×C411yescharacteristic
56C23×Dic7C2×C411yescharacteristic
57C23×Dic7C2311yescharacteristic
58C23×Dic7C2311yescharacteristic
59C22×Dic14C2×C411yescharacteristic
60C22×Dic14C2×C411yescharacteristic
61C22×Dic14C2×C411yescharacteristic
62C4×C7×D4—22no—
63C4×C7×D4—22no—
64C2×C7×C4⋊C4C2×C411yescharacteristic
65C2×C7×C22⋊C4C2×C411yescharacteristic
66C2×C7×C22⋊C4C2312yes—
67C2×C7×C22⋊C4C2311yescharacteristic
68C2×C7×C22⋊C4C2312yes—
69C2×C42×C7—22no—
70C2×C42×C7C2×C411yescharacteristic
71C2×C22⋊Dic7C2×C411yescharacteristic
72C2×C22⋊Dic7C2×C411yescharacteristic
73C2×C22⋊Dic7C2312yes—
74C2×C22⋊Dic7C2312yes—
75C2×C22⋊Dic7C2311yescharacteristic
76C2×C22⋊Dic7C2311yescharacteristic
77D4×Dic7—22no—
78D4×Dic7—22no—
79D4×Dic7—22no—
80D4×Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7C2×C411yescharacteristic
83C2×C4⋊Dic7C2×C411yescharacteristic
84C2×C4⋊Dic7C2×C411yescharacteristic
85C2×C4⋊Dic7C2×C411yescharacteristic
86C2×C4⋊Dic7C2×C411yescharacteristic
87#6487—22no—
88#6487—22no—
89#6487—22no—
90#6487—22no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4C2×C411yescharacteristic
98C2×Dic7⋊C4C2×C411yescharacteristic
99C2×Dic7⋊C4C2×C411yescharacteristic
100C2×Dic7⋊C4C2×C411yescharacteristic
101C2×Dic7⋊C4C2×C411yescharacteristic
102C2×Dic7⋊C4C2×C411yescharacteristic
103C2×Dic7⋊C4C2×C411yescharacteristic
104C2×Dic7⋊C4C2×C411yescharacteristic
105C2×Dic7⋊C4C2×C411yescharacteristic
106C2×Dic7⋊C4C2×C411yescharacteristic
107C2×Dic7⋊C4D412yes—
108C2×Dic7⋊C4D412yes—
109C2×Dic7⋊C4D412yes—
110C2×Dic7⋊C4D412yes—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—22no—
113C2×C4×Dic7C2×C411yescharacteristic
114C2×C4×Dic7C2×C411yescharacteristic
115#6453—22no—
116#6453—22no—
117#6451—22no—
118#6451—22no—
119#6441—22no—
120#6441—22no—
121#6441—22no—
122#6441—22no—
123#6441—22no—
124#6441—22no—
125#6441—22no—
126#6441—22no—
127#6433—22no—
128#6433—22no—
129C4×Dic14—21no—
130C4×Dic14—21no—
131C4×Dic14—21no—
132C4×Dic14—21no—
133C7×#99—22no—
134C7×#99Q814yescomplemented
135C7×#95—22no—
136#6408—22no—
137#6408—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C2×#554—71no—
144#2345—72no—
145#1996—72no—
146#1996—72no—
147#1996—72no—
148#1799—71no—
149#1799—71no—
150#1799—71no—
151C4×#99—71no—
152C4×#99—71no—
153C4×#99D711yescharacteristic
154C24×C7C22×C411yescharacteristic
155C24×C7C2411yescharacteristic
156C2×C7×D4—22no—
157C2×C7×D4—22no—
158C2×C7×D4C2×Q812yes—
159C2×C7×D4#4112yes—
160C22×C4×C7—22no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—22no—
164C22×C4×C7—81no—
165C22×C4×C7—81no—
166C22×C4×C7C22×C411yescharacteristic
167C22×C4×C7C22×C411yescharacteristic
168C22×C4×C7C22×C411yescharacteristic
169C22×C4×C7C22×C411yescharacteristic
170C22×C4×C7C22×C411yescharacteristic
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D412yes—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—42no—
180C22×Dic7—42no—
181C22×Dic7—81no—
182C22×Dic7—81no—
183C22×Dic7C22×C411yescharacteristic
184C22×Dic7C22×C411yescharacteristic
185C22×Dic7C22×C411yescharacteristic
186C22×Dic7C22×C411yescharacteristic
187C22×Dic7C22×C411yescharacteristic
188C22×Dic7C22×C411yescharacteristic
189C22×Dic7C22×C411yescharacteristic
190C22×Dic7C22×C411yescharacteristic
191C22×Dic7C2×D412yes—
192C22×Dic7C2×D412yes—
193C22×Dic7C2×D412yes—
194C22×Dic7C2×D412yes—
195C2×Dic14—21no—
196C2×Dic14—21no—
197C2×Dic14—22no—
198C2×Dic14—22no—
199C2×Dic14—42no—
200C2×Dic14—81no—
201C2×Dic14—81no—
202C7×C4⋊C4—22no—
203C7×C22⋊C4—22no—
204C7×C22⋊C4—22no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4—22no—
207C7×C22⋊C4—22no—
208C7×C22⋊C4C2×Q814yes—
209C42×C7—21no—
210C42×C7—21no—
211C42×C7—82no—
212C22⋊Dic7—22no—
213C22⋊Dic7—22no—
214C22⋊Dic7—22no—
215C22⋊Dic7—22no—
216C22⋊Dic7—22no—
217C22⋊Dic7—22no—
218C22⋊Dic7—22no—
219C22⋊Dic7—22no—
220C4⋊Dic7—22no—
221C4⋊Dic7—21no—
222C4⋊Dic7—21no—
223C4⋊Dic7—22no—
224C4⋊Dic7—22no—
225C4⋊Dic7—22no—
226C4⋊Dic7—82no—
227Dic7⋊C4—21no—
228Dic7⋊C4—21no—
229Dic7⋊C4—21no—
230Dic7⋊C4—21no—
231Dic7⋊C4—22no—
232Dic7⋊C4—22no—
233Dic7⋊C4—21no—
234Dic7⋊C4—21no—
235Dic7⋊C4—21no—
236Dic7⋊C4—21no—
237Dic7⋊C4—44no—
238Dic7⋊C4—82no—
239Dic7⋊C4C22⋊C411yescharacteristic
240Dic7⋊C4C22⋊C411yescharacteristic
241Dic7⋊C4C22⋊C411yescharacteristic
242Dic7⋊C4C22⋊C411yescharacteristic
243Dic7⋊C4C22⋊C412yes—
244Dic7⋊C4C22⋊C412yes—
245Dic7⋊C4C22⋊C412yes—
246Dic7⋊C4C22⋊C412yes—
247Dic7⋊C4C22⋊C412yes—
248Dic7⋊C4C22⋊C412yes—
249C4×Dic7—21no—
250C4×Dic7—21no—
251C4×Dic7—21no—
252C4×Dic7—21no—
253C4×Dic7—44no—
254C4×Dic7—82no—
255#554—142no—
256#554—142no—
257#554—142no—
258#554—142no—
259C2×C4⋊Q8—71no—
260C2×#125—71no—
261C2×#125—71no—
262C2×C22⋊Q8—71no—
263C2×C22⋊Q8—71no—
264C2×C22⋊Q8—71no—
265C2×C22⋊Q8—71no—
266C2×C22⋊Q8—71no—
267C2×C22⋊Q8—71no—
268C2×C4×Q8—71no—
269C2×C4×D4—71no—
270C2×C4×D4—71no—
271C2×C4×D4C2×D711yescharacteristic
272C22×C4⋊C4—71no—
273C22×C4⋊C4—71no—
274C2×#99—71no—
275C2×#99—71no—
276C2×#99C2×D711yescharacteristic
277C2×#99C2×D711yescharacteristic
278#389—142no—
279#387—142no—
280#387—142no—
281#380—72no—
282#380—72no—
283#380—72no—
284C4×C4⋊C4—142no—
285C4×C22⋊C4—72no—
286C4×C22⋊C4—72no—
287C4×C22⋊C4C2×D712yes—
288#342—72no—
289#342—72no—
290#342—72no—
291#342—72no—
292#342—72no—
293#342C2×D712yes—
294C23×C7—21no—
295C23×C7—21no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7C4×Q812yes—
301C23×C7C23×C411yescharacteristic
302C23×C7C22×D412yes—
303C23×C7C22×Q811yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C23×C72−1+412yes—
306C7×D4—24no—
307C7×D4—24no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—24no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—81no—
325C2×C4×C7—81no—
326C2×C4×C7C2×C22⋊C411yescharacteristic
327C2×C4×C7C2×C22⋊C411yescharacteristic
328C2×C4×C7C2×C22⋊C412yes—
329C2×C4×C7C4×Q812yes—
330C2×Dic7—24no—
331C2×Dic7—22no—
332C2×Dic7—21no—
333C2×Dic7—21no—
334C2×Dic7—21no—
335C2×Dic7—21no—
336C2×Dic7—42no—
337C2×Dic7—42no—
338C2×Dic7—41no—
339C2×Dic7—41no—
340C2×Dic7—42no—
341C2×Dic7—41no—
342C2×Dic7—42no—
343C2×Dic7—42no—
344C2×Dic7—41no—
345C2×Dic7—41no—
346C2×Dic7—41no—
347C2×Dic7—41no—
348C2×Dic7—42no—
349C2×Dic7—42no—
350C2×Dic7—42no—
351C2×Dic7—42no—
352C2×Dic7—42no—
353C2×Dic7—42no—
354C2×Dic7—81no—
355C2×Dic7—81no—
356C2×Dic7C2×C22⋊C411yescharacteristic
357C2×Dic7C2×C22⋊C411yescharacteristic
358C2×Dic7C2×C22⋊C411yescharacteristic
359C2×Dic7C2×C22⋊C412yes—
360C2×Dic7C2×C22⋊C412yes—
361C2×Dic7C2×C22⋊C411yescharacteristic
362Dic14—42no—
363Dic14—42no—
364Dic14—82no—
365Dic14—82no—
366C22×Q8—71no—
367C22×Q8—71no—
368C22×Q8—71no—
369C22×D4C22×D711yescharacteristic
370C23×C4—71no—
371C23×C4—71no—
372C23×C4—71no—
373C23×C4—71no—
374C23×C4C4×D711yescharacteristic
375C23×C4C22×D711yescharacteristic
376C4⋊Q8—142no—
377C4⋊Q8—142no—
378#125—142no—
379#125—142no—
380#125—142no—
381#125—142no—
382C22⋊Q8—142no—
383C22⋊Q8—142no—
384C22⋊Q8—142no—
385C22⋊Q8—142no—
386C22⋊Q8—142no—
387C22⋊Q8—142no—
388C22⋊Q8—142no—
389C22⋊Q8—142no—
390C22⋊Q8—142no—
391C22⋊Q8—142no—
392C22⋊Q8—142no—
393C22⋊Q8—142no—
394C4×Q8—141no—
395C4×Q8—141no—
396C4×Q8—141no—
397C4×Q8—141no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—142no—
401C4×D4—142no—
402C4×D4—142no—
403C4×D4—142no—
404C2×C4⋊C4—71no—
405C2×C4⋊C4—71no—
406C2×C4⋊C4—71no—
407C2×C4⋊C4—71no—
408C2×C4⋊C4—72no—
409C2×C4⋊C4—72no—
410C2×C4⋊C4—72no—
411C2×C4⋊C4—72no—
412C2×C4⋊C4—71no—
413C2×C4⋊C4—71no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—71no—
419C2×C4⋊C4—71no—
420C2×C4⋊C4—71no—
421C2×C4⋊C4—71no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—141no—
424C2×C4⋊C4—141no—
425C2×C4⋊C4—141no—
426C2×C4⋊C4—141no—
427C2×C4⋊C4—142no—
428C2×C4⋊C4—142no—
429C2×C4⋊C4—142no—
430C2×C4⋊C4C4×D711yescharacteristic
431C2×C22⋊C4—71no—
432C2×C22⋊C4—71no—
433C2×C22⋊C4—71no—
434C2×C22⋊C4—71no—
435C2×C22⋊C4—72no—
436C2×C22⋊C4—72no—
437C2×C22⋊C4C4×D711yescharacteristic
438C2×C22⋊C4C22×D712yes—
439C2×C22⋊C4C22×D711yescharacteristic
440C2×C22⋊C4C22×D712yes—
441C2×C42—22no—
442C2×C42—71no—
443C2×C42—71no—
444C2×C42—142no—
445C2×C42—142no—
446C2×C42C4×D711yescharacteristic
447#99—22no—
448#99—142no—
449#99—142no—
450#99Dic1414yescomplemented
451#95—22no—
452#95—142no—
453#95—142no—
454#95—142no—
455#95—142no—
456#95—142no—
457C22×C7—22no—
458C22×C7—21no—
459C22×C7—22no—
460C22×C7—21no—
461C22×C7—22no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—42no—
465C22×C7—42no—
466C22×C7—42no—
467C22×C7—41no—
468C22×C7—41no—
469C22×C7C22×C22⋊C411yescharacteristic
470C22×C7C2×C4×Q811yescharacteristic
471C22×C7#51911yescharacteristic
472C22×C7#54812yes—
473C22×C7D4×Q812yes—
474C4×C7—22no—
475C4×C7—22no—
476C4×C7—21no—
477C4×C7—21no—
478C4×C7—44no—
479C4×C7—41no—
480C4×C7—41no—
481C4×C7—82no—
482Dic7—21no—
483Dic7—22no—
484Dic7—22no—
485Dic7—21no—
486Dic7—21no—
487Dic7—41no—
488Dic7—41no—
489Dic7—41no—
490Dic7—41no—
491Dic7—82no—
492Dic7—82no—
493Dic7#41012yes—
494C24C2×C4×D711yescharacteristic
495C24C23×D711yescharacteristic
496C2×Q8—141no—
497C2×Q8—141no—
498C2×Q8—142no—
499C2×Q8—142no—
500C2×Q8—282no—
501C2×Q8—561no—
502C2×Q8—561no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4C2×Dic1412yes—
506C2×D4#115712yes—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—71no—
512C22×C4—72no—
513C22×C4—71no—
514C22×C4—71no—
515C22×C4—71no—
516C22×C4—72no—
517C22×C4—72no—
518C22×C4—72no—
519C22×C4—71no—
520C22×C4—71no—
521C22×C4—71no—
522C22×C4—71no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—141no—
526C22×C4—141no—
527C22×C4—141no—
528C22×C4—141no—
529C22×C4—142no—
530C22×C4—142no—
531C22×C4—282no—
532C22×C4—282no—
533C22×C4—561no—
534C22×C4—561no—
535C22×C4C2×C4×D711yescharacteristic
536C22×C4C2×C4×D711yescharacteristic
537C22×C4C2×C4×D711yescharacteristic
538C22×C4C2×C4×D711yescharacteristic
539C22×C4C2×C4×D711yescharacteristic
540C22×C4D4×D712yes—
541C22×C4D4×D712yes—
542C4⋊C4—22no—
543C4⋊C4—71no—
544C4⋊C4—71no—
545C4⋊C4—71no—
546C4⋊C4—71no—
547C4⋊C4—72no—
548C4⋊C4—72no—
549C4⋊C4—72no—
550C4⋊C4—72no—
551C4⋊C4—72no—
552C4⋊C4—72no—
553C4⋊C4—141no—
554C4⋊C4—141no—
555C4⋊C4—141no—
556C4⋊C4—141no—
557C4⋊C4—142no—
558C4⋊C4—142no—
559C4⋊C4—142no—
560C4⋊C4—142no—
561C4⋊C4—141no—
562C4⋊C4—141no—
563C4⋊C4—142no—
564C4⋊C4—141no—
565C4⋊C4—141no—
566C4⋊C4—141no—
567C4⋊C4—141no—
568C4⋊C4—142no—
569C4⋊C4—284no—
570C4⋊C4—562no—
571C4⋊C4—562no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—142no—
578C22⋊C4—142no—
579C22⋊C4—142no—
580C22⋊C4—142no—
581C22⋊C4—142no—
582C22⋊C4—142no—
583C22⋊C4—142no—
584C22⋊C4—142no—
585C22⋊C4C2×Dic1414yes—
586C42—21no—
587C42—21no—
588C42—82no—
589C42—141no—
590C42—141no—
591C42—141no—
592C42—141no—
593C42—284no—
594C42—562no—
595C2×C7—22no—
596C2×C7—22no—
597C2×C7—21no—
598C2×C7—21no—
599C2×C7—42no—
600C2×C7Q8×C22⋊C411yescharacteristic
601C2×C7C2×#41011yescharacteristic
602C2×C7#288311yescharacteristic
603C23—21no—
604C23—21no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C4×Dic1412yes—
610C23C22×Dic1411yescharacteristic
611C23C22×C4×D711yescharacteristic
612C23C2×#115711yescharacteristic
613C23C2×D4×D712yes—
614C23#655412yes—
615Q8—282no—
616Q8—282no—
617Q8—562no—
618Q8—562no—
619D4—24no—
620D4—24no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—24no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—71no—
638C2×C4—71no—
639C2×C4—71no—
640C2×C4—71no—
641C2×C4—72no—
642C2×C4—72no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—144no—
646C2×C4—142no—
647C2×C4—141no—
648C2×C4—141no—
649C2×C4—141no—
650C2×C4—141no—
651C2×C4—282no—
652C2×C4—282no—
653C2×C4—282no—
654C2×C4—282no—
655C2×C4—281no—
656C2×C4—281no—
657C2×C4—281no—
658C2×C4—282no—
659C2×C4—281no—
660C2×C4—281no—
661C2×C4—281no—
662C2×C4—281no—
663C2×C4—282no—
664C2×C4—282no—
665C2×C4—282no—
666C2×C4—282no—
667C2×C4—282no—
668C2×C4—282no—
669C2×C4—561no—
670C2×C4—561no—
671C2×C4C4×Dic1412yes—
672C2×C4D7×C22⋊C411yescharacteristic
673C2×C4D7×C22⋊C411yescharacteristic
674C2×C4D7×C22⋊C412yes—
675C7#2251311yescharacteristic, complemented, Sylow
676C22—22no—
677C22—21no—
678C22—22no—
679C22—21no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—41no—
687C22—41no—
688C22C2×C4×Dic1411yescharacteristic
689C22C2×D7×C22⋊C411yescharacteristic
690C22#9020711yescharacteristic
691C22D4×Dic1412yes—
692C22#9024312yes—
693C4—21no—
694C4—21no—
695C4—22no—
696C4—22no—
697C4—44no—
698C4—41no—
699C4—41no—
700C4—72no—
701C4—82no—
702C4—141no—
703C4—141no—
704C4—142no—
705C4—141no—
706C4—142no—
707C4—281no—
708C4—281no—
709C4—281no—
710C4—281no—
711C4—562no—
712C4—562no—
713C2—22no—
714C2—22no—
715C2—21no—
716C2—21no—
717C2—42no—
718C2C22⋊C4×Dic1411yescharacteristic
719C2#1173613311yescharacteristic
720C2D7×#41011yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC4×C7×#99C2
socleC22×C7C22×C22⋊C4
prime radicalC22×C7×D4C23
cosocleC24×C7C24
hypercenterC4×#99D7
hypocenterC7#22513
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #11730903C2semidirect
9. #11727211C2semidirect
10. #11726709C2semidirect
11. #11726709C2semidirect
15. C2×#6487C4semidirect
17. C22×Dic7⋊C4C4semidirect
23. C2×#6453C4semidirect
24. C2×#6451C4semidirect
25. C2×#6441C4semidirect
26. C2×#6441C4semidirect
29. C2×#6433C4semidirect
30. C2×C4×Dic14C4semidirect
134. C7×#99Q8semidirect
450. #99Dic14semidirect
675. C7#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#902302
#117309032
C4×C7×#992
#117293732
#117277822
Dic7×#992
#117272112
#117267092
#225137